Maverick Philosopher

I thank Peter Lupu for raising essentially this objection to my view.

Can I defuse the objection? Let's see. The paradox cannot arise unless the following schema is valid:

a. It is rational for S to believe that p.
b. It is rational for S to believe that ~p.
-----
c. It is rational for S to believe that (p & ~p).

It is not clear that the schema is valid. Rational believability, unlike truth, is a relative property. What it is rational to believe is relative to background knowledge among other things. Relative to the author's knowledge that he exercised due diligence in the researching and writing of his book, it is rational for him to believe that every statement in the book is true. But relative to considerations of human fallibility, it is rational for him to believe that it is not the case that every statement in his book is true. So what (a) and (b) above really amount to is the following:

a*. It is rational for S to believe relative to BK1 that p.
b*. It is rational for S to believe relative to BK2 that ~p.

From these two premises one cannot arrive at the desired conclusion.

"But doesn't the author's background knowledge (BK) include both the truth that he exercised due diligence and the truth that human beings are fallible?" Well suppose it does. Then how could it be rational for him to believe that every statement in the book is true? It is rational for him to believe that every statement is true only if he leaves out of consideration that people are fallible. Relative to his total background knowledge, it is not rational for him to believe that every statement in his book is true.

What this example suggests is that the Law of Non-Contradiction (LNC) is a semantic constraint: it is a principle we must abide by to make sense to ourselves and to others and to interpret what others mean. The idea that (LNC) is a semantic constraint is that one cannot mean anything definite or make any definite judgment unless one abides by, and thus presupposes, the principle that no subject of discourse both has and does not have a property at the same time, in the same respect, and in the same sense.

This, I take it, is what the Philosopher had in mind in Metaphysics Gamma 3, 4.

If this is right, then we have a sort of 'proof' of (LNC), a proof by the impossibility of denial. For if one were to deny it, by saying e.g. '(LNC) is false,' or indeed by saying anything at all, then one would willy-nilly presuppose the principle. For if adherence to the principle is a necessary condition of all meaningful discourse, then the principle cannot be meaningfully denied without presupposing its validity.

The fact, if it is a fact, that (LNC) cannot be denied by us, or by any rational being, does not show that it is true of reality. Or does it? This very difficult question — the question whether this logical law is also an ontological law — is not the topic of this post.

What concerns me at the moment is an objection one can make to the notion that (LNC) is a semantic constraint. If this notion is right, then there are no meaningful contradictions: when Jones 'asserts' that he both got and did not get tenure, he asserts nothing at all. But it seems easy enough to prove that there are meaningful contradictions:

1. If a proposition p is meaningful, then so is its negation ~p.
2. If propositions p, q are meaningful, then so is their conjunction p & q.
3. Tom is a man is meaningful.
4. Tom is not a man is meaningful. (from 1, 3)
5. Tom is a man & Tom is not a man is meaningful. (from 2, 3, 4)
Therefore
6. There are meaningful contradictions. (from 5)

Now if there are meaningful contradictions, as I have just seemed to prove, then (LNC) does not constrain what we mean, it constrains the truth of what we mean: nothing that we mean can be true unless it conforms to (LNC). It is a necesssary condition of truth, not of meaning. Accordingly, Tom is a man & Tom is not a man is meaningful, but necessarily false. And Professor Jones above is not talking nonsense, but talking sense, albeit necessarily false sense.

Can we reconcile these two approaches? If you are unprejudiced, you will have to agree that both have merit. But both can't be correct. Here again we have an application of (LNC). Both of the following cannot be true: There are meaningful contradictions; there are no meaningful contradictions.

Here is a stab at a solution. There is a difference between an act of asserting and the content asserted. Thus my asserting that Tom is tall is distinct from the content of my assertion, namely, that Tom is tall. Both the act of asserting and the proposition asserted can be said to be meaningful. But it may be that 'meaningful' is being used in distinct albeit analogical senses when applied to assertings and to propositions asserted. And it may be that there are meaningful contents that cannot be meaningfully asserted.

In one sense it is clear that Tom is a man and Tom is not a man is meaningful. See the above argument. In another sense, it is clear that the asserting of this contradiction is not meaningful. For when I 'assert' a contradiction, I fail to convey anything definite to myself or another. Suppose I tell you that I am both in good health and not in good health. You will not respond by saying, "I'm happy to hear that" or "I'm sorry to hear that." You will most likely reply, "What are you saying?" This response is a request for something non-contradictory. If I fail to proffer something noncontradictory, then you will take me to be saying nothing at all.

So I propose we distinguish between what is meaningfully assertible and what is meaningful in abstraction from assertibility. Contradictions are not meaningfully assertible, but they are meaningful in abstracto. (LNC) is then the ultimate constraint on meaningful assertibility.

One who asserts a contradiction thus contradicts himself: in the very act of asserting, he purports to assert some definite proposition. To assert, after all, is to assert something, some definite content. But in 'asserting' a contradiction he 'asserts' something that neither to himself nor to another has a definite meaning. He who does not abide by (LNC), then, entangles himself in a performative inconsistency. His purported performance, asserting, is inconsistent with the content of his performance.

Final Consideration. Although one can assert a false proposition, one cannot assert any proposition, true or false, without asserting it as true. Thus if I assert that snow is black, I assert as true that snow is black. (There is no such thing as asserting as false, though there is the asserting of a proposition that it is false.) If I attempt to assert the contradiction that snow is white and snow is not white, then I assert as true what I know cannot be true, and as a result assert nothing at all. My performance (asserting) contradicts — is performatively inconsistent with — the content of my performance.

Thus one cannot assert a contradiction knowing that it is a contradiction. No doubt one can mouth the words 'Snow is white and snow is not white.' But such mouthing does not get the length of a speech act. One who merely mouths words is not speaking, strictly speaking.

Is this just a factual inability? And is (LNC) merely an abstract codification of this factual inability? Or is (LNC) truly normative? Is this a case in which factuality and normativity coincide?

I find this worthy of rumination since I do not see how logic can proceed except from the basis of a pre-theoretical understanding of inference and the difference between good and bad inferences, just as I don't see how ethics can proceed except from the basis of a pre-theoretical understanding of human action and the difference between right and wrong actions. So let me sketch in broad strokes a possible approach to logic.

It is plain fact that people reason. For present purposes and to keep things simple we can identify reasoning with the drawing of inferences. It is also a fact that most people appreciate that there is a difference between good and bad reasoning. They sense that some arguments are 'good' and some are 'bad.' These are not technical terms, but terms ordinary people employ prior to any exposure to logical theory. Thus an untutored fellow in a pub, hearing some argument, might say, 'that doesn't hold water.' Although he would be hard pressed to say what he means by that, he has a pre-analytic grasp of the notion of correct reasoning and of its difference from incorrect reasoning.

Now logic as a discipline arises when we reflect upon our inferential practices and try to uncover the criteria that distinguish correct from incorrect inferences. Logic begins when, following the intentio obliqua rather than the intentio recta, we step back from our actual reasonings about this and that and focus our mental glance on what we are doing when we reason, and what we ought to be doing in order to reason correctly. Simply put, logic is an attempt to specify, quite generally, the principles that allow us to sort arguments into two classes, the correct and incorrect.

In the course of developing logical theory we attach precise meanings to terms that are used imprecisely in ordinary life. 'Valid,' for example, is used in different ways in ordinary language, and vaguely in any given use; but the logician means something precise by it. And same goes for a host of words: inference, implication, premise, conclusion, fallacy, syllogism, converse, obverse, contrary, contradictory, subcontrary, sound, unsound, antinomy, quantifier, etc.

Take 'syllogism.' The ordinary person, if he is familiar with the word at all, probably thinks it means the same as 'argument.' But in logic it has a technical meaning: a syllogism is a deductive argument with exactly two premises, exactly one conclusion, and exactly three terms. So not every argument is a syllogism. Inductive arguments are not syllogisms, and arguments with more than two premises are not syllogisms.

Or take 'fallacy.' The man in the street probably thinks it has the same meaning as 'false belief.' But that it is not what it means in logic: it refers to a typical mistake in reasoning. Not just any old mistake, but a typical one, one that recurs, one that has some tendency to seduce, and that therefore deserves a name.

In sum: the development of logical theory presupposes a pre-theoretical understanding of reasoning and of the difference between good and bad reasoning. Without this basis, logical theory cannot arise. For logical theory is developed by reflection upon everyday inferential practices. It is an attempt to tease out, to make explicit, what is already implicit in ordinary reasoning. But Peter Lupu apparently sees it differently. He thinks one can proceed without even a "pre-theoretical concept of inference." But this makes no sense to me. For unless we have a rough-and-ready understanding of inference, we won't be able to attach any sense at all to a theoretical concept of inference. Peter writes, "Once the formal notion of 'follows from' is defined precisely, we can go ahead and point out how it relates to the pre-theoretical concept."

This has it backwards. We have no notion at all of 'follows from' except on the basis of ordinary inferential practices. So one cannot work out a formal notion and then compare it to the pre-theoretical notion. What we can do is 'precisify' (make precise) the ordinary concept. Note also that the correctness and utility of the formal notion depends entirely on whether it illuminates the pre-theoretical notion. The only source of its 'validation' is in the ordinary notion.

3. Murder is wrong
4. Suicide is murder
-----
5. Suicide is wrong.

Someone who gives (i.e., makes, mounts, forwards, advocates, etc.) this argument, as opposed to merely quoting it or mentioning it as I am doing here for purposes of logical theory, is asserting the premises and also asserting the conclusion as a logical consequence of the premises. But someone who asserts (2) or asserts

6. If murder is wrong, and suicide is murder, then suicide is wrong

is not asserting the antecedent or the consequent.

Therefore, arguments and conditionals should not be confused. Nevertheless, they are closely related in that arguments have corresponding conditionals and some conditionals have corresponding arguments. The early Stoics were onto this as well. Thus, (6) is the conditional corresponding to the (3)-(5) argument. We can go further and state that an argument is valid only if its corresponding conditional is a necessary truth. Furthermore, an argument is valid if and only if its corresponding conditional is a narrowly-logical truth. If we are operating within the Propositional Calculus (PC), we can say that an argument encoded in PC whose validity/invalidity rides on the logical structure captured by this encoding is valid if and only if its corresponding conditional is a tautology in the sense in which this term is used in the PC.

