Maverick Philosopher

Footnotes to Plato from the foothills of the Superstition Mountains

More on Asserting and Arguing

James Anderson comments astutely via e-mail:

I have a worry about your post Asserting and Arguing.

You seem to affirm all of the following:

(1) An assertion is a mere assertion unless argued.
(2) Mere assertions are gratuitous.
(3) The premises of arguments are assertions.
(4) One cannot argue for every premise of every argument.

This is an accurate summary except for (3).  I did not say that the premises of arguments are assertions since I allow that the premises of an argument may be unasserted propositions.  The constituent propositions of arguments considered in abstracto, as they are considered in formal logic, as opposed to arguments used in concrete dialectical situations to convince oneself or someone else of something, are typically unasserted.

Since the conclusion of an argument cannot be any stronger (or less gratuitous) than its premises, doesn't it follow from these claims that the conclusion of every argument is gratuitous?

Well, if the conclusion follows from the premises, then it has the support of those premises, and is insofar forth less gratuitous than they are.  Your point is better put by saying that, if the premises are gratuitious, then the conclusion canot be ultimately non-gratuitous, but only proximately non-gratuitous.

You distinguish between 'making' arguments and 'entertaining' arguments, but that doesn't offer a way out here because the kind of argument required in (1) and (3) is a 'made' argument rather than an 'entertained' argument.

Isn't the answer here to reject (1) and to grant that some assertions (e.g., the assertion that your cats are on the desk) can be neither mere assertions nor argued assertions?  We need a category like 'justified' assertions:  no justified assertion is a mere assertion and not every justified assertion is an argued assertion.

Professor Anderson has put his finger on a real problem with the post, and I accept his criticism.  I began the post with the sentence, "Mere assertions remain gratuitous until supported by arguments."  But that is not quite right.  I should have written:  "Mere assertions remain gratuitous until supported, either by argument, or in some other way."  Thus my assertion that two black cats are lounging on my writing table  is not a mere assertion although it is and must be unargued; it is an assertion justified by sense perception.

Expressed more clearly, the main point of the post was that ultimate justification via argument alone cannot be had.  Sooner or late one must have recourse to propositions unsupportable by argument.  Argument does not free us of the need to make assertions.  (I am assuming that there is no such thing as infinitely regressive support or circular support.  Not perfectly obvious, I grant: but very plausible.)

 

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Bill Vallicella

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6 responses to “More on Asserting and Arguing”

  1. peterlupu Avatar
    peterlupu

    Bill,
    You seem to concede the following claim:
    “Since the conclusion of an argument cannot be any stronger (or less gratuitous) than its premises,doesn’t it follow from these claims that the conclusion of every argument is gratuitous?”
    But as stated (and without suitable qualifications) this claim has obvious counterexamples. Consider the following simple pair of arguments:
    1. (Ex)(x =a) for a contingent a. Therefore, a = a.
    2. The cat is on the table. Therefore, The cat is on the table or it is not the case that the cat is on the table.
    In both cases the conclusion is a logical truth, hence necessarily true, whereas the premise is merely contingent. Therefore, in both cases the conclusion is “stronger” than the premises in both epistemic as well as logical senses.
    This is so for a simple reason. While the primary purpose of logical reasoning is to secures against losing truth (or degrees of strength), it is indifferent to gaining truth (hence, inferences which go from false premises to true once are fine from a logical point of view.)

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  2. George R. Avatar
    George R.

    Would you say that all valid philosophical arguments (not theological or merely logical arguments) are reducible to “assertions justified by sense perception?” In other words, can a unsupported assertion ever be a premise in a valid argument?

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  3. Bill Vallicella Avatar
    Bill Vallicella

    George,
    No. There are other sources of non-inferential knowledge besides sense perception, memory for example.
    >>can a unsupported assertion ever be a premise in a valid argument?<< Yes. Your two questions are not equivalent.

