Deduction is a Mistake

Deduction is a bad idea which Popper accepted. The idea is that certain arguments are “deductively valid”. A valid argument is one such that if the premises are true then the conclusion MUST be true. Deduction thus has an anti-fallibilist character because it seeks certain knowledge about the implications of premises.

Deductivists believe that we can create valid arguments, and we can evaluate whether arguments are deductively valid or not. They believe philosophers accurately do this dozens of times in their life. Validity isn’t an impossible ideal but is within our grasp. This implies that violating fallibility can be done routinely.

Note: This is not an attack on logic in general. We can and do have conjectural knowledge of logic, the implications of premises, and so on.

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15 Responses to Deduction is a Mistake

  1. Lee Kelly says:

    Deduction “seeks certain knowledge”? People seek certainty, not deduction. If you merely intend to say that our conjecture that an argument is valid is fallible, then I agree. However, to say “deduction is a mistake” is severely misleading and unnecessary.

  2. Elliot says:

    You suggest people make conjectures that arguments are valid.

    Fallibly conjecturing a claim to infallibility (i.e. a validity claim) doesn’t make sense.

  3. Lee Kelly says:

    If an argument is valid, then it is infallibly valid, whatever that means.

    To say that an argument is valid is to say that a proposition about that argument is true, i.e. “if the premises are true, then the conclusion is true, on pain of contradiction,” or “there exists a sequence of elementary inferences from the premises to conclusion–a proof.”

    If people conjecture that propositions are true, are they fallibly conjecturing a claim to infallibility? I suppose they are, in a sense. Afterall, a true proposition is absolutely not false, by definition.

    But all this is completely besides any point I can think of worth discussing.

  4. Elliot says:

    What is the point of emphasizing the *certainty* that the conclusion follows from the premises, do you think? Is there a legitimate reason to put so much emphasis on the absolute certainty of the transfer of truth from premises to conclusion? Why not just say that, as far as you know, the conclusion follows from those premises?

  5. Lee Kelly says:

    Elliot, that’s what I do say. But if I am right, then I am not wrong: the conclusion must follow from the premises. “Certainty” is a subjective feeling, not a property of an argument.

  6. Matt says:

    “A valid argument is one such that if the premises are true then the conclusion MUST be true.”

    *Including* the premises one makes about logic and so on. I don’t see the problem. You’re arguments would be easier to understand and therefore criticize if there was direct reference to something Popper stated.

    Popper consider the law of identity a fallible proposition, at least as I understand him. I can find the specific passage if you need it, but it’s in his autobiography in the place where he discusses logic.

    So Popper regarded deductive conclusions as fallible.

    There is probably a separate but related issue here, where Popper tried to develop a specific logical language of sorts that could be used for deductive arguments. I don’t understand this well, but I think Popper regarded his endeavors in this direction as a failure he learned from. (He wanted to outline a general theory of derivation — so maybe not really a language, but I think he ultimately decided this couldn’t be done. It might even be he agrees with you in some sense. But I don’t think he would ever reject deduction.)

  7. Elliot says:

    > if I am right, then I am not wrong: the conclusion must follow from the premises.

    Are you claiming validity is nothing but an insubstantive tautology? “If X follows from Y, then X does follow from Y”? If so, why ever talk about it? (Or if you think it shouldn’t be talked about, then I’ll take that as agreement that it’s a mistake.) And why did you say “must” instead of “does”? What is to be gained with the emphasized MUST?

    > Popper regarded deductive conclusions as fallible.

    I agree with that. Do you think validity claims — claims to know what MUST follow from what — have any useful place in philosophy? If so, when and why? (And, as a side note, would you agree with me that Popper neglected to object to validity claims in general?)

  8. Matt says:

    Do you think validity claims — claims to know what MUST follow from what — have any useful place in philosophy? If so, when and why?

    I don’t understand this. It’s the “MUST know” that confuses me. So I can’t answer the question.

    I’ll note, it seems obvious to me that when we apply our theories, it’s really useful to know what they imply. So the study of deductive logic is very useful. Not only that, by studying what our theories imply we can better apply modus tollens. So deductive logic seems really helpful to me.

    would you agree with me that Popper neglected to object to validity claims in general?

    I regard that as an error. Here is something I posted to the critical rationalism forum about seven years ago:



    That’s a conjecture, right?

    Perhaps it would be better to say it like this:

    For all numbers, each number is equal to itself.
    If *a* is a number, then *a* is equal to itself.

    The reason we accept this is because there are no counter examples, isn’t that correct?

    Now, if I want to *prove* that 2=2, I can use the above conjecture.

    But then I am being circular, am I not? Perhaps not, perhaps the problem is with the word prove or proof.

    Do we ever really have *proof* in mathematics, or is a proof, just the application of well-known theories?

    That is I can use “all swans are white” to prove the swan in the next room is white. But that doesn’t really mean the swan is *really* white.

    So my real question is this: is there any difference at all between *proving* the swan in the next room is white and *proving* 2=2.

    I am wondering if the notion of proof in mathematics is just a relic of justificationism, and the term misleading …

    Does that make sense?

    For reference:

    “There is only one way to make sure of the validity of a chain of logical reasoning. This is to put it in the form in which it is most easily testable: we break it up into many small steps, each easy to check by anybody who has learn the mathematical or logical technique of transforming sentences. If after this anybody still raises doubts then we can only beg him to point out an error in the steps of the proof, or to think the matter over again. In the case of empirical sciences, the situation is much the same. Any empirical scientific statement can be presented (by describing experimental arrangements, etc.) in such a way that anyone who has learned the relevant technique can test it. If, as a result, he rejects the statement, then it will not satisfy us if he tells us all about his feelings of doubt or about his feelings of conviction as to his perceptions. What he must do is to formulate an assertion which contradicts our own, and give us his instructions for testing it. If he fails to do this we can only ask him to take another and perhaps a more careful look at our experiment, and think again.

