Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

Kripke, Belief, Irrationality, and Contradiction

London Ed comments:

I also note a confusion that has been running through this discussion, about the meaning of ‘contradiction’. I do not mean to appeal to etymology or authority, but it’s important we agree on what we mean by it. On my understanding, a contradiction is not ‘the tallest girl in the class is 18’ and ‘the cleverest girl in the class is not 18’, even when the tallest girl is also the cleverest. Someone could easily believe both, without being irrational. The point of the Kripke puzzle is that Pierre seems to end up with an irrational belief. So it’s essential, as Kripke specifies, that he must correctly understand all the terms in both utterances, and that both utterances are logically contradictory, as in ‘Susan is 18’ and ‘Susan is not 18’.

Do we agree?

Well, let's see.  The Maverick method enjoins the exposure of any inconsistent polyads that may be lurking in the vicinity.  Sure enough, there is one:

An Inconsistent Triad

a. The tallest girl in the class is the cleverest girl in the class.
b. The tallest girl in the class is 18.
c. The cleverest girl in the class is not 18.

This trio is logically inconsistent in the sense that it is not logically possible that all three propositions be true.  But if we consider only the second two limbs, there is no logical inconsistency:  it is possible that (b) and (c) both be true.  And so someone, Tom for example, who believes that (b) and also believes that (c) cannot be convicted of irrationality, at least not on this score.  For all Tom knows  — assuming that he does not know that (a) — they could both be true:  it is epistemically possible that both be true.  This is the case even if in fact (a) is true.  But we can say more: it is metaphysically possible that both be true.  For (a), if true, is contingently true, which implies that it is is possible that it be false.

By contrast, if Tom entertains together, in the synthetic unity of one consciousness, the propositions expressed by 'Susan is 18 years old' and 'Susan is not 18 years old,' and if Tom is rational, then he will see that the two propositions are logical contradictories of each other, and it will not be epistemically possible for him that both be true.  If he nonetheless accepts both, then we have a good reason to convict him of being irrational, in this instance at least.

Given the truth of (a), (b) and (c) cannot both be true and cannot both be false.  This suggests  that the pair consisting of (b) and (c) is a pair of logical contradictories.  But then we would have to say that the contradictoriness of the pair rests on a contingent presupposition, namely, the truth of (a).  London Ed will presumably reject this.  I expect he would say that the logical contradictoriness of a pair of propositions cannot rest on any contingent presupposition, or on any presupposition at all.  Thus

d. Susan is 18

and

e. Susan is not 18

form a contradictory pair the contradictoriness of which rests on their internal logical form — Fa, ~Fa — and not on anything external to the propositions in question.

 So what should we say?  If Tom believes both (b) and (c), does he have contradictory beliefs?  Or not? 

The London answer is No!  The belief-contents are not formally contradictory even though, given the truth of (a), the contents are such that they cannot both be true and cannot both be false.  And because the belief-contents are not formally contradictory, the beliefs themselves — where a belief involves both an occurrent or dispositional state of a person and a belief-content towards which the person takes up a propositional attitude — are in no theoretically useful sense logically contradictory.

The Phoenix answer suggestion is that, because we are dealing with the beliefs of a concrete believer embedded in the actual world, there is sense to the notion that Tom's beliefs are contradictory in the sense that their contents are logically contradictory given the actual-world truth of (a).  After all, if Susan is the tallest and cleverest girl, and the beliefs in question are irreducibly  de re, then Tom believes, of Susan, that she is both 18 and not 18, even if Tom can gain epistemic access to her only via definition descriptions.   That belief is de re, irreducibly, is entailed  by (SUB), to which  Kripke apparently subscribes:

SUB:  Proper names are everywhere intersubstitutable salva veritate.

A Second  Question

If, at the same time,  Peter believes that Paderewski is musical and Peter believes that Paderewski is not musical, does it follow that Peter believes that (Paderewski is musical and Paderewski is not musical)?  Could this conceivably be a non sequitur? Compare the following modal principle:

MP:  If possibly p and possibly ~p, it does not follow that possibly (p & ~p).