Truth and validity are distinct, and one betrays logical ignorance if one speaks of an argument as either true or false. Still, for every valid argument there is a necessarily true corresponding conditional.

I said that, for every argument, there is a corresponding conditional. It does not matter whether the argument is valid or invalid, explicit or enthymematic. But is it true that for every conditional there is a corresponding argument? In other words, can every conditional be unpacked as, be expressed in the form of, an argument? No, it is only some conditionals that can be expressed as arguments. These conditionals are ones in which antecedent and consequent are logically related, whether narrowly or broadly. Examples:

7. If Tom is tired, then someone is tired.
8. If Tom is tired, and all tired people are irritable, then Tom is irritable.
9. If Tom is a bachelor, then Tom is unmarried.

These propositions are arguments in conditional disguise. But the following are not:

10. If Tom is drunk, then he is apt to be belligerent.
11. If a fetus potentially possesses rights-conferring properties, then it is a person in the moral sense.

One who asserts (10) is not claiming that Tom's aptness for belligerence logically follows from his being drunk in the way that one who asserts (7) is claiming that someone's being tired logically follows from Tom's being tired. No doubt, there is the enthymematic argument:

Tom is drunk
---
Tom is apt to be belligerent

and the explicit argument

All who are drunk are apt to be belligerent
Tom is drunk
---
Tom is apt to be belligerent.

But these arguments are not implicit in (10).

The additivity of good reasons would seem to hold also in the case of beliefs. The case for the existence of God, for example, is a cumulative case argument. It is not based on one argument or consideration but on a number of reinforcing arguments and considerations.

A thorough discussion would have to distinguish between cumulative case arguments in which each reason is sufficient to justify the action or belief in question, and cumulative case arguments in which one or more or all of the reasons are individually insufficient to justify the action envisaged.

Suppose each reason in a cumulative case argument is individually sufficient to justify the action envisaged. Then in what sense are the reasons additive? They are additive in that each additional sufficient reason provides an additional fail-safe mechanism. If an agent has many reasons each of which is both good and sufficient for doing X, then, if one of the reasons should turn out to be either bad or insufficient, then the other reasons are available to shoulder the justificatory burden.

The strategy of ‘Divide and Conquer’ cannot be used against a cumulative case argument. Suppose Jack has several individually insufficient reasons for marrying Jill: she’s nubile and pretty, moneyed and witty; they are physically and psychologically compatible; they share the same values; she has beautiful eyes, and there is beauty at the opposite pole of her being as well. So Jack has nine good reasons. It simply won’t do to point out that each of them, taken singly, is insufficient to justify the marriage. Her having a curvacious derriere — the ninth reason — is obviously an insufficient reason for getting hitched to the derriere's possessor. But it is a still a good reason given Jack's predilections. A good reason is not the same as a sufficient reason. A good reason can be either sufficient or insufficient. What then are examples of bad reasons? A bad reason for marrying here would be her having a police record.

The point is that several good, but individually insufficient, reasons can add up to a good and sufficient reason. If so, then ‘Divide and Conquer’ is a fallacious form of refutation. But that is how many leftists argued against the Iraq war, and how many atheists argue against theism. Suppose that the cumulative case consists of R1, R2, and R3, each of which is insufficient by itself to justify doing X or believing that p. The ‘Divide and Conquer’ objector wrongly infers ‘no reason’ from ‘individually insufficient reason.’ Thus he thinks that if R1 is insufficient, then R1 is no reason, and similarly for R2 and R3. He then concludes: no reason + no reason + no reason = no reason. He fails to appreciate the additivity of individually insufficient but good reasons, just as the typical poor person fails to appreciate the additivity of the small amounts of money he throws away on cigarettes, lottery tickets, and overpriced convenience store items.

For example, if a conservative gives liberation of the Iraqi people as a reason for the invasion, the leftie is likely to object: "But then why don’t we liberate the North Koreans?" This is a poor response since it it is based on a failure to appreciate that the liberation reason is only one part of a cumulative case, not to mention the fact that an attempted liberation of the North Koreans could easily lead to nuclear war. Granting that liberating the Iraqi people is an insufficient reason for the war, it does not follow that it is no reason at all. It is a good reason which, though insufficient taken by itself, is part of a cumulative case which arguably amounts to a good and sufficient reason for the war.

Another mistake that some people make is to confuse a reason with a motive. There are reasons that motivate and reasons that do not motivate, and a nonmotivating reason is no less a reason. A reason is a motive when it plays a motivating role within the psychic economy of an agent or thinker. Suppose Jack has available to him an objectively good reason R for marrying Jill. But Jack is not consciously or subconsciously aware of R. Obviously, R can in that case play no role in the etiology of his envisaged action. R does not motivate. Yet R remains an objectively good reason for performing the act in question, a reason that is available to him, though he does not avail himself of it. A good reason need not be a motivating reason, and a motivating reason need not be a good reason.

Suppose Bush II’s sole motive for invading Iraq was to avenge Saddam’s assasination attempt on his father, Bush I. Even on this wildly counterfactual assumption, there were good reasons for the invasion. For an action to be justified, all that is required is that there be objectively good reasons for the action; it is not necessary that the agent’s motives be objectively good reasons. Even if an agent is not justified in doing X – because he is either not aware of or motivated by the good reasons for doing X – the act itself (the act-type itself) can have justification. Our man Jack, for example, may be driven to marry Jill by his lust and nothing besides; but this does not entail that his marrying her lacks justification. Jack’s father might say to him: "Son, you made the right decision, but for the wrong reason." The rightness of the decision is due to the availability of good reasons even if horny Jack did not avail himself of them.

At this point an objector might maintain that what I am calling good reasons are simply ex post facto rationalizations. But a rationalization after the fact is not the same as a good reason that plays no motivating role in bringing about the fact. For a rationalization is a bad reason. Suppose Ali physically assaults Benjamin because B is a Jew and A believes that Jews are the "sons of pigs and monkeys." After the fact, A explains his behavior by saying that B insulted him. Suppose B did insult A. A is rationalizing after the fact as opposed to giving a good reason after the fact. B’s insulting of A did not give A a good reason for initiating physical violence against B.

Now let us suppose that Bush II’s sole motive for ordering the Iraq invasion was his desire to deprive Saddam of the WMDs that he, Bush, believed Saddam to possess. Suppose, plausibly, that the belief is false. In that case, Bush II’s motivating reason was not an objectively good reason – based as it was on a false belief – but it could still count as a subjectively good reason in this sense: he had a reason that was a good reason based on the information he had available to him at the time of the decision. I would then argue that the other reasons, which are objectively good, bear the justificatory burden.

An astonishing number of people, some of them intelligent, believe that the motivating reason for the Iraq invasion was the desire to secure access to Iraqi oil. But if that was the motivating reason, it is was a very bad reason since (i) the oil was flowing; (ii) starting a war with an opponent believed to have WMDs and known to have ignited oil wells in the past is clearly a stupid way to secure access to Iraqi oil; (iii) the projected cost of the war would be scarcely offset by the value of the oil secured; and (iv) deposing Saddam and his sons was not at all necessary to insure the flow of oil. I would argue that since this oil reason is so obviously bad, it is not reasonable to impute it to Bush and his advisers as the motivating reason for the invasion.

To sum up. The case for invading Iraq was a cumulative case. One reason for going to war was the widely shared belief that Saddam had WMDs. Another was that he was a known sponsor of Palestinian Arab terrorists and a reasonably surmised sponsor of other terrorists. (On the second point, see Stephen F. Hayes, The Connection: How al-Qaeda's Collaboration with Saddam Hussein Has Endangered America, Harper Collins, 2004) A third was humanitarian: the liberation of the Iraqi people from a brutal dictator and his sons. A fourth was to enforce unanimous U.N. resolutions that this august body did not have the cojones to enforce itself. A fifth was to end the ongoing hostilities, e.g., Iraqi attacks on coalition warplanes. Even if no one of these reasons is sufficient to justify the invasion, the five taken together arguably provide good and sufficient reason for the action.

A cumulative case argument cannot be refuted by ‘Divide and Conquer.’ A good reason need not be a sufficient reason. A reason is not the same as a motive: there can be objectively good reasons for an action even if the agent of the action is not motivated by any of these reasons. To find good reasons after the fact is not to engage in ex post facto rationalization. This is because a rationalization is the providing of a bad reason. But of course, liberals and leftists are so blinded by their passionate hatred of Bush II, that patient analysis of the foregoing sort will be lost on them.

Now it might occur to someone to wonder whether logical arguments from evil for the nonexistence of God also beg the question. Is there anything to this notion?

Logical arguments from evil start with a fact, the fact of evil. No doubt evils exist. But for evils to prove the nonexistence of the omni-qualified God of traditional Judaism, Christianity, and Islam, these evils must be gratuitous. A gratuitous evil is one that cannot be reconciled with the existence of the omni-qualified God, for example, an evil that God has no morally sufficient reason to permit, or an evil that God cannot prevent because it is the deed of a free agent. A gratuitous evil, then, is one the existence of which is logically inconsistent with the existence of God conceived in the traditional way.

Granted, evils exist. But only gratuitous evils are inconsistent with the existence of God. Only they pose a problem for the existence of an all-good God. Consider the pain of a just punishment, the pain of imprisonment, say, that convinces a miscreant, an armed robber for example, to reform his life. (Few penal punishments are truly rehabilitating, but certainly some are.) The pain of punishment is evil. But in my example, it is necessary for the achievement of a greater good. Thus the evil in question is not gratuitous.

How do we know that there are gratuitous evils? To know this, we would have to know that God does not exist. Thus we would have to know the conclusion of the LAFE to be true in order to know that its key premise -- Gratuitous evils exist -- is true. But this is the very definition of begging the question.

Therefore, it seems that LAFE begs the question. To appreciate my point, compare:

1. If there are gratuitous evils, then God does not exist.

2. If creation exists, then a creator exists.

Both of these propositions are analytically true. So if one knows that there are gratuitous evils, then one knows that God does not exist. Likewise, if one knows that creation exists, then one one knows that a creator exists. But how does one know either of these things? Suppose I witness a brutal and unprovoked assault on a human being by another human being. Witnessing this, I witness an evil. But by what mark do I recognize the gratuitousness of the evil? By no empirical mark since what I observe is consistent both with the assault's being gratuitously evil and with its being nongratuitously evil.

Something similar holds for (2). How do I know that what I see, mountains and valleys, cacti and sky is creation or created nature as opposed to uncreated nature? By what mark do I know that nature has the status of having been created? By no mark.

