Logic and Philosophy

Martin thinks logic doesn’t seem to help philosophy much. I am a great friend of logic, and think it both a) worthy of philosophical investigation in its own right and b) a very useful tool in the furthering of other philosophical goals. Nevertheless, I am aware it has limits. I’ll try and say something about all of these things, to convince you logic iz cool.

logic_made_fun-1280x960

Logic is the study of what follows from what. Intuitively, we know what that means: for instance, John is happy follows from John is happy and John is tall, but not from John is happy or John is tall. For a remarkably large category of similar cases, people appear to agree on the nature of this “follows from” relation. But:

a) what is the “follows from” relation? The natural view that it boils down to linguistic convention, championed by Carnap & Wittgenstein, has been thoroughly demolished by Quine in the paper “truth by convention”. (In a nutshell, conventions are rules, and applying rules consistently requires logic. Thus we could not have adopted the rules of logic by convention; for we should have been without a guide for putting the conventions in place.) What then is it? And how do we all agree on such a large body of cases?

b) There are cases where “most” “ordinary” people “get it wrong”. Logicians, beginning in the mid 19th century with Boole, abstracted something like the familiar truth tables from reflecting on logical rules. These fit the vast majority of cases, and have proved very useful – the development of Boolean algebras and modern logic was instrumental in the computing revolution – but there are many logical truths and patterns of inference they to validate, such as (A -> B) v (B -> A), and from (A -> B) and ¬B infer ¬A, and from A -> B and B you may not infer A, which many “ordinary” people appear to get “wrong”. What is the status of such inferences?

c) there are also many interesting questions on the border of logic & mathematics, espeically in what’s known as “meta-logic”, that I won’t go in to here, but may in a future post.

Very well, you might say. Logic does offer a new quagmire for philosophers to get stuck in. But if logic itself has philosophical problems to be addressed, how can we hope for it to help us in other areas of philosophy?

We cannot hope that translating philosophical debates into logical languages will solve them. But *sometimes* it will serve to clarify what’s at stake. Descartes once argued:

1) I know I have a mind

2) I do not know that I have a body

—–

c) the mind is distinct from the body.

Part of the practice of logic is “schematising” arguments, abstracting from the particular content to see of a particular argument form is valid. This project can help us to assess philosophical arguments. Martin might be happy to see that Descartes’ argument for dualism is in fact invalid, as logical schematization reveals. The argument has the form:

1) I know that Fa

2) I do not know that Fb

c) ¬(a = b)

This argument is not valid: consider

1) I know Clark Kent

2) I do not know superman

c) Clark Kent is not superman

The premises of that argument can be true while the conclusion false; thus the form is not valid. This is not to say, of course, Descartes’ conclusion was wrong, only that we don’t have to worry about his particular argument for it.

Let me finish with a cautionary note on the limits of such gee-whizzery. The above example requires that we know how to “parse” Descartes’ argument correctly. For instance, we might also translate “I know that I have…” as *one* predicate, call it G. Then the formalization of Descartes’ reasoning would be:

1) Ga

2) ¬Gb

c) ¬(a = b)

which is straightforwardly *valid* by Leibniz’s law (two things are identical only if they have all the same properties, of which G is one). As is well known, there is no “algorithm” for parsing statements of ordinary language in the “correct” way, so just having tools of logic is not going to be enough to assess such arguments. Nevertheless, there is a clear and intuitive sense in which the latter parsing misses something out. If we employ logic in tandem with our intuitions, it is a useful – I would almost say necessary(1) – tool for telling good from bad arguments. To my mind, Descartes’ mistake *just was* to implicitly parse “I know that I have a…” as one predicate. Had we been there to schematize his argument, he might not have made the mistake.

However, as a further cautionary note, even if we do parse the argument “correctly” so that we include the operator “know”, we still have to know how that operator behaves. Those familiar with modal logic can observe the validity of the following argument ([]Fa reads “it is necessary that a is F”):

1) []Fa

2) ¬[]Fb

¬(a = b)

(since 2 implies there is a world at which b is not F, while 1 rules this out for a. I may be wrong about this though, as my first-order modal logic is not super refined). Thus we need to have an *antecedent* understanding of, e.g., the difference between knowledge and necessity as modal operators in order to carry out the formalization correctly in the first place. The task of working out plausible intuitions about the behaviour of operators like “S knows that p” or “it is necessary that p” or “S ought to p” is a central task of philosophical logic – it is extremely tricky, requiring good philosophy & good technical skill. At any rate, while I think logical formalizations can help to clarify lines of argument and objections to them, they will never be anything more in philosophy than a helpful device of clarification, at the end of the day, we shall always rely on our intuitive understanding of everyday concepts. We won’t be able to solve philosophical problems on computers by formalizing them or anything like that – at least not for the forseeable future!