For example, I am now seated, so it is possible that I now be seated; but it is also possible that I now  not be seated, where all three occurrences/tokens of 'now' rigidly designate the same time.  But surely it doesn't follow that it is possible that (I am now seated and I am now not seated).  Is it perhaps conceivable that

BP:  If it is believed by S that p and it is believed by S that ~p, it does not follow that it is believed by S that (p & ~p)?

Has anybody ever discussed this suggestion, even if only to dismiss it?

 Related articles

What Exactly is Kripke's Puzzle About Belief?
Ortcutt and Paderewski: Against the Millian Theory of Proper Names
Begging the Question Against Meinong
The Grand Central Conundrum in the Philosophy of Fiction
Is it a Contradiction?
Islam is not Islam!
London Ed on Reference to What is Not
Nietzsche, Truth, and Power

Posted

in

, , , ,

by

Bill Vallicella

Tags:

Comments

19 responses to “Kripke, Belief, Irrationality, and Contradiction”

  1. Ed from London Avatar
    Ed from London

    >>it will not be epistemically impossible for him that both be true.
    Do you need to shave off a ‘not’ or an ‘im’ somewhere? Or have I misunderstood?

    Reply
  2. Ed from London Avatar
    Ed from London

    Your second question is an interesting one which I discussed once with Sainsbury, in the context of utterances, rather than that-clauses. This is more clear cut, given that the logic of that-clauses is not settled. I think a Millian would agree that all of the following are impossible:
    (1) S assents to ‘Pad is bald and not bald’
    (2) S assents to ‘Pad is bald and he is not bald’
    (3) S assents to ‘Pad is bald and Pad is not bald’
    The reason is anaphora. Even for (3), the Millians see that the same thing is both explicitly affirmed and denied of the same subject, i.e. the subject is recognised and understood as the same, and thus the utterance not assented to.
    But (3) is not equivalent to
    (4) S assents to ‘Pad is bald’ and S assents to ‘Pad is not bald’
    So what precisely is the difference between (3) and (4)? I suggest something like this, uttered by S:
    (5) There is someone called Pad’ and I agree that Pad is bald. There is another person called ‘Pad’, and I agree that Pad is not bald.
    If we take ‘I agree that p’ to be equivalent to ‘I assent to ‘p’’, then (5) is a clear cut case of (4). Would you agree?

    Reply
  3. Bill Vallicella Avatar
    Bill Vallicella

    Thanks for the correction. You read it right.
    What you say in your second comment seems right.
    Do do you agree with my
    BP: If it is believed by S that p and it is believed by S that ~p, it does not follow that it is believed by S that (p & ~p)?
    And isn’t Kripke committed to something like (BP)?
    What did you think of the rest of my analysis?

    Reply
  4. Lukas Novak Avatar
    Lukas Novak

    Dear Bill,
    I think (BP) is true because believing is “hyperintensional”. Suppose a person does not have the logical connetive of conjunction in its mental repertory. Such a a person is psychologically incapapble of believing any conjunctions. But if (BP) were true, it would imply that such a person can believe at most one proposition. That seems absurd.
    And even if a person is capable of conjunctive beliefs, there seems to be no necessity that would, for any beliefs a, b, force a person believing both a and b to believe (a & b). It would imply that any person believing more than one proposition believes infinitely many propositions, which is a psychological impossibility.
    Given that it is psychological impossibility, one cannot even claim that a person can not believe (a & b) while believing both a and b, though, but only irrationally. One is not irrational by failing to do what is impossible to do for him.

    Reply
  5. Bill Vallicella Avatar
    Bill Vallicella

    Hi Lukas,
    I would like you to define ‘hyperintensional’ for me.
    I don’t understand your first paragraph, but the second para contains a good argument, or the makings of one.