Return to the brutal assault. Imagine it to be perpetrated against a loved one. Atheists will naturally take such crimes as 'proof' that there is no God. But it is no more 'proof' than the existence and order of nature is 'proof' of an intelligent creator. Both athetist and theist interpret the data in the light of a worldview that precedes the data and is imposed upon them. Each can fit the data into his scheme. But fitting data into a scheme is not the same as data proving a scheme. Thus the brutal assault fits the atheist's scheme but does not prove it, and the existence and order of nature fits the theist's scheme but does not prove it.

So here is my challenge to Peter and others: explain how LAFE does not beg the question against the theist.

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If (1) is true, then it is false, and if false, then true. This is an example of an antinomy. In pursuit of a taxonomy, we might call this Grade I of self-referential inconsistency. Grade I, then, is the class of self-referentially inconsistent sentences that issue in antinomies.

There are other self-referential sentences that are not antinomies, but imply their own necessary falsehood. These are such that, if true, then false, and if false, then false, and are therefore necessarily false. For example,

2. All generalizations are false.

If (2) is true, then, since (2) is itself a generalization, (2) is false. But its falsity does not imply its truth. So, if false, then false. Assuming Bivalence, it follows that (2) is necessarily false, whence it follows that its negation — Some generalizations are true — is necessarily true, and moreover an instance of itself. A second example might be

3. There are no truths.

If (3) is true, then it is false. And if false, then false. So, (3) is necessarily false, whence it follows that its negation — There are truths — is necessarily true.

Examples (2) and (3) belong to Grade II in my tentative taxonomy. These are self-referential sentences that entail their own necessary falsehood. Grade III comprises those self-referential sentences that are such that if true, then neither true nor false, and if false, then false. For example,

4. There are no truth-bearers.

If (4) is true, then, since (4) is a truth-bearer, (4) is neither true nor false. But if false, then false. If we define the cognitively meaningful as that which is either true or false, then (4) is either cognitively meaningless or false. A more interesting example that seems to belong in Grade III is the Verifiability Principle of the Logical Positivists:

5. Every cognitively meaningful sentence is either analytic or empirically verifiable in principle.

If (5) is supposed to be cognitively (as opposed to emotionally) meaningful, and thus not a mere linguistic recommendation or pure stipulation, then it applies to itself. So if (5) is true, then (5) — which is clearly neither analytic nor verifiable — is meaningless. So, if true, then meaningless, and if false, then false. Therefore, either meaningless or false. Not good!

Grade IV comprises those self-referential sentences that can be described as self-vitiating (self-weakening) though they are not strictly self-refuting. For example,

6. All truths are relative.

If (6) is true, then, assuming that (6) is intended to be true, it follows that (6) is relative, i.e., relatively true. It is not the case that if (6) is true, then (6) is false. So (6) is not self-refuting. Nevertheless, (6) is self-vitiating in that it relativizes and thus weakens itself: if true, it cannot be absolutely true; it can only be relatively true. Other examples which seem to fall into this category:

7. Every statement is subject to revision. (Quine)
8. Every theory reflects class interests. (Marxism)
9. All theory is ideology. (Marxism)
10. Nothing can be known.
11. Nothing is known.
12. Nothing is certain.
13. All truth is historical.
14. All is opinion.

What is wrong with self-vitiating propositions? What does their weakness consist in? Consider (8). If (8) is true, then the theory that every theory reflects class interests itself reflects class interests. Suppose (8) reflects the class interests of the proletariat. Then what is that to me, who am not a proletarian? What is it to anyone who is not a proletarian? If (8) is true only for you and those with your interests, and your interests are not my interests, then I have been given no reason to modify my views. The trouble with (7)-(14) and their ilk is that they make a claim on our rational attention, on our common rational interest, while undercutting that very claim.

It seems we need a fifth category. The sentences of Grade V are such that, if they are true then they are, not false, but non-assertible. Consider

15. No statement is negative.

(15) applies to itself and so at first appears to refute itself: if (15) is true, then it is false. And if false, then false; hence necessarily false. But consider a possible world W in which God destroys all negative statements and makes it impossible for anyone to make a negative statement. In W, (15) is true, but non-assertible. (15) does not prove itself to be false; it proves itself to be non-assertible.

Can the same said of

16. All is empty (Buddhism)?

I think not, for reasons supplied here.

Finally, we consider

17. All memory reports are deceptive.

This is subject to the retort that one who asserts (17) must rely on memory, and so must presuppose the reliability of the faculty whose reliability he questions by asserting (17). For if anyone is to be in a position to affirm (17), he must remember that on some occasions he has misremembered. He must remember and remember correctly that some of his memories were merely apparent. It seems obvious, then, that the truth of (17) is inconsistent with its being affirmed. If true, it is unaffirmable as true. But this is different from saying that (17), if true, is false. Although (17) is unaffirmable or non-assertible if true, it seems that (17) could be true nonetheless.

Here is a first rough formulation of the problem. A proposition is a whole of parts. Thus the proposition expressed by the declarative sentences 'Sokrates albus est' and 'Socrates is white' is a whole the parts of which are the semantic values of 'Socrates,' 'is,' and 'white.' Now the whole in question has the property of being either true or false, a property that the parts taken distributively do not have. Thus the semantic value of 'Socrates' is neither true nor false. And the same holds for the other constituents of the proposition. It is also the case that the constituents taken collectively, as a collection, is neither true nor false.

Let v('x') denote the semantic value of the expression 'x.' Then my point is that the set {v('Socrates'), v('is'), v('white')} is neither true nor false. No set is either true or false. The same holds for the corresponding mereological sum. No sum is either true or false. And if you balk at the notion of semantic values and think more nominalistically, then the point is that the declarative sentence 'Socrates is white' is toto caelo different from the list: 'Socrates,' 'is,' 'white.' The difference is that, whereas the sentence is either true or false, the list is neither true nor false. No list is either true or false. A proposition/declarative sentence, then, is not a set, sum or list of its constituents.

The problem, then, is to specify what it is about a declarative sentence that distinguishes it from a list, or what it is about a proposition that distinguishes it from a set or sum or its constituents. This amounts to specifying what it is about a declarative sentence or a proposition that gives it the property of being either true or false. Since a proposition is a unity of constituents, the problem is to explain the peculiar unity of a proposition whereby its constituents become fit to be either true or false.

Since a proposition is a whole of parts, but is more than its parts, as their unity, a unity that is not that of a set, sum, or list, one might think to solve the problem of unity by introducing into the proposition a special unifying constituent, one that ties the primary constituents into a unity capable of being either true or false. But this leads to Bradley's regress. Suppose the primary constituents are S and P. The truth-valued whole SP is not identical to {S, P} or to the corresponding sum or list. This for the simple reason that the set can exist without the truth-valued whole existing. So we introduce c to connect S and P. But what makes these three entities into a truth-valued whole? The truth-valued whole ScP is not identical to {S, c, P} or to the corresponding sum or list. This is obvious from the fact that the set can exist withgout the truth-valued whole existing. Something more is needed to 'cement' the constituents S, c, and P together into a truth-valued whole. If a fourth constituent, c*, is introduced then the problem arises all over again inasmuch as there is a difference between the truth-valued whole Scc*P and the set {S, c, c*, P}.

We see that the attempt to solve the unity problem by introducing a unifying constituent leads to a regress that is both infinite and vicious. So how are we to solve the unity problem?

3. There are occurrent beliefs.

Therefore

4. There are propositions.

To understand this argument, one must understand that no particular theory of propositions is being argued for. (It even allows for such wacky theories of propositions as that propositions are sets of possible worlds. That penetrating minds have championed such theories shows that such minds can descend into wackiness under various materialist and extensionalist pressures.) The argument is to the conclusion that something or other must play the roles of truth-bearer, object of such attitudes as knowing and believing, and ground of the possibility of two or more minds' coming to believe or know the same thing. It is an argument for the existence of propositions that leaves open their exact nature. (Analogy to be explored: in the way Aquinas' God-arguments leave open the exact (and in deed unknowable) nature of God.)

Perhaps the argument could be strengthened by restricting it to de dicto as opposed to de re beliefs. Compare 'S believes of some black that he is articulate' with 'S believes that some black is articulate.' The first is de re, the second de dicto. The first does not entail the second. Suppose S is a redneck who believes that no black is articulate. He hears a man on the radio speaking in an articulate manner, a man who, unbeknownst to S is black. It follows that S believes of some black man that he is articulate without believing that some black man is articulate.

Be this as it may. Like any argument, the Metaphysics 101 argument for propositions can be countered in several ways. Alan Rhoda discusses one way in his post, Propositions and Make-Believe. My own view is that the argument is more credible than any of its attempted counterings. More later.

This is correct except for one crucial detail. The 'modern view,' I take it, is the post-Fregean view. On this view propositions are indeed structured entities expressible by tokenings of indicative sentences. But a singular proposition such as 'Socrates is a man' need not have Socrates himself as one of its constituents. It could have some abstract representative of Socrates as its subject-constituent. In a Fregean proposition, it is not Socrates, but the sense of 'Socrates,' that enters as constituent into the proposition, while in a Russellian proposition it is Socrates himself who enters as constituent. Don't get hung up on these labels. If you don't like them, choose others. It is the distinction that counts, and it is not pegged to the actual views of the luminaries in question. (And as you know, these views changed, especially in the case of Russell.)

But Ockham is surely correct that on the traditional approach all propositions (as opposed to sentences) are general, i.e., either particular or universal. I made that point myself more than once. Ockham continues:

Singular propositions do not therefore exist as such in the traditional logic, although logicians after the scholastic period (such as Arnauld) treated them as universal propositions. Aquinas did not regard them, in our sense, as propositions at all. There are singular sentences, such as 'Socrates is wise'. But there is no proposition, in our sense, expressed by this sentence. Aquinas explains that (following Aristotle) the intellect only understands universal concepts such as 'man', 'mortal' and so on, by abstracting from the 'intelligible species' in perception. The intellect can only understand singulars in an indirect way, by what he calls 'turning round to sense-appearances'.

Now I come to my critical point. By failing to note that a singular proposition need not be Russellian, commenter Ockham falls into the error of thinking that there are no singular propositions at all. But this is belied by the plain fact that we reason with them.