 

(1) Arguments of continetnal philosophers are sometimes flat out contradictory or circular. I have particular arguments of Deleuze and Heidegger in mind. I’m not sure if logic can properly be used to assess such arguments, hence wavering on necessity. Maybe a future post.

 

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15 thoughts on “Logic and Philosophy

  1. I would be interested to understand more about what makes something “worthy of philosophical investigation in its own right” and things that are “useful in the furthering of other philosophical goals”. It seems widely fashionable these days for people to say that it is impossible to describe what philosophy is really ‘about’. Most academic philosophers seem to pride themselves on this inability to define their subject, in terms that are more than merely technical: i.e. say it is to acquire competence in whatever skills those people we happen to call philosophers these days happen to require of the next generation that aspires to call itself so. The discipline that is concerned more than most about finding truth seems strangely relaxed about its conventional, convenient agreement that there is no truth to be found about the very nature of the discipline that purports to be about truth. The easy way out of that is the threadbare story about the Socratic aporia. However, when we say that something is “worthy” of philosophical investigation, it seems there is more clarity about these matters than we are led to expect. When we say that something is “furthering philosophical goals”, it seems there is clarity about what exactly those goals are. This is question-begging. It is clear what makes logic worthy of psychological and linguistic investigation: linguistically formalizing the repeated experience of when we are cold we are not warm, and when John is taller than Mark, and Mark is taller than George, John is taller than George, is just a way of capturing these experiences (psychology) in symbols (linguistics), ways of articulating the (memory of) regret that we experience when we mistakenly think that turning on the cold water tap in the bath is no different from turning on the hot water tap, and the mistake of thinking that fielding George in a basketball team does not make a significant difference from fielding John (technical talents being equal for argument’s sake). Once we have clarified the above psychological and linguistic nature of logic, i.e. once science has said what there is to say about logic, what is it that about philosophy that adds extra insight into logic, insight that we cannot find when we analyse it in psychology or linguistics (that particular part of linguistics that is not about natural language but formal language (mathematics, logic, etc))?

  2. Frank,

    >> once science has said what there is to say about logic, what is it that about philosophy that adds extra insight into logic?

    good question. I think there is a continuity between philosophy and science, so the question is very hard for me to answer! But at the same time there are enquiries that are more philosophical, and enquiries that are more scientific. I think that the “more scientific” enquiries are those in which there is considerable prior agreement ( temporally prior to the enquiry itself, not in any metaphysical sense) about what exactly a conclusive result to the enquiry would be. For instance in the Michelson-Morely experiment, it was known that if certain fringe shifts were observed we could infer the existence of ether drift (and hence of ether). This is plainly scientific enquiry; we know exactly what constitutes a conclusive result. Similarly one might decide to see if some complicated sentence follows from some other complicated set of sentences, or if some logical system had the same set of consequences as some other logical system. I think these enquiries are also “more scientific”; everyone knows what would constitute a resolution to such an enquiry.

    On the other hand the question: what are the correct logical axioms and rules of inference? (which amounts to the question: what follows from what?) this question is more philosophical, for it is not generally agreed what would constitute a conclusive answer to that question. Suppose we observe lots of people and see how they do reason. Even then philosophical argument would be required to the effect that how people *do* reason is how they *ought* to reason, since many find that contentious. Lots of “ordinary” people think that if A then B and not A imply not B, but most logicians will tell you that’s false, so the descriptive account of logical consequence seems not to be right; or if it is, we need to convince the logicians otherwise. If observing people can’t tell us how we ought to reason, then what can? Michael Dummett thought that general meaning-theoretic ideas tell us what logical principles are valid; Carnap thought that it was a matter of linguistic convention; JC Beall and Greg Restall think the notion of consequence is vague and that there are many admissible consequence realtions.*

    Note that all of the above are sort of meta-answers. We want to know what follows from what, but before that we need to work out the parameters for a proper answer even are. That is, fundamental conceptual clarification is required, (and is what is offered by the above accounts) and that seems to me like a “more philosophical” task, though as I said I’m not sure there is a sharp divide between science and philosophy.