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  4. Lukáš Novák Avatar
    Lukáš Novák

    Dear Bill,
    it seems to me that you failed to consider several other factors.
    First, the argument by reduction to contradiction, or more broadly, by reduction to absurdity, does not have, in the relevant sense, any premises. Therefore, there is a possibility of ultimate justification through argument alone. I would even say that the most powerful and basic philosophical arguments are of this kind.
    What is, epistemically, the purpose of an argument? I would say: to make it somehow impossible, or difficult, for the addressee, to reject its conclusion without irrationality, i.e., to force him to accept the conclusion on pain of irrationality. What does it mean that an assertion is gratuitous? That it _can_ be rejected without irrationality, I would say.
    It seems to me that there several kinds of non-gratuitous assertions – as there are several kinds of epistemic justification. Beside sensory evidence, I would also name rational evidence, and reliable authority.
    And besides it not being true that every argument has some premise (reductive arguments do not), it also is not true that every premise is an assertion (whether mere or not). Nominal definitions are not assertions but they are often premises; as such, they are irrational to reject (as there is, in the relevant sense, nothing to reject) of themselves, and therefore not gratuitous.
    Best regards,
    Lukas

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  5. Bill Vallicella Avatar
    Bill Vallicella

    Thanks for the comment, Lukas. You make the very interesting claim that RAA arguments do not have premises, or maybe your claim is that they don’t have asserted premises. But you don’t provide an example. So let me provide one.
    Reductio ad Absurdum Proof of the Uniqueness of the Null Set
    0. The null set, by definition, has no members.
    1. The null set is not unique: there are two (or more) such sets. Call them N1, N2. (Assumption for reductio.)
    2. Axiom of Extensionality: Sets are the same if they share all members; sets are different if one has a member the other doesn’t have, or vice versa.
    Ergo
    3. N1 has a member that N2 doesn’t have or vice versa.
    Ergo
    4. Either N1 is null and non-null or N2 is null or non-null. Contradiction.
    Ergo
    5. (1) is false.
    Now the above is an RAA proof. But it has premises, three of them. And two of them are most definitely asserted premises, (0) and (2).
    So is this not a counterexample to your claim?
    I suppose you could insist that none of the premises are asserted. But then the conclusion would not be the negation of (1), but the following disjunctive proposition: either (0) is false or (1) is false or (2) is false.

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  6. Lukáš Novák Avatar
    Lukáš Novák

    Dear Bill,
    several points.
    1) Your example is indeed an example of what is commonly considered a RAA proof. In my opinion, however, it is, as it stands, a fusion of a pure RAA proof and of a direct proof. The conclusion of the pure RAA proof is, as you mention, “(0), (1) and (2) are not jointly true”. I claim that this conclusion does not depend, logically and epistemically, on any premises, it is not justified by the assumed truth of any premises, but merely by the evidence of contradiction being implied by its negation. The other element of the reasoning is a direct argument taking (0), (2), and the conclusion of the indirect argument as premises.
    2) Regarding (0) and (2) – you correctly suspect that I would be loath to concede that these premises express assertions. (0) is a nominal definition; so it does not assert anything, or, if it is construed as asserting something, it asserts something that is per se immediately evident. Similarly; (2), though not a definition, may at least in one interpretation be seen as part of an implicit definition of a set given by the set of ZF axioms. The interpreation, namely, according to which the axioms do not purport to veridically describe certain pre-established object called sets, but they merely state the necessary and jointly sufficient conditions of something being a set.
    3) What if you took the realist position about setsand claimed that (2) is a real, substantive assertion about sets? Then indeed the argument would contain a true direct-reasoning element, and as such it would depend on (2) as on a premise. However, in this interpretation, its conclusion would have to be understood much stronger than on the alternative (“formalist”) reading. For in this case the term “set” must be assumed to have some pre-established meaning, which is _richer_ than the meaning conveyed by the ZF axioms, whereas on the formalist interpretation the conclusion speaks of set as of whatever satisfies the ZF axioms.
    Regards,
    Lukas

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