Suppose I reason to the general conclusion that Some Athenian is wise from the singular premises, Socrates is wise and Socrates is an Athenian. One cannot reason from sensible marks, although one can reason about them. One reasons from senses. There has to be an intelligible structured entity, call it what you want, before the mind. The intellect must grasp (understand) a sense and this involves more than an eye detecting certain marks on a piece of paper or computer screen. So it is propositions that figure in the argument qua argument, not sentences. And two of these propositions are singular. Again, we reason from truth-bearers, not from physical strings that may or may not express these truth-bearers. These truth-bearers are propositions, and in the specimen of reasoning just given, two of these propositions are singular.

So we need singular propositions to explain the obvious datum I adduced. No doubt one can ask difficult questions about the subject-constituents of Fregean propositions, but these do not overturn the arguments for the postulation of Fregean propositions.

Despite the critical remark, I am inclined to agree with Ockham that propositions cannot be Russellian. When I understand that Marilyn is at the door, it is not Marilyn the concretum, all 130 lbs of her, warts and all, that is in my mind. And the same goes for my massive door. In or before my mind is a proposition all of the constituents of which are abstracta.

And now let me speculate a bit. If we can't speculate in philosophy, where the hell can we speculate? Our minds are finite and ectypal, which is why I can't get the whole of Marilyn into mine. But it might be a different story for an intellectus archtypus. For an infinite archetypal intellect, it may be that the Fregean/Russellian distinction collapses. For God there are perhaps no intermediate sense-structures. Sinn ist Sein und Sein ist Sinn.

Given the goal of truth, how ought I reason so as to attain truth and avoid falsehood? The question is not how I or anyone does reason, except insofar as this is relevant to the question of how we ought to reason. The question is how we ought to reason. This implies that logic is not an empirical discipline. It is not concerned with the empirical facts about how people (or any species of rational being) reasons. Suppose that 75% of a population reasons in accordance with this pattern:

Some Fs are Gs
-----
Some Fs are not Gs.

This fact, if a fact, is an interesting fact of concern to the psychology of reasoning. But it is not a fact that interests the logician qua logician. His concern is with the validity of the argument-pattern. He pronounces the pattern invalid, which does not mean that the pattern is not instantiated in the reasonings of actual people. He would judge the pattern invalid whether everyone or no one reasoned in accordance with it. Suppose there were no people at all. The pattern would still be invalid in the sense that if there were a person, and this person reasoned in accordance with the pattern, then the person would reason incorrectly.

Here is an analogy. Whether everyone kills someone for the fun of it, or no one kills anyone for the fun of it, or there are no people at all, it remains the case that killing people for the fun of it is morally wrong.

And the same goes for valid patterns. Suppose there is a necessarily truth-preserving pattern of reasoning in accordance with which it is possible for beings like us to reason, but in accordance with which no one of us in fact reasons, it would still be the case that the pattern is valid. In this sense, the valid patterns are norms. As such, they cannot be gleaned from the ways our minds in fact operate. For as a matter of fact, our minds operate in the damndest ways.

The normativity of logic is consistent with the fact that logical laws are not prescriptive as to their content. The Law of Non-Contradiction, applied to propositions, states that it is not the case that a proposition and its negation are both true: ~(p & ~p). LNC states a very general fact; it does not prescribe any action. But although LNC is not prescriptive in its content in the way that No felon shall own a firearm is prescriptive, or rather proscriptive, in its content, LNC does imply prescriptions. Thus it implies that one ought not affirm both a proposition and its negation.

Ockham would have us conclude, however, that "there genuinely does exist a condition under which a [valid] standard form has an instance with TPFC." The condition in the present case is that 'Alexander' does not denote the same individual in both of its occurrences or tokenings. If this condition is satisfied, then it can easily be that both premises are true. 'TPFC' abbreviates 'has true premises and a false conclusion.' So what Ockham is urging is that the argument-form depicted above is only conditionally valid; it is valid, but only on condition that 'a' be taken to denote the same individual in both of its occurrences. The argument-form is not unconditionally valid because it has an instance, the Alexander argument above, that has true premises and a false conclusion.

My thesis is and has been all along that this distinction is bogus: there is no justification for any distinction between conditional and unconditional validity. Argument-forms are not arguments; argument-forms are the primary bearers of the properties of validity and invalidity; and the validity of an argument-form is in no way conditional upon whether terms in natural language are used univocally or not.

I turn aside Ockham's argument by denying what he takes to be "manifestly and undeniably" the case, namely, that the Alexander argument, given his proviso about the reference of 'Alexander,' is of the form depicted above. We need to be clear that 'a' in the form diagram is not an abbreviation for 'Alexander.' It is a place-holder. The distinction between abbreviations and place-holders was explained earlier. Although 'a' is an individual constant, and not an individual variable like 'x' or 'y,' it is an arbitrary individual constant. This means that any name for an individual (as opposed to a name for a property) can be its substituend. But since 'a' is a constant, whichever proper name is substituted for 'a' in one place in the argument must be substituted in every other place.

What's more (and this is crucial), the proper name substituted for 'a' must be used in the same way in each of its occurrences if it is to count as a genuine substituend of 'a.' It is an obvious fact that proper names are in one sense quite common: 'Alexander' can be used and has been used to refer to many different people and animals. No doubt some cats and dogs rejoice under this name. But 'Alexander' is not functioning as a proper name unless it is being used by a person in a context with the intention of referring to exactly one individual, and perhaps to exactly one individual in every possible world in which that individual exists.

Now 'a' is a place-holder for any proper name used as a proper name. It follows that 'Alexander' cannot be substituted for 'a' if it refers to a man in one occurrence and a dog in another, or to two different men.

My point contra Ockham is simply that the Alexander 'argument' does not instantiate the valid form given above. Since it does not, it cannot function as a counterexample to the validity of the form depicted. It cannot be used to show that the form is invalid or that it is only conditionally valid. For the condition Ockham wants to impose ab extra is already bulit into the form diagram. To repeat, 'a' is an arbitrary individual constant. Qua constant, it is a place-holder only for names used univocally.

It should also be obvious that existential generalization on a singular term such as 'a' presupposes that 'a' in all occurrences denotes the same individual. That is, to infer '(Ex)(Fx & ~Fx)' from 'Fa' and '~Fa,' by the inference rule of Existential Generalization, it must be assumed that 'a' denotes the same individual in both of its occurrences. Otherwise, what would follow from the premises would be '(Ex)(Fx) & (Ex)(~Fx)' which, of course, is not equivalent to the previous existentially quantified formula.

All occurrences of the variable 'x' in '(Ex)(Fx & ~Fx)' are bound by, and come under the scope of, one and the same existential quantifier. The binding captures the pronominal back-reference which in English is expressed by 'There is an F and it is not F.' But this would not be the case were 'a' interpreted as denoting distinct individuals.

What say you loyal readers? Have I refuted Ockham? Can we move on now?

1. P --> Q
2. Q
---
3. P

Both are arguments; it is just that the second is an abbreviation of the first in which sentences are replaced with upper-case letters and the logical words with symbols from the propositional calculus. But it is easy to confuse the second argument with the following argument-form:

1. p --> q
2. q
---
3. p

An argument-form is a one-over-many: many arguments can have the same form. And the same goes for its constituent propositional forms: each is a one-over-many. 'p --> q' is the form of indefinitely many conditional statements. But an argument, whether spelled out or abbreviated, is a particular, and as such uninstantiable. One cannot substitute different statements for the upper-case 'P' and 'Q' above.

Some of you will call this hair-splitting. But I prefer to think of it as a distinction essential to clear thinking. For suppose you confuse the second two schemata. Then you might think that the original argument, the one in 'canonical English,' is an instance of the formal fallacy of Affirming the Consequent. But the second schema, though it is an instance of the third, is also an instance of a valid argument-form:

(x)(Cgx)
---
(Ex)(Cgx).

In sum, the confusion of abbreviations with place-holders aids and abets the mistake of thinking that an argument that instantiates an invalid form is invalid. Validity and invalidity are asymmetrical: if an argument instantiates a valid form, then it is valid; but if it instantiates an invalid form, then it may or may not be invalid.

But talk of how people ought to reason, talk of what they ought to do and leave undone in matters of argument, presupposes that at least some belief formation comes under voluntary control. No one will contend that all our beliefs are subject to the control of the will, but if none of them are, then there is no possibility of reasoning, strictly speaking. And if there is no possibility of reasoning, strictly speaking, then there is no possibility of that normative study of reasoning called logic, which of course itself involves reasoning, namely, reasoning about correct and incorrect reasoning. Peirce:

Now, that which is uncontrollable is not subject to any normative laws at all; that is, it is neither good nor bad; it neither subserves an end nor fails to do so. But it is only the deliberate adoption of a belief in consequence of the admitted truth of some other proposition which is, properly speaking, reasoning. (p. 120)

If I see that p is true, and understand that p entails q, then I am logically required to accept the truth of q. This logical requirement, however, is not to be confused with any kind of natural necessity: though I am logically required to accept q, I am yet free to reject q. People do contradict themselves, and sometimes willfully: they will not accept the truth that they are logically required to accept given their other doxastic acceptances.

This suggests that our being rational beings is incompatible with our being deterministic systems. But to develop this properly would take a lot of scribbling. Instead, I'll just hand the ball to Victor Reppert and quit the field.

p --> q
p
---
q.

This argument-form is surely above reproach in point of validity.

Could this form be valid without being unconditionally valid? From what O. is saying above, it would be valid, but not unconditionally, if there were no proviso to the effect that the same indicative sentence be substituted for the place-holder 'p' in both of its occurrences and the same indicative sentence be substituted for 'q' in both of its occurrences. Without this proviso, the following could count as an instance of modus ponens:

If Wilson drowned, then Wilson is dead
Phil Spector lives in Alhambra, California
-----
Wilson is alive.

But surely two things are true: (i) this argument is not valid, and (ii) it is not an instance of modus ponens. There simply is no distinction, apart from a merely verbal distinction, between 'valid' and 'unconditionally valid.' Every valid argument-form is unconditionally valid, and conversely. For Ockham to justify his distinction, he must give us an example of an argument-form that is valid, but not unconditionally valid, or vice versa. I don't see how this could be done. But I am open to refutation.

I believe I can show how Ockham is going wrong. This debate began with the Pittacus argument:

Pittacus is a good man
Pittacus is a wise man
-----
Some wise man is a good man.