    Best,

    Chris

    *As an aside, linguists themselves will tell you very little about it indeed (in fact logical consequence is a particularly thorny issue for linguists – see e.g. problems for Montague’s semantics). You might think that this means there is nothing to be said on the matter. In which case, let the chattering classes chatter I suppose!

    • I also wanted to come back to your point about what looks like a philosophical matter, when you say: “On the other hand the question: what are the correct logical axioms and rules of inference? (which amounts to the question: what follows from what?) this question is more philosophical, for it is not generally agreed what would constitute a conclusive answer to that question. Suppose we observe lots of people and see how they do reason. Even then philosophical argument would be required to the effect that how people *do* reason is how they *ought* to reason, since many find that contentious. Lots of “ordinary” people think that if A then B and not A imply not B, but most logicians will tell you that’s false, so the descriptive account of logical consequence seems not to be right; or if it is, we need to convince the logicians otherwise. If observing people can’t tell us how we ought to reason, then what can?”

      I do not believe that question is anything other than a scientific question, i.e. something that has a clear empirical validation: (1) how people ‘do’ reason is clearly a scientific question, as we both seem to agree: this is a matter for psychology: to see what inferences people draw from premises, to study the regularities in that cognitive activity and derive a theory about it that is supported by experimental observation of people who think, infer, conclude …; (2) equally, how people ‘ought’ to think is a scientific question: it is answered by which consequences are ‘frustrated’ when people draw incorrect inferences about the world: e.g. if people pretend they understand how Newton got to articulate his theory of gravity and they drop a heavy object from a tall building and it kills a cat, and yet they are surprised by that consequence, we can safely conclude that they ought to have made a different inference, the correct one according to Newton: that if you drop a heavy object from a considerable hight on a small creature the consequences will be unsurprisingly disastrous. I.e. as far as ‘synthetic’ truths are concerned, it seems we can rely on scientific method to tell us what are sound inferences (or as you would say: what we ‘ought’ to think, which I think is a somewhat antiquated and misleading way of saying things: nobody ‘ought’ to do anything in my book, unless they choose to (see the etymological origins of that strangest of English words: ‘ought’. It means “to be under an obligation to do such”. In my book one is only ever under an obligation if one agrees to put oneself under obligation, i.e. one commits to do so). When we turn to ‘analytical’ (rather than ‘synthetic’) questions, something similar seems to be the case (this may well be what Quine meant about this unnecessary dichotomy?): when I think that 2 + 2 = 5 an I use this inference when I buy articles in the cornershop, I will quite quickly find out empirically that my inferences from things I learned at primary school (1 + 1 = 2; etc) are not as they ‘ought’ to be. So again, I do not see where you draw the line between science and philosophy. However, competence in science is not at ALL a matter of whims of fashion. How to resolve this tragic paradox?

  3. Oh yes, we have to let the chattering classes chatter – that is the true meaning of hyper-egalitarian communities: to keep the peace we had better let everyone think they have something meaningful to say. If not we risk unpopularity, that gravest of modern sins. Joking aside: when you say “we need to work out the parameters for a proper answer” I am worried that this means there are no criteria for philosophical excellence: we (each?) need to work out what we believe the criteria are? How?! When do we know the criteria are such that we can establish who is ‘competent’ in philosophy? And if we cannot, is there an actual field of competence that we can call philosophy? Or is philosophy just chattering for people who read obscure books and memorise those unusual vocabularies?

  4. >>to keep the peace we had better let everyone think they have something meaningful to say.

    I see what you mean.

    Jokes aside:

    >>I am worried that this means there are no criteria for philosophical excellence

    My claim was not intended to relate to criteria for philosophical excellence. I meant that what distinguishes more from less philosophical problems is the degree to which one knows in advance what a solution to a problem might look like – when one knows what the “parameters” for a “proper answer” are. E.g. an answer to the Goldbach conjecture will be a stepwise derivation from the axioms of Peano Arithmetic. OTOH what would an answer to the paradox of promising look like? No one really knows.

    How can we establish who is competent in philosophy?
    Rough and ready criteria subject (to my mind) to whims of fashion to some degree.
    How can we establish who the great artists are?

