Thursday, March 20, 2008

Is Logic Overrated?

Good reasoning is invaluable; it's what philosophy is all about. But I'm more skeptical of formal logic's value. Logic is a powerful tool we can use to structure our reasoning and highlight entailment relations. But - like any tool - it can be misused. In particular, I worry that it's just too easy for the manipulation of symbols to substitute for careful thought.

Modal logic is especially susceptible to misapplication, in my experience. The most famous example would have to be the S5 modal argument for God's existence. But it's also not uncommon to come across blog posts where the employed logical apparatus merely serves to build in misunderstandings. The formal steps of the argument may be flawless, but that's all for naught if the entire argument is based on a mistake -- due to failing to understand precisely what all those formalisms really mean.

If one opts to engage in formalism, the hard (philosophical) work lies in interpretation, i.e. ensuring that the formalism adequately captures the intuitive ideas we started with. It's easy to neglect this point, and so produce a formal 'proof' that doesn't really speak to the issue at hand. That's the risk of formalism. The advantages are more well known: they force us to make explicit intermediate steps in our reasoning, and allow these to be easily checked for validity. Do the risks or benefits tend to be greater in practice, do you think?

My tentative (and admittedly under-informed) opinion is that logical formalisms are rarely indispensible, and often well dispensed with. As a rule of thumb, I'd be wary of using formalisms as the central means of making your case. Their best use may instead be to provide a bare-bones outline of the argument's structure, as a supplement to the argument given in prose. Formalism may prove helpful, but it shouldn't be considered sufficient, since there is more to good reasoning than logic alone.

5 comments:

  1. I largely agree with the points you raise in the post. I'd add that it's worth distinguishing, in this context, regimentation from proof. That is, let's distinguish (i) the translation of statements in a natural language into formulas in a calculus from (ii) the running of a formal proof. I think it's important for philosophers to keep in mind and be able to do the former and there's probably very little occasion to do the latter. Keeping in mind the most plausible ways of formalizing our key claims helps force us to be clear as possible. But if an argument can be straightforwardly put as a proof in a formal calculus, it's unlikely that it's philosophy anymore.

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  2. I agree that logical formalism in itself won't generally be sufficient to clarify whether an argument is any good. As you point out, there are questions of interpretation, and furthermore the 'correct' or 'best' logic for a given discourse is often as contested as the issue to which one would apply it. On the other hand, I think you perhaps underplay the significance of logic by focusing only on its applicability to philosophical methodology. The more significant dimension of such formalism is that it simply helps to make precise the logic (well, duh) of key phenomena (and one might add: the extent and limits of coherent conceptions of those phenomena).

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  3. "If one opts to engage in formalism, the hard (philosophical) work lies in interpretation, i.e. ensuring that the formalism adequately captures the intuitive ideas we started with."

    Word.

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  4. The problem of induction presents no problems to your logical mind?

    Ian Hacking, Jonathan Cohen, David Hume, and obviously Sir Karl Popper did not make an impression on you?

    Here we are again very different.

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  5. David Hume would be the first to agree that there is more to good reasoning than logic alone. He tells us that more than once. In fact, it's arguably his dominant theme (and it certainly is in his discussion of induction).

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