I said that this argument is valid, and O. objected that it is not "unconditionally valid." But surely the argument is valid and unconditionally so. The following is a crucial principle:

An argument is valid iff there is a valid argument-form that it instantiates.

To understand the bolded principle you must keep straight the distinction between an argument and an argument-form, and you must understand that a valid argument is valid in virtue of the validity of its logical form. It is argument-forms, not arguments, that are the primary bearers of the properties of validity and invalidity. An argument is said to be valid only insofar as it instantiates a valid argument-form. I hate to be pedantic, but just to make sure that we are on the same page, I will now make a list of some obvious corollaries:

No argument-form is an argument
Every argument has one or more forms
An argument can be valid even if it has an invalid form
Every argument-form is either valid or invalid
No argument-form is sound.

Now does the Pittacus argument instantiate a valid form? Of course. It instantiates this form:

Fa
Ga
---
(Ex)(Fx & Gx)

This form is provably valid within MPL. Therefore, the Pittacus argument is valid. It is valid because it instantiates a valid argument-form.

Now Ockham's reason for saying that the Pittacus argument is not unconditionally valid is presumably that 'Pittacus' might refer to different things in its two occurrences. Well, suppose it does. Then it is a different argument with a different form, the following invalid form:

Fa
Gb
---
(Ex)(Fx & Gx).

But none of this gives us any reason to distinguish between validity and unconditional validity. The original Pittacus argument is valid, as I showed, and unconditionally so. The second Pittacus argument, if you want to call it an argument at all, is invalid, and unconditionally so. That's all there is to it.

Now I deny that this is an argument for reasons already given. But even if it is an argument, call it the 'Stooge argument,' it certainly does not have the logical form that Ockham ascribes to it, namely:

Ha
~Ha
---
(Ex)(Ha & ~Ha)

This form is clearly valid: no argument of this form is such that the premises are all true and the conclusion false. (Obviously, the premises cannot both be true). So the argument-form is technically valid, though of course no argument of this form is sound. (A is sound =_df A has a valid form and true premises.)

Ockham reasons as follows: Since the Stooge argument has true premises and a false conclusion, the Stooge argument is invalid; but the Stooge argument instantiates the form just depicted; ergo, the form just depicted is invalid!

The Ockhamite argument is bad in my humble opinion, resting as it does on what I take to be a false presupposition, namely, that arguments are composed of sentences rather than propositions. The proposition that Larry expresses when he tokens 'I am happy' is or is equivalent to the proposition Larry is happy, while the proposition Moe expresses is or is equivalent to the proposition, Moe is not happy. You will have noticed that while 'I am happy' and 'I am not happy' appear to be contradictories, the corresponding Larry and Moe propositions are not contradictories, but are indeed logically independent.

Therefore, the form of the Stooge argument is:

Ha
~Hb
---
(Ex)(Ha & ~Ha)

which is invalid. So I consider myself to have won Round One of the debate. Round Two begins with an Ockhamite attack on the very idea of a proposition as an entity distinct from a sentence. What follows in italics is by Ockham:

(1) Propositions must be complex entities. Otherwise we could not use an existing, finite stock of words to express propositions that have never before been expressed.

Agreed. Barry Miller thinks that there are logically simple propositions, but I criticized him in print for this.

(2) There must be a part of a proposition corresponding to the proper name. For example, the sentence 'Etna is higher than Vesuvius', contains the name 'Etna', which occurs also in other sentences, e.g., in the sentence 'Etna is in Sicily'. There must therefore be something similar in the two corresponding propositions, that corresponds to the word 'Etna'. (But not in the propositions corresponding to 'Alexander did not seize Helen' and 'Alexander seized Helen', for reasons we agree on, of course).

Agreed.

(3) This cannot be something material and observable. Otherwise, the thought corresponding to 'Etna is not higher than Mont Blanc' would contain two large mountains, thus every piece of frozen, solidified lava in one, and every snowfield in the other.

This is true for Fregean propositions, though not true for Russellian propositions. But let's stick to Fregean propositions. I agree that the subject-constituents of such propositions cannot be physical objects. The propositions are not physical items and their parts cannot be physical either.

(4) But if not material or observable, how can we speak of propositions having the same 'form'? If two numerically different things possess the same form, it is because their shape is observable to the senses. In what sense can two unobservable things possess the same form?

You were doing so well up to now! But now you blunder by assuming, falsely in my humble opinion, that 'form' as when we speak of the 'logical form' of an argument or of a proposition must mean something like physical pattern or shape.

I of course reject that. And unless you have some extremely powerful arguments, you will not budge me from my view. The propositions Larry is taller than Moe and Moe is taller than Joe have the same logical form which might be depicted Rab or aRb. What's the problem? Each stooge is a physical particular, and the relation of being taller than is physically measurable. But the propositions are not physical, nor is their common form physical.

(5) Further, how does a propositional name represent the object that the corresponding spoken or written name is a name of? Is this representation imposed by convention? But if it is, we have an infinite regress. For I will use the 'Alexander argument' again. We could change the meaning of the propositional name 'Alexander' to signify Alexander of Troy instead of Alexander of Macedonia, and then the propositions 'Alexander did not seize Helen' and 'Alexander seized Helen' would contain the same propositional name, but both propositions true. If you say that the propositions signify other propositions, then I use the argument again, and so on.

You will have to spell this out for me to understand exactly what you mean. But I agree that one can legitimately ask how the subject-constituent of a Fregean proposition represents what it represents. Similarly, what makes my thought of you right now a thought of you? These questions about intentionality are interesting and important but I don't have to answer them to justify my introduction of propositions.

(6) But if the relation is not by convention, we have the absurdity that some abstract entity immutably and eternally represents Alexander, even before Alexander existed. Indeed, even if Alexander had never existed, the sentence 'Alexander seized Helen' expresses a proposition containing something eternally representing him. That's absurd.

Plantinga maintains a theory like this, so I would hesitate to say that it is absurd. Why can't proper names have senses? Why can't senses be Platonica? Why can't they exist uninstantiated? I am not endorsing all this, but where is the absurdity, i.e., the logical contradiction? Or are you using 'absurd' only in an emotive way?

(7) For similar reasons you previously rejected the idea of haecceities. Doesn't your 'solution' of my problem involve this very idea?

Interesting objection. I have indeed rejected nonqualitative haecceities. I find it hard to swallow the idea that before I was born there was a necessarily existent property, the property of being identical to BV, a property that can exist uninstantiated. So the proposition BV is happy cannot involve such an haecceity-property. Perhaps the proposition involves a qualitative haecceity. But this is a large topic.

The bottom line for me is that the arguments for the introduction of propositions (not necessarily Fregean propositions) are so strong, that the kinds of questions you raise do not amount to a good reason to dismiss them.

Alexander lived in Troy (where the expression 'Alexander' refers to Alexander of Troy)
Alexander did not live in Troy (where the expression 'Alexander' refers to Alexander of Macedonia)
-----
Someone lived in Troy and did not live in Troy.

'TPFC' abbreviates 'true premises false conclusion.' Ockham now argues as follows:

1. Any form of any TPFC argument is invalid
2. The Alexander argument is TPFC
3. Any form of which the Alexander argument is an instance, is invalid
4. If the Alexander argument is an instance of the form 'Fa, Ga, therefore (Ex)(Fx & Gx)', that form is invalid
5. The Alexander argument is an instance of the form 'Fa, Ga, therefore (Ex)(Fx & Gx)'
6. The form 'Fa, Ga, therefore (Ex)(Fx & Gx)' is invalid.

Ockham adds this remark:

Again, the argument is perfectly valid. Well, actually it's not, if it is sound, because its validity depends on the validity of forms, which the very same argument proves to be invalid. But leave that for now.

THE UNSOUNDNESS OF THE OCKHAMITE ARGUMENT

Premise (1) of the Ockhamite argument is of course true. If an argument has true premises and a false conclusion, then no form of such an argument is valid. But I see no reason to accept the truth of premise (2). And this for the simple reason that the 'Alexander argument' is not an argument!

What is an argument anyway? The word has of course several meanings. In logic it has two main meanings. Consider the propositional function 'x is wise.' This function has the value True for Socrates as argument. But this is not the presently relevant sense of 'argument.' An argument in the present context is a sequence of statements together with the claim that one of them, the conclusion, follows from the others, the premises. To argue is to adduce reasons in order to support, justify, prove or demonstrate a certain proposition. The reasons adduced are the premises of the argument and the proposition which they are supposed to support is the conclusion.

Now given this understanding of what an argument is, the 'Alexander argument' is not an argument. When a person gives an argument, he intends that all occurrences (tokens) of a proper name such as 'Zeno' should have the same reference. Thus if one argues, 'Philosophers respect reason; Zeno is a philosopher; ergo, Zeno respects reason,' the arguer is charitably understood to be referring or trying to refer to the same individual during the time in which the argument unfolds. But in the 'Alexander argument' the proper name 'Alexander' does not refer to the same individual in both of its occurrences. This 'argument' (sneer quotes!) is therefore a sequence of statements that does not amount to an argument. Obviously, not every sequence of statements is an argument.

Although (3) follows from (1) and (2), the falsity of (2) renders (3) false. (UPDATE 29 April: the falsity of (2) does not render (3) false. See retraction here

(4) may be granted, but (5) should not be granted. The 'Alexander argument' is not an instance of the argument-form depicted above, it is an instance of the following argument-forms:

Fa
Gb
---
(Ex)(Fx & Gx)

or better

Fa
~Fb
---
(Ex)(Fx & Gx)

both of which are obviously invalid.

Since (5) is false, the conclusion (6) is also false. I have just given two reasons why the Ockhamite argument is unsound: (2) is false; (5) is false. But as Ockham concedes, his argument is invalid! So this is a third reason to deem his argument unsound.

THE INVALIDITY OF THE OCKHAMITE ARGUMENT

The Ockhamite argument proves entirely too much: it proves among other things that modus ponens is invalid. Consider

If Zeno is breathing, then Zeno is alive
Zeno is breathing
-----
Zeno is alive.

Suppose 'Zeno' refers to my cat in its first three occurrences, and to the largest rock in my backyard in its fourth and final occurrence. Then the premises are true and the conclusion is false. By the Ockhamite reasoning, modus ponens is invalid since the above argument has the form of modus ponens and the above argument has true premises and a false conclusion.

Now if this isn't sophistry, what would be? And the sophistry speards since the 'argument' can be iterated for any argument-form including the argument-form instantiated by the Ockhamite argument. So the ockhamite argument is hoist by oys own petard: if sound, then unsound because invalid.