    Reply
  6. Lukas Novak Avatar
    Lukas Novak

    A hyperintensional operator is such that its operands can be replaced, salva veritate, iff they have the same hyperintension.
    Hyperintension of a term is that part or aspect of its meaning in which two expressions that have the same extension in all possible worlds, i.e. the same intension, can differ.
    Or perhaps more simply: A hyperintensional operator is such that its operands cannot be replaced, salva veritate, even if they share the same intension (an operator that operates on hyperintensions).
    For example, (1+1) and (SQRT(4)) differ merely hyperintensionally.
    I meant that although two separate propositions are intensionally equivalent to a conjunction of them, they are not hyperintensionally equivalent. Therefore, since (de dicto) beliefs relate to hyperintensions, it is possible for the conjunction not to be an object of belief even if each of its conjuncts is.
    ***
    BTW, I would like to hear your arguments in favour of the Millian theory of proper names. I agree that the arguments presented above effectively disprove it. It seems to me that the theory must fail as soon as its psychological implications are considered (those about beliefs are among them). In a judgement “Peter is wise” Peter must be somehow represented, not just linguistically but mentally. And since we are not omniscient, Peter-qua-represented will not equal Petr-qua-real (“warts and all”). In other words, there will have to be some conceptual content corresponding to “Peter” through which Peter will be represented; i.e. a “Sinn” or imperfect “Art der Gegebenheit” of Peter.
    This seems to me completely unrelated to the question of rigidity/non-rigidity of reference. It seems to me that all Kripke &comp. can (and do) prove is that names (normally) refer rigidly. But in my opinion rigidity/non-rigidity is not part of the semantics of an expression (Kripke’s tacit assumption), but a way of its usage. Undeniably, you can use even a description rigidly, if you choose so. (“The president of the U.S. might very well not be a president” is perfectly meaningful and true, if “the president of the U.S.” is meant to rigidly refer to whomever satisfies the description in the actual world.).
    But IMHO there is something true in the “mere label” intuition about names. I take names to have a dual role: First, they serve as imagined labels we use to mark individuals in order to be able to uniquely identify them. So far Kripke’s intuitions are correct. But this role of a name is non-linguistic; in this role the name is not a sign but an imagined quasi-property of the individual. We could as well use real labels, real or imagined colours, numbers etc.
    Once an individual is named (“baptized”), we always have a descriptive content the one who (in this context) bears the name so-and-so uniquely representing that individual at our disposal. If we marked our individuals by means of colours, we would need a special linguistic item to represent such a description: the linguistic phrase “the one who (in this context) is marked by the colour so-and-so”. But since we used words and not colours as our labels, we can use these very words as shorthands for such descriptions – and this is (usually) the other, properly linguistic role of proper names. Just like all other categorematic (extra-logical) terms, names in this role stand for a mental content, a “something-qua-mentally-represented” and in virtue of this can linguistically refer to the named individual. Note that this relation of “referring to” is distinct from (and conditioned by) the extra-linguistic relation of “naming” or “being a label of”. This is why the theory is not circular (pace Kripke).
    Many names have this “minimal” meaning; but there are others, like “Jack the Ripper”, that are shorthands for more substantial descriptions. But this does not preclude their capability to be used to refer rigidly – which, I would say, is the same thing as to supposit de re (in modal and other (hyper)intensional contexts). You need not expel the “reference-fixing descritpion” from the sphere of meaning in order to save the possibiliy of rigid reference.