    “An assertion which owning to its logical form is not testable can at best operate, within science, as a stimulus: it can suggest a problem. In the field of logic and mathematics, this may be exemplified by Fermat’s problem, and in the field of natural history, say, by reports about sea-serpents. In such cases science does not say that the reports are unfounded; that Fermat was in error or that all the records of observed sea-serpents are lies. Instead, it suspends judgment.”
    Logic of Scientific Discovery, 1959, page 99-100

    “The view is still widely held that in logic we have to appeal to intuition because without circularity there cannot be arguments for or against the rules of deductive logic: all arguments must presuppose logic. Admittedly, all arguments make use of logic and, if you like, “presuppose” it, though much may be said against this way of putting things. Yet it is a fact that we can establish the validity of some rules of inference without making use of them. (Footnote:  This holds even for the validity of some very simple rules, rules whose validity has been denied on intuitive grounds by some philosophers (esp. G. E. Moore);  the simplest of all these rules is: from any statement *a*, we may validly deduce *a* itself. Here the impossibility of constructing a counterexample can be shown very easily. Whether or not anybody accepts this argument is his private affair. If he does not, he is simply mistaken. See also my [1947 (a)].) To sum up, deduction or deductive validity is objective, as is objective truth. Intuition, or a feeling or belief or of compulsion, may perhaps sometimes be due to the fact that certain inferences are valid; but the validity is objective, and explicable neither in psychological nor in behaviorist nor in pragmatist terms.” From Popper’s Autobiography in the Schilpp volume, 1974, page 115.


    Answering my own question, I don’t think we have proof in the sense that we ever *prove* anything. Nor do I think Popper thought we did. But it’s still useful to work out proofs and study these issues.

  9. Elliot says:

    The way validity is taught, and understood by most philosophers, is something like this, “A valid argument is one in which the conclusion ABSOLUTELY MUST be true if the premises are true.”

    If you think this MUST is nonsense, or incomprehensible, then perhaps we agree? If the standard concept of deductive validity is confusing, that’s a serious flaw — a mistake.

    I think it’s comprehensible but mistaken (I take it to express a yearning for guarantees, certain truth, JTB, etc).

    > I am wondering if the notion of proof in mathematics is just a relic of justificationism, and the term misleading …

    FYI this topic is covered in _The Fabric of Reality_. It points out that proving is a physical process — it uses a pen, a hand, a paper, a brain to store memories, eyes, motion, etc — and so our proofs must depend on our understanding of the physical objects used. But pretty much no one even thinks our knowledge of physics is certain, so it’s kind of ridiculous they can think proofs performed with physical objects could be certain.

    Also, of course, any time you have to do thinking — e.g. to evaluate if a math proof contains an error — your thinking might contain an error, so you can’t guarantee anything.

  10. Matt D. says:

    I guess I typed in “MUST know” instead of “MUST follow”.

    I agree with you that a thoroughgoing fallibilism is best.

    I think that what generally goes under the title of deductive logic is a lot of useful stuff, that I wouldn’t want to jettison. However, I guess I’d be willing to make alterations in the way I refer to this stuff so as to make sure people understand I look at most of it in a conjectural, fallible way. How specifically I would go about this, I’m not sure without going back and reviewing the topic more.

    The point you made from _the Fabric of Reality_ is a very interesting one.

  11. Elliot says:

    > I think that what generally goes under the title of deductive logic is a lot of useful stuff

    Yes. Most of it is useful. I’m just saying it also contains a mistake.

    For phrasing, I’d generally avoid claiming arguments are “valid”, or saying anything with a MUST. I’m content to claim my arguments are non-refuted or uncriticized, that they are good explanations, that they seem to solve some problem, that they are traditional, that kind of thing, without reaching for more. And I definitely wouldn’t say (as you quoted Popper saying):

    “There is only one way to make sure of the validity of a chain of logical reasoning”

    That “making sure” doesn’t sound very fallibilist. (I doubt Popper really intended the anti-fallibilist meaning — thought it through and decided it was correct — I’d guess he just spoke unclearly and/or carelessly here.)

  12. Matt says:

    I’m preparing a *long* post on this. I don’t know when I’ll post it, but I hope soon. I just want to note, I just received _The Fabric of Reality_ and quickly skimmed it to see what David Deutsch says about logical validity. I’ll be going back to read it more closely soon, but was quite impressed with his opinion. It was the complete opposite of what I had expected, and nearly identical to Popper’s opinion — if not identical. I’ll definitely add some quotes when I post on this.

    If I am right, I have to ask why Popper was singled our for criticism here, and not David Deutsch as well, as his opinion is almost surely the same.

  13. Elliot says:

    I am talking to David about it too.

  14. Peter D Jones says:

    Valid deductive argument only guarantees that a conclusion is AS TRUE AS the premises. If your epistemology tells you that no premiss is certain, then no conclusion
    is either. Fallibilists are in no way disbarred from using logic

  15. Andrew Crawshaw says:

    Miller in His CT:R&S states the same. All deductive arguments are question begging, so yeah the conclusion cannot be false if the premises are true, but that means the conclusion is still as fallibe as the premises. furthermore Bartley talks about a conlusions being no stonger than its premises. This is becausne actually the conclusion is comtained in the premises, if it was stronger it would convey more informatiom and therefore would not be implied by the premises and the argument would not be valid. If there was not this idea that premises imply the conclusion, then modis tollens could not be exploited to transmit falsity back
    through the premises.

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