DIAGNOSIS

As explained in earlier posts in this chain, Ockham's troubles spring from a failure to distinguish between indicative sentences and the propositions they are used to express or the statements they are used to make. Some such distinction is simply unavoidable, and has the status of a datum denial of which leads to absurdity.

One who makes this unavoidable distinction sees immediately that the 'Alexander argument' does not have the logical form that Ockham thinks it has.

Ockham will demand to know what a proposition is. For present purposes, however, all we need to know is the self-evident point that propositions cannot be identified with indicative sentences. 'I am happy' said (assertively uttered) by me and said by Joe Blow express two different propositions. But it is one and the same sentence. Can anyone in his right mind deny that?

Note the asymmetry between validity and invalidity. To be valid, it is sufficient that an argument instantiate a valid argument-form. To be invalid, however, it is not sufficient that an argument instantiate an invalid argument-form. For an argument that instantiates an invalid form may also instantiate a valid form. I gave examples of this in earlier posts in this chain.

Valid Form: None of its instances have true premises and a false conclusion.
Invalid Form: Some of its instances have true premises and a false conclusion, and some do not.

This suggests that there is room in logical theory for the concept of contravalidity:

Contravalid Form: All of its instances have true premises and a false conclusion.

Note that what we have here is a tripartition in the sense that the set of argument-forms is divided or partitioned into three disjoint and mutually exhaustive proper subsets, the valid, the invalid, and the contravalid.

According to David H. Sanford (If P, then Q: Conditionals and the Founbdations of Reasoning, Routledge 1989, p. 42), the above tripartition and the concept of contravalidity is traceable to Johannes de Celaya. But Professor Sanford says something that strikes me as incorrect. He writes, "All contravalid arguments are invalid, but not all invalid arguments are contravalid." (p. 42) But this can't be right given that the Celaya classification is a tripartition. If an argument is contravalid, then ALL instances of its form have true premises and a false conclusion. But if an argument is invalid, then SOME instances of its form have true premises and false conclusion and SOME do not. So if an argument is contravalid it is not invalid. Sanford makes it sound as if contravalid arguments are a proper subset of invalid arguments when in fact they are neither valid nor invalid. But it is easy to fall into confusion here since invalidity and contravalidity are usually not distinguished. What Sanford should have said is that all contravalid arguments are not-valid, the not-valid comprising both the invalid and the valid.

Here is an example of a contravalid argument-form:

If p, then either p or not p
-----
p if and only if not p.

Since the premise is a tautology and the conclusion a contradiction, every instance of this schema has a true premise and false conclusion. From a practical point of view, contravalidity is uninteresting -- which is why it is not discussed in logic textbooks. But it is theoretically interesting because its symmetry with validity throws into relief the asymmetry of validity and invalidity. Consider this argument:

If an argument has a valid form, then it is valid
-----
If an argument has an invalid form, then it is invalid.

This is a non sequitur, and the conclusion is false to boot. Someone who thinks that the conclusion is true can be said to be confusing invalidity with contravalidity. For if an argument has a contravalid form, then it is contravalid. So it does seem useful for purposes of logical theory to distinguish the valid, the invalid, and the contravalid.

Therefore, sameness of linguistic meaning is neither necessary nor sufficient for sameness of proposition expressed.

Now logic is concerned with the inferential relations between propositions, or else sentences used assertively. (One might want to identify a proposition with a sentence in the indicative mood used assertively, but I leave this undecided.) Since an argument is a sequence of propositions together with the claim that one of them, the conclusion, follows from the others, the premises, I would deny that the above Ockhamite example is an argument. The above, expressed as an argument, might look like this:

John is a man
Sue is called 'Sue'
-----
Sue is a man.

The logical form of this in MPL is:

Mj
Cj
---
Ms.

And this form is invalid.

In sum, for an argument to have a logical form, there must be an argument. But an argument is composed of propositions, or else sentences in assertive use. When a sentence is used to make an assertion, such indexicals elements as 'I,' 'now,' 'today,' etc. get assigned referents. Thus the Ockhamite example is not an argument, and so does not have a logical form.

Although Ockham's second sentence is in one sense true, it is obscure and misleading. What makes an argument valid or invalid is its form and nothing else. An argument is valid because of, in virtue of, its form. It is not the case that a form is valid because of, in virtue of, some valid argument that has that form. For there may be no argument that has the form in question. There are more valid and invalid forms than there are arguments. This is obvious if you think of an argument as an instantiation in human thought or speech of an argument-form.

Let me put it another way. When we say of a particular argument that it is valid, we are saying that it is an instance of a valid form. Validity (invalidity) are primarily predicated of argument-forms, and only secondarily of arguments that instantiate those forms. That is, it is in virtue of an argument-form's being valid that an argument of that form is valid, and not vice versa. The validity of the form 'makes' the argument valid, and this 'making' is asymmetrical. Or you could say that a valid argument 'inherits' its validity from its instantiating of a valid form, where this inheritance relation is asymmetrical.

It follows that to determine whether or not a particular argument is valid we must look to see if there is a valid form that it instantiates. So consider this example:

Las Vegas is called 'Sin City'
Las Vegas is a city in New Mexico
-----
There is a city in New Mexico called 'Sin City.'

Is this a valid argument? It is if it has one valid form. Now how does one get to the logical form of an argument? One removes the 'nonlogical' words and replaces them with either place-holders or else with variables. (Memo to BV: write a separate post on this distinction.) And note that when one removes an occurrence of 'Las Vegas' and replaces it with an occurrence of the arbitrary individual constant 'a,' one must proceed uniformly. Thus we get this:

a is F
a is G
-----
(Ex)(Fx&Gx)

where the domain of quantification is restricted to cities.

Now the form just depicted is provably valid within MPL. Since the Vegas argument has one valid form, the Vegas argument is valid regardless of the fact that it also has invalid forms. Here is an invalid form in the Propositional Calculus of the same argument:

p
q
---
r.

Here is another invalid form:

a is F
b is G
-----
(Ex)(Fx&Gx).

Now EVEN IF this second invalid form is a form of the Vegas argument, this does nothing to show that the Vegas argument is invalid. The Vegas argument is valid because it has one valid form. But surely this second invalid form is NOT a form of the Vegas argument. For if some child or foreigner were giving the Vegas argument, no one could charitably construe the person to be using 'Las Vegas' to denote different places in its two occurrences.

This is also true of non-argumentative discourse. Suppose I am telling you about my cat Zeno. "Zeno was this, Zeno was that; Zeno liked to dominate the female cats; Zeno was a horny bastard, etc, etc." Would anyone interpret me to be referring first to a feline, then to a Parmenidean philosopher, then to a Stoic philiosopher, and ending up referring to a local butcher?

Let's now consider Ockham's example and what he says about it:

Alexander lived in Troy (where the expression 'Alexander' refers to Alexander of Troy)
Alexander did not live in Troy (where the expression 'Alexander' refers to Alexander of Macedonia)
-----
Some one lived in Troy and did not live in Troy.

IF (note the conditional here) the argument above were an instantiation of the argument-form below, the argument-form would be invalid, because it would have an invalid instantation.

a is F
a is not F
-----
some F is not F

Clearly, the form just depicted is valid because no argument of that form has all true premises and a false conclusion. So Ockham reasons that if the Alexander argument is of this form, then this form is invalid. But since the form is not invalid, the Alexander argument is not of this form.

But nobody would say that the Alexander argument as presented is of the form just depicted. It is of the following form:

a is F
b is not F
-----
Some F is not F.

This form is obviously invalid. But if we remove the parenthetical matter, then the Alexander argument has the valid form depicted above. Suppose the argument is presented like this:

Alexander lived in Troy
Alexander did not live in Troy
-----
Someone lived in Troy and did not live in Troy.

Is this argument valid or invalid? Since it has a valid form, it is valid. It is irrelevant that it has an invalid form as well. This is what Ockham does not appreciate. Furthermore, it is simply false that the Alexander argument just presented can be reasonably contrued as having the invalid argument-form immediately above.

I think Ockham's confusions are due to failing to realize that it is argument-forms that are the primary bearers of validity and invalidity.

3. Zeno is famous for his paradoxes of motion
4. Zeno is a Stoic
-----
5. Some Stoic is famous for his paradoxes of motion.

Is this argument valid? It obviously is despite the scholastic quibbling of my friend Ockham in an earlier thread. He would have us distinguish validity from unconditional validity, a distinction without a difference. The argument above is plainly valid inasmuch as it instantiates a valid form. The problem with the argument, of course, is that it is unsound: if (3) is true, then (4) is false, and if (4) is true, then (3) is false. For (3) to be true, 'Zeno' must refer to Zeno of Elea, but for (4) to be true, 'Zeno' must refer to Zeno of Citium. And of course neither can refer to my cat, Zeno (may peace be upon him).

Now consider this argument:

6. If God created something, then God created everything
7. God created everything
-----
8. God created something.

This instantiates the formal fallacy of affirming the consequent. Is the argument therefore invalid? No! For it also instantiates a valid form:

Everything is such that: Fx
-----
Something is such that: Fx.

In order to evaluate the argument within TFL, it must be put into syllogistic form, otherwise the rules of the syllogism cannot be applied to it. Thus,

Every Pittacus is a wise man
Some Pittacus is a good man
-----
Some wise man is a good man.

This has the form:

Every P is a W
Some P is a G
-----
Some W is a G.

It is easy to prove that this form is valid by using a Venn diagram (not to be confused with an Euler diagram), or by applying the syllogistic rules. You will notice that I have rigged the argument so that those who deny that universal propositions have existential import will be satisfied that it is valid. Note also that the Venn diagram test would not work if the argument were given the following form:

Every P is a W
Every P is a G
-----
Some W is a G.

You can verify for yourself that if you diagram the premises you will not thereby have diagrammed the conclusion.

But is it logically acceptable to attach a quantifier to a singular term? How could a proper name have a sign of logical quantity prefixed to it? 'Pittacus' denotes or names exactly one individual. 'Every Pittacus' denotes the very same individual. So we should expect 'Every Pittacus is wise' and 'Pittacus is wise' to exhibit the same logical behavior. But they behave differently under negation.