    Reply
  7. Ed from London Avatar
    Ed from London

    >>Do do you agree with my [BP: If it is believed by S that p and it is believed by S that ~p, it does not follow that it is believed by S that (p & ~p)?] And isn’t Kripke committed to something like (BP)?
    I am uncertain about how to deal with belief+ that clauses, rather than assent+utterances. One problem is that belief is dispositional. Sartre’s analysis of bad faith suggests (correct me if I am wrong, not an expert on Sartre) that a person can have conflicting beliefs.
    What we are missing is a suitable verb for the judgment that occurs precisely as a result of assenting to an utterance, precisely at the time of utterance (or time of writing, if a written statement). Before Russell, philosophers used the term ‘judgment’, but this refers to a mental act on its own, with or without the spoken or written sentence. We also have ‘agrees that’, but this refers to an outward act of agreement. If we ask Pierre if Pad is musical, and he replies ‘yes’, the assent is in the reply, not in the question.
    Is judging that p and judging that not-p equivalent to judging that p and not p? Not sure. You refer to ‘if Tom entertains together, in the synthetic unity of one consciousness’, which is sort of getting there, but ‘synthetic unity of one consciousness’ sounds Teo
    As for what Kripke is committed to, who can say.
    >> What did you think of the rest of my analysis?
    Which analysis? You say “I expect he [Londiniensis] would say that the logical contradictoriness of a pair of propositions cannot rest on any contingent presupposition’. Yes, well judged. You say ‘That belief is de re, irreducibly, is entailed by (SUB), to which Kripke apparently subscribes’. Again, the principle that proper names are everywhere intersubstitutable salva veritate, is different from MILL, namely that co-referential proper names have the same meaning or sense. It is MILL with which Kripke is concerned. Indeed he says right at the beginning of the famous paper that it is about de dicto and not de re. The confusion about what his paper is about dogged our earlier discussion, as you realise.

    Reply
  8. Ed from London Avatar
    Ed from London

    Lukas>>in this role the name is not a sign but an imagined quasi-property of the individual.
    I have been thinking about titles, e.g. The 7th Earl of Lucan. it does not signify any real attribute of the individual, but is merely a way of uniquely identifying him.

    Reply
  9. Ed from London Avatar
    Ed from London

    I meant to say ‘synthetic unity of one consciousness’ sounds Teutonic. I am increasingly inclined to vote for Brexit.

    Reply
  10. Bill Vallicella Avatar
    Bill Vallicella

    You should vote for Brexit. And the phrase is indeed Teutonic, from Kant. I figured it would annoy you. British philosophy can be insular like the isles themselves.
    You are quite right to bring up the bit about beliefs being dispositional. Do you believe that coyotes communicate by cell phone? Of course not, even though I’d wager you have never considered this question. You disbeleive it. But not occurrently. Do you believe that 4789 + 1 – 3 = 4787? Of course you do, though you have never thought of this until now.
    You have beliefs and disbeliefs that are merely dispositional, as well as beliefs and disbeliefs that are occurrent.
    Surely not all belief is dispositional as you seem to think. There are occurrent (actual) believings that such-and-such.
    As I was reading Kripke, I thought that perhaps one could have contradictory beliefs if one or both of the beliefs is dispositional. But Kripke does not bring up the disposition-occurrent contrast.
    If Peter believes occurrently and de dicto that Pad is musical and Peter believes occurrently and de dicto that Pad is not musical, and Peter is rational, then ‘Pad’ refers to two different men.
    So what the hell is Kripke’s puzzle supposed to be about?
    What is your final assessment of Kripke’s paper?

    Reply
  11. London Ed Avatar
    London Ed

    >>What is your final assessment of Kripke’s paper?
    Goodness.
    First, it’s a seminal paper and its influence on modern theories of reference has been immense. It’s a persuasive argument for direct reference, as I have said.
    Second, the fundamental assumption underlying it, namely that a proper name can be learned twice, is glossed over and he gives no persuasive argument for it.
    Third, it was an influence (a negative influence) on my own apparently incomprehensible theory of reference. We should discuss later.
    >>And the phrase is indeed Teutonic, from Kant. I figured it would annoy you.
    That’s mean.

    Reply
  12. Bill Vallicella Avatar
    Bill Vallicella

    I guess I don’t see how the paper in question is an argument for direct reference.