The negation of 'Pittacus is wise' is 'Pittacus is not wise.' So, given that 'Pittacus' and 'every Pittacus' denote the same individual, we should expect that the negation of 'Every Pittacus is wise' will be 'Every Pittacus is not wise.' But that is not the negation (contradictory) of 'Every Pittacus is wise'; it is its contrary. So 'Pittacus is wise' and 'Every Pittacus is wise' behave differently under negation, which shows that their logical form is different. My argument can be put as follows:

a. Genuinely singular sentences have contradictories but not contraries.
b. Sentences like 'Every Pittacus is wise' have both contradictories and contraries.
Therefore
c. Sentences like 'Every Pittacus is wise' are not genuinely singular.
d. 'Pittacus is wise' is genuinely singular.
Therefore
e. The TFL representation of singular sentences as quantified sentences does not capture their logical form, and this is an inadequacy of TFL, and a point in favor of MPL.

If A is predicated of all B, and B of all C, A must be predicated of all C: We have already explained what we mean by 'predicated of all.' Similarly also, if A is predicated of no B, and B of all C, it is necessary that no C will be A. But if the first term belongs to the middle, but the middle to none of the last terms, there will be no syllogism in respect of the extremes. (Quoted in D. Sanford, p. 14)

Aristotle is concerned with evaluating arguments with forms such as the following:

All Bs are As
All Cs are Bs
-----
All Cs are As

No Bs are As
All Cs are Bs
-----
No Cs are As

These two are valid forms. But the following is not since it has an undistributed middle term:

All Bs are As
All Cs are As
-----
All Cs are Bs

It is essential to note that 'A,' 'B,' and 'C' denote terms not propositions or statements. This is why I described the Aristotelian syllogistic as a term logic. To the best of my knowledge, Aristotle never considers the validity/invalidity of such argument forms as the following, where the letters are propositional variables (or else abbreviations for whole declarative sentences) and not term variables (or else abbreviations for terms):

Modus ponendo ponens
If p, then q
p
-----
q

Modus tollendo tollens
If p, then q
not q
-----
not p

Modus tollendo ponens
p or q
not p
-----
q

Modus ponendo tollens
p or q
p
-----
not q

3. Murder is wrong
4. Suicide is murder
-----
5. Suicide is wrong.

Someone who gives (i.e., makes, mounts, forwards, advocates, etc.) this argument, as opposed to merely quoting it or mentioning it as I am doing here for purposes of logical theory, is asserting the premises and also asserting the conclusion as a logical consequence of the premises. But someone who asserts (2) or asserts

6. If murder is wrong, and suicide is murder, then suicide is wrong

is not asserting the antecedent or the consequent.

Therefore, arguments and conditionals should not be confused. Nevertheless, they are closely related in that arguments have corresponding conditionals and vice versa. The early Stoics were onto this as well. Thus, (6) is the conditional corresponding to the (3)-(5) argument. We can go further and state that an argument is valid only if its corresponding conditional is a necessary truth. Furthermore, an argument is valid if and only if its corresponding conditional is a narrowly-logical truth. If we are operating within the Propositional Calculus (PC), we can say that an argument encoded in PC whose validity/invalidity rides on the logical structure captured by this encoding is valid if and only if its corresponding conditional is a tautology in the sense in which this term is used in the PC.

Truth and validity are distinct, and one betrays logical ignorance if one speaks of an argument as either true or false. Still, for every valid argument there is a necessarily true conditional.

Philo says that a sound conditional (sunemmenon) is one that does not begin with a truth and end with a falsehood, e.g., when it is day, and I am conversing, the statement, 'If it is day, I am conversing.' But Diodorus says it is one that neither could nor can begin with a truth and end with a falsehood. According to him the conditional statement just quoted seems to be false, since when it is day and I have become silent it will begin with a truth and end with a falsehood. (The Development of Logic, pp. 128-129)

There seems to be a blending of temporal and modal considerations in this passage. Modally interpreted, Diodorean implication is the necessitation of Philonian implication just as strict implication is the necessitation of material implication. Thus

1. p D-implies q =df necessarily, p P-implies q.

On this reading, 'If it is day, then I am conversing' comes out true when construed as a Philonian conditional (given that I am conversing) but false when construed as a Diodorean conditional. For it is not true necessarily that if it is day then I am conversing. There are possible worlds in which it is day but I am not conversing.

Commenter Ockham in effect confuses the necessity of the consequence with the necessity of the consequent by construing the Diodorean conditional to be true when the antecedent is true and the consequent cannot be false. He thus seems to be confusing (1) with

2. p D-implies q =df p P-implies necessarily q.

He makes a second mistake when he says, "I think the latter is sometimes called semantic implication." But strict or Diodorean implication is just as extensional, i.e., not based in the meanings of the propositions involved as is material or Philonian implication. This is why there are 'paradoxes' of strict implication as well as 'paradoxes' of material implication.

Another way to interpret the difference between Philo and Diodorus is temporally. We might then say that

3. p D-implies q =df for any time t, p P-implies q at t.

This makes 'If it is day, then I am conversing' true when construed Philonianly and false when construed Diodoreanly. For, as Diodorus suggests, if I fall silent during the day, as even the most vigorous windbag must, then 'If it is day, I am conversing' is false.

Further reading: Diodorean Conditionals.

The paradox disappears, however, if the reader dismisses from his mind the prejudice in favor of the usual meaning of the word "implication" and recognizes that, by definition, we have made it denote something else in the propositional calculus. (An Introduction to Logic, p. 127)

The meaning of '-->' is given by its truth table. The essential point is that 'p --> q' is false only in one of the four cases, the one in which p is true and q false. The truth table definition involves an element of stipulation, but it is not a mere or arbitrary stipulation. It is a regimentation of what we ordinarily mean by 'implies' for the logical purposes of the propositional calculus. What the regimentation does is isolate a necessary but not sufficient condition for p to imply (ordinary sense) q. This necessary but not sufficient condition is that it not be the case that p is true and q false.

The idea is that no ordinary conditional can be true if its antecedent is true and its consequent false. And surely no true ordinary conditionals have true antecedents and false consequents. To that extent, '-->' captures something essential to all conditionals. But what about the examples of false ordinary conditionals with false antecedents and false consequents? Do these tell against material implication? Dennis Monokroussos supplied 'If everyone has less money than I do, then everyone has more money than I do' and Spur offered 'If all roses are red, than all roses look exactly alike.'

It is not clear to me that these anomalies cause trouble. They would cause trouble only if they interfered with argument evaluation. So consider the argument:

If all roses are red, then all roses look exactly alike.
It is not the case that all roses look exactly alike.
Therefore
It is not the case that all roses are red.

The argument can be shown to be valid using a truth table. Since the argument form is valid, and the conclusion and the second premise are true, the logic of the situation allows for the first premise to be either true or false. According to the truth table definition of '-->,' the first premise should be assigned the value 'T.' But common sense bids us assign it the value 'F.' But it makes no difference to the validity of the argument which value we assign.

So, unless someone can convince me otherwise, I see no difficulty here. The main thing to understand is that material implication is a technical notion introduced for a specific purpose within the context of a logical theory whose purpose is to aid us in evaluating as valid or invalid a certain subset of arguments, namely, those deductive arguments whose validity/invalidity hinges on such logical particles as 'and,''or,' etc. (To ward off possible misunderstanding, I am well aware that the predicate calculus includes the propositional calculus.)

Now one thing that should be obvious is that a genus cannot be defined in terms of a species thereof. And yet that is precisely what some of the definitions on the linked page do. For example,

An increase in the Earth's temperature caused by human activities, such as burning coal, oil and natural gas.

This fails as a definition of 'global warming' because it is too specific. Not all global warming is anthropogenic (man-made). And even if all global warming were anthropogenic, it is not a matter of definition that this be so. The opposite mistake is committed by the following 'definition':

Also called climate change.

This is too general. All global warming is climate change, but not all climate change is global warming. There is also global cooling. And again, even if, contrary to fact, there never has been in the history of the earth any case of global cooling, this is not a question that ought to be decided at the level of a definition. Here is another defective definition:

the theoretical increase of global temperatures caused by the greenhouse effect.

Theoretical as opposed to what? What is the difference between a theoretical increase and an increase? And why is a cause specified in the definition? Suppose something other than the greenhouse effect is the cause of global warming. Would it not still be global warming? The business of a definition is to isolate the phenomenon in question, to say what it is. The question as to what causes it is logically secondary and does not belong in the definition. Here is a real winner:

Increased levels of gases such as carbon dioxide that trap heat in the earth's lower atmosphere potentially causing global warming.

Where's my logic stick? First, causes should be left out of definitions. Second, global warming can occur without the build-up of gases like carbon dioxide. Third, the weasel word 'potentially.' Fourth, the definition is circular: the definiendum occurs in the definiens. The following definition seems adequate:

Global warming is a term used to describe an increase over time of the average temperature of Earth's atmosphere and oceans.

I would delete the pleonastic 'over time.' How could there be an increase that was not 'over time'? More importantly, note the word 'average' which I think is essential to a good definition. The claim that global warming is taking place is not the claim that at every place at or near the surface of the earth the temperature is higher than it was at that place and on that date in the past. Dennis Prager, an AM talk jock whom I respect, seemed to fall into this fallacy recently. He cited a place at which there had been a record low temperature as evidence against global warming. But it is nothing of the sort.

It should be obvious that an average increase in some quantity need not be steady or ubiquitous. Suppose the average price of a house in some locality has increased over a ten year period from X to Y. This is consistent with (i) some houses losing value, and (ii) the average value being at some times during the period less than X.

Good to hear from you again, Gary. Let's start with some mathematical examples. The natural numbers are closed under the operation of addition. This means that the result of adding any two natural numbers is a natural number. What is a natural number? On one understanding of the term, the naturals are the positive integers, the counting numbers, the members of the set {1, 2, 3, 4, 5, . . .}. On a second understanding, the naturals are the positive integers and zero: {0, 1, 2, 3, 4 . . .}. Either way, it is easy to see that adding any two elements of either set yields an element of the same set. It is also easy to see that the naturals are also closed under multiplication. But they are not closed under subtraction. If you subtract 9 from 7, the result (-2) is not an element of the set of natural numbers.

Now consider the squaring operation. The square of any real number is a real number. So the reals are closed under the operation of squaring. But the reals are not closed under the square root operation. The square root of -4 cannot be 2 since 2 squared is 4; it cannot be -2 either since -2 squared is 4. The square root of -2 is the complex number 2i where i is the square root of -1. The square roots of negative numbers are complex or imaginary; hence, the reals are not closed under the square root operation.

Generalizing, we can say that a set S is closed under a binary operation O just in case, for any elements x and y in S, xOy is an element of S. In Group Theory, a set S together with an operation O constitutes a group only if S is closed under O.

Now for some philosophical examples. Meinongian objects (M-objects) are not closed under entailment. The M-object, the yellow brick road, although yellow is not colored even though in reality nothing can be yellow without being colored. M-objects are incomplete objects. So we say that the properties of M-objects are not closed under property-entailment. Property P entails property Q iff necessarily, if anything x has P, then x has Q.

What goes for M-objects goes for intentional objects. (On my reading of Meinong, an M-object is not the same as an intentional object: there are M-objects that are not the accusatives of any actual intending.) Suppose I am gazing out my window at the purple majesty of Superstition Mountain. The intentional object of my perception has the property of being purple, but not the properties of being colored or being extended even though in reality nothing can be purple without being both colored and extended. Phenomenologically, what is before my mind is an instance of purple, but not an instance of colored item. What I see I see as purple but not as colored.

Now consider: If S knows that p, and S knows that p entails q, then S also knows that q. If you acquiesce in the bolded thesis, then you acquiesce in the closure of 'knows' under known entailment. For what you are then committing yourself to is the proposition that a proposition q entailed by a proposition p you know — assuming you know that p entails q — is a member of the set of propositions you know.

First of all, not all Christians believe the Bible is inerrant. But let that pass. The passage alluded to in the second premise is MT 6: 5-8:

When you pray, do not be like the hypocrites, who love to stand and pray in the synagogues and on street corners so that others may see them. Amen, I say to you, they have received their reward. But when you pray, go to your inner room, close the door, and pray to your Father in secret. And your Father who sees in secret will repay you.

The plain sense of the passage is that one should pray sincerely and not for show. Charitably interpreted, and taken in context, this is consistent with public prayer. Surely the message is not that one should never pray in the company of others.

Elsewhere, I have called for logico-philosophical umpires. Would that one had been on the spot to slap Dean down.

Reppert: "What this amounts to, it seems to me, is a denial of the absolute necessity of logic. If the laws of logic just tell us how truth-finding machines work, then if the world were different a truth-finding machine would work differently. [. . .] William Vallicella provides an argument against the claim that the laws of logic are empirical generalizations."

What I am concerned to show in the (slightly revised) argument below is that logic cannot consist of propositions that merely describe the way people reason as a matter of contingent fact. Thus, contra Carrier, they are not like laws that describe the physical universe or some part thereof. Their content is normative, thus prescriptive/proscriptive, not descriptive.

'LNC' below stands for Law of Non-Contradiction. In terms of propositional logic, LNC is the principle that no proposition and its negation are both true at the same time and in the same respect and in the same sense. In symbols: ~(p & ~p). It is important to realize that my argument neither assumes the truth of LNC, nor attempts to prove its truth. The point of the argument is that whatever system of logic one adopts, even a dialetheist system that admits the truth of some contradictions, the principles that make up this logic cannot be empirical generalizations. Now for the argument:

1. The laws of logic are empirical generalizations. (Assumption for reductio).
2. Empirical generalizations, if true, are merely contingently true. (By definition of ‘empirical generalization’: empirical generalizations record what happens to be the case, but might not have been the case.)
3. The laws of logic, if true, are merely contingently true. (From 1 and 2)
4. If proposition p is contingently true, then it is possible that p be false. (True by definition of 'contingently true.')
5. The laws of logic, if true, are possibly false. (From 3 and 4)
6. LNC, if true, is possibly false: it is true that ~(p & ~p), but there are logically possible worlds in which p & ~p is true. (From 5)
7. But (6) is absurd (self-contradictory): it amounts to saying that it is logically possible that the very criterion of logical possibility, namely LNC, be false. Therefore 1 is false, and its contradictory, the claim that the laws of logic are not empirical generalizations, is true.

The Blue Devil Knight, in the comments to Reppert's post, responds by mentioning Graham Priest and his dialetheism. This is the view that some contradictions are true. It is not to be confused with trivialism, the doctrine that all contradictions are true. Well, suppose that some contradictions are true. (Priest looks with favor on the Hegelian notion that motion is a true contradiction: the response to Zeno's Arrow Paradox is that said arrow is both moving and not moving at the same time. I'm not endorsing this!) If some contradictions are true, then LNC, which implies that all contradictions are false, is itself false. This implies that LNC cannot be the criterion of logical possibility, and that some dialetheist principle or set of principles is.

Whether one is an Aristotelian or a dialetheist, something like the above argument goes through. Logical truths are not contingent. If they were, their falsity would be a logical possibility. But it can't be since they set the standard of logical possibility. They don't depend on the physical facts being one way rather than another. They don't describe how people think; they prescribe how they ought to think if they are to arrive at truth.

The exclusive meaning, corresponding to the Latin aut, is exemplified by the standard menu inscription, ‘soup or salad,’ which means one or the other, but not both. Logicians view the inclusive ‘or’ as a basic propositional connective. Thus our first example would be symbolized by p v q, where p is the proposition expressed by ‘He is morally obtuse’; q the proposition expressed by ‘He is intellectually obtuse’; with ‘v’ -- in honor of vel -- standing for inclusive disjunction. Exclusive ‘or’ can now be defined as follows: p aut q =df p v q & ~(p & q), where the tilde and the ampersand, both propositional connectives, represent negation and conjunction respectively.

How is ‘or’ functioning in this sentence: ‘Philosophers of a realist bent posit facts or states of affairs as truth-makers.’ Clearly, no disjunction is being conveyed. The idea is that facts just are states of affairs, or that ‘fact’ and ‘state of affairs’ are being used interchangeably. Indeed, the preceding sentence exemplifies a use of ‘or’ that does not express a disjunction. Hence, ‘or’ of identity. Such uses of ‘or’ can be replaced by ‘i.e.,’ id est.

Why is this important? Well, it is important if your aim to is write and think with precision and self-awareness. If that is not your aim, then it ought to be.

1. c temporally preceded e.
-----
2. c caused e.

But what about this inference:

3. Events of type C happen immediately prior to events of type E.
-----
4. Events of type C cause events of type E.

Note that in the second inference pattern there are two ideas involved: temporal precedence and what Hume called "constant conjunction." Now although both argument-patterns are deductively invalid, the second has some inductive merit. If I know that all C-type events hitherto encountered are immediately followed by E-type events, does that not count as evidence of a causal connection? Defeasible evidence, no doubt, but evidence nonetheless.

So although the first inference-pattern is clearly fallacious, I hesitate to say that the second is. Consider now a third pattern:

5. Events of type C happen immediately prior to, and in spatiotemporal contiguity with, events of type E.
-----
4. Events of type C cause events of type E.

Someone who accepts Hume's analysis of causation in terms of temporal precedence, spatiotemporal contiguity, and constant conjuction, would have to say that the third inference-pattern is not fallacious at all, but is deductively valid. (The validity of course requires adding Hume's analysis of causation as a tacit premise.)

There are of course contexts in which we naturally say that one proposition presupposes another. Compare

1. A thing's being red presupposes that it has a color.
2. A thing's having properties presupposes that it exists.
3. A thing's existing presupposes that it has properties.
4. A person's having the right to vote presupposes that she is a citizen.

By a natural extension, properties can be said to presupposes properties:

5. Knowledge presupposes truth, but truth does not presuppose knowledge.
6. Being-known presupposes being-believed, but not vice versa.

In these cases, presupposition is a relation between propositions/properties, a relation that appears to be indistinguishable from entailment.

So my suggestion is that presupposition in the strict sense is the prerogative of persons. If this is right, then presupposition is not a strictly formal-logical notion but a transcendental-logical one, i.e., one to be investigated in a theory of the conditions of the possibility of inquiry.

Of course, it is an empirical question as to how astronomers and others use 'planet.' Suppose there are three main ways that 'planet' is used. Establishing that there are three ways, and what those three ways are, does not help us determine the number of planets. To do that, we must decide on one of the ways. One must decide on what will count as a planet. We must fix our use of 'planet' thereby making a conceptual decision. No amount of empirical inquiry will help us with this decision; indeed, empirical inquiry is possible only after various conceptual decisions have been made.

To take an example closer to the ground, consider the question of how many suicides occurred in New York City in 2001. This is of course an empirical question, one not answerable a priori. But to answer it, to count the number of suicides, one must know what counts as a suicide. Is suicide an act of self-killing? If yes, then you will get one answer. But if you define suicide as an act of intentional self-killing, then you will get a smaller number as answer. You won't count the Molotov-cocktailer who insisted on smoking while making his bomb. Now some of the 9/11 hijackers intentionally brought about their own deaths in NYC in 2001. Did they commit suicide? Do you count them when you count up the number of suicides in NYC in 2001?

My point is that the resolution of empirical questions presupposes antecedent conceptual decisions. There is a fact of the matter as to how many suicides occurred once the use of 'suicide' is fixed. But there is apparently no fact of the matter as to what ought to count as a suicide. Now let's get back to the planets and their number. One definition of 'planet' runs:

An object orbiting a star that is not a brown dwarf but bigger than an asteroid. This is somewhat ambiguous. In our solar system it is really an historical definition which boils down to "a planet is a member of the set {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto}". All the known planets orbiting other stars are large gas planets so no ambiguity yet arises there. ...

The first thing to notice about this definition is that it confuses ambiguity with vagueness. The opening sentence is not ambiguous — it does not have two or more distinct meanings — it is vague: it lacks a precise meaning. But that is not the main problem with the definition. The main problem is that this definition by enumeration makes it impossible for there to be a tenth planet. But Xena is a serious contender for planetary status. For if x is a planet iff x is a member of {Mercury, Venus, Earth, Mars, Jupiter, Uranus, Neptune, Pluto}, then there cannot be fewer than nine or more than nine planets.

What's more, the definition implies that no object distinct from each of the 'standard' planets could have been a planet. Thus it rules out the possibility that there be nine planets, except that Xena count as a planet but not Pluto. The definition implies that there must be nine planets, and that no other planets could have been those nine. But this is an empirical question that cannot be decided definitionally. That is, it is not only an empirical question as to how many planet there are, but is is also an empirical question as to which objects are those nine.

So is 2003 UB313 (Xena) the tenth planet or not? More on this later. Here is a list of definitions of 'planet.'