    Reply
  13. David Brightly Avatar
    David Brightly

    This is by way of a follow up to my comment on the What exactly is Kripke’s puzzle about belief thread. We are supposing that Tom believes (b) and (c). We believe that at least one of (b) and (c) is false but that (a) is true, and the girl in question has the name ‘Susan’. Bill says,

    After all, if Susan is the tallest and cleverest girl, and the beliefs in question are irreducibly de re, then Tom believes, of Susan, that she is both 18 and not 18…

    This misrepresents Tom’s belief. He knows nothing of Susan. He believes the tallest girl and the cleverest girl are distinct, believing one thing of one and the opposite thing of the other. This ‘de re belief’ attributed to Tom is a curious amalgam of Tom’s belief and our belief that ends up representing nobody’s belief! How on earth did we get led so badly astray? The answer, I suspect, has to do with the existential commitments underlying Tom’s beliefs and our beliefs. Tom must believe in at least two girls. We can get by with just one. But we are trying to represent Tom’s beliefs in terms of our own existential commitments. The two are incompatible.

    Reply
  14. London Ed Avatar
    London Ed

    >>I guess I don’t see how the paper in question is an argument for direct reference.
    It’s a negative argument, a reply to the SUB reductio. The reductio is that by assuming SUB, we reach the conclusion that people have contradictory beliefs. Therefore we must reject the conclusion, and infer that SUB is false. Kripke’s point is that SUB is not required.

    I shall present—and this will form the core of the present paper—an argument for a paradox about names in belief contexts that invokes no principle of substitutivity […] such a principle, when combined with our normal disquotational judgments of belief, leads to straightforward absurdities. But we will see that the ‘same’ absurdities can be derived by replacing the interchangeability principle by our normal practices of translation and disquotation, or even by disquotation alone.

    Reply
  15. London Ed Avatar
    London Ed

    I broadly agree with David. Pierre believes that the contradictory predicates are satisfied by different people. But that’s the puzzle. The normal usage of a proper name is to determine what I call ‘sameness of subject’. Two predicates have the same subject if it is signified that they are satisfied by a single individual, and it is the purpose of a proper name to signify precisely this, and nothing else, I believe. Kripke’s puzzle is that this doesn’t always happen.

    Reply
  16. Bill Vallicella Avatar
    Bill Vallicella

    Hi David,
    Very good criticism. Let’s see if I can answer it. Yes, Tom knows nothing of Susan. And if Tom is rational, then he believes de dicto that the tallest girl and the cleverest girl are distinct. This assumes that rationality is governed by the law of non-contradiction. This assumption is not now being questioned.
    But unbeknownst to Tom there is only one girl who is both the tallest and the cleverest, Susan. Given that Tom believes both (b) and (c), and given that there is irreducibly de re belief, Tom believes of some girl that she is 18 and he believes of some girl that she is not 18. Given that these are the same girl, Tom believes of one and the same girl that she is both 18 and not 18.
    But this is absurd. It is however a consequence of (SUB), which is a consequence of (MILL).
    So I reject (SUB) and I reject (MILL) and I reject irreducibly de re belief.

    Reply
  17. London Ed Avatar
    London Ed

    >>I reject (SUB) and I reject (MILL) and I reject irreducibly de re belief.
    But do you agree with BACKSUB, namely terms with the same back-reference are substitutable salva veritate? Surely, whoever assents to ‘Pad is musical and he is not a politician’ assents also to ‘Pad is musical and Pad is not a politician’. Or do you disagree that there is back-reference in the second case?

    Reply
  18. Bill Vallicella Avatar
    Bill Vallicella

    First answer this question:
    In the sentence, ‘Pad is musical and he is not a politician’ does ‘he’ back-refer to Pad or to ‘Pad’?

    Reply
  19. London Ed Avatar
    London Ed

    In the first case, ‘He’ back-refers ‘Pad’
    In the second, ‘Pad’ back-refers to ‘Pad’.

    Reply

Leave a Reply

Your email address will not be published. Required fields are marked *