    C

  5. My point was that your requirement for ‘proper’ answers implies that we require a standard for propriety, i.e. for answers that are more appropriate than others, i.e. for competence and, therefore, excellence (in philosophy in this case). It seems your answer is that there aren’t any other than ‘whims of fashion’, that, as regards competence, the philosopher’s predicament is akin to that of the artist. This seems to blow up the age-old divide between continental and analytical philosophy: the inference of what you say is that we cannot say that Derrida is less competent than Dummett in their chosen subject we all call philosophy? The inference following from that is that we seem to be able to define philosophy in whatever way we want. Which brings me back to my original criticism at the start of our exchange.

  6. >> It seems your answer is that there aren’t any other than ‘whims of fashion’
    I did not say that.

    >>the inference of what you say is that A) we cannot say that Derrida is less competent than Dummett in their chosen subject we all call philosophy? The inference following from that is B) that we seem to be able to define philosophy in whatever way we want. Which brings me back to my original criticism at the start of our exchange.

    A) relies on your mistaken interpretation of me. I said:

    >> How can we establish who is competent in philosophy?
    Rough and ready criteria subject (to my mind) to whims of fashion to some degree.

    Note the first part: rough and ready criteria. These change to some extent with time but some things are presumably constant. I think clarity and meaningfulness are important constraints on good philosophy violated by certain people, Derrida included. Though for example at the moment metaphysics is somewhat in vogue, whereas just under a hundred years ago it was not.

    B) does not “follow from” A) at all, but I see what you mean. I think your mistake in B) is to assume that because art and philosophy are social phenomena, “we” can simply arbitrarily choose what’s to be good and bad. This is plainly false, as a moment’s reflection reveals. Who’s “we”?

  7. It is clear that you did not say that exactly i.e. literally, and it is also possible that my interpretation of what you said may be mistaken. However: unless you spell out what exactly you were trying to say I do not think any of us can respond in a more productive way than I did: I asked about clear criteria for judging what you call “proper”, and you respond with: “rough and ready” “whims of fashion to some degree” “they change with time” “presumably” “I think ” “in vogue” etc? As I said before, I am not sure what to make of this? So the question, unfortunately, very much remains, and I would ask you to have another go: what do any criteria look like for what you called “proper”? If, as you require and mention, clarity is one of your criteria for philosophy, then clarity about these criteria would be a first helpful step. And whether it is or is not a criterion for philosophy, it seems to me a mere requirement for academic etiquette, good manners. Anything else sounds like sophistry, rhetoric, bad philosophy. And, therefore, bad manners.

    Also, your logic is defective: I can very much assure you that B VERY much follows from A: in the absence of criteria for competence we REALLY cannot say that X is more competent than Y (in practice, of course, we can, but we would sound very silly 🙂 ). That was all I said: it is a perfectly sound inference.

    You make another incorrect inference in your last paragraph: from what I wrote it is not at all obvious (to put it politely) that I “assume that because art and philosophy are social phenomena, “we” can simply arbitrarily choose what’s to be good and bad. This is plainly false, as a moment’s reflection reveals. Who’s “we”?”.

    Please re-read what I wrote: where did I say that?! Not only did I not express that premise (about social phenomena), I CERTAINLY did not draw the inference (about good and bad), and even if I had, it would not at ALL have been “plainly false” (as you say) unless you can spell out why? I.e. we simply cannot have philosophical arguments peppered with cheap rhetorical devices like “a moment’s reflection reveals…” – not to mention blatant misrepresentation of what anyone allegedly said. And a very long “moment’s reflection” reveals something very different. We seem to have very different “moments” 🙂

    Finally, to answer your question “Who’s we?”: I hope it is clear that it is all of us (how can it be otherwise?) who are trying to make sense of the common words we all use?! Again, it addresses your requirement for clarity (for all of us!)). Just curious: why are you so puzzled? Who did you THINK it (“we”) was?!

    In short, allow me to say (1) you lack clarity (about the original question (criteria, propriety) and (2) jump to conclusions as (a) I cannot make sense of what you imply about your ‘proper’ criteria and (b) I do not believe there are any inferences in anything I said that are ‘mistaken’: if I did not understand what you were trying to convey then I would kindly ask you to have another go at articulating it more clearly: what are those criteria we should use to judge “proper” questions and answers in philosophy? And why? In other words: the job cannot be just to imply misunderstandings on other people’s accounts, the job is to be clear about your ‘positive’ statements that triggered this debate: your beliefs about what it means when you say “proper”.

  8. You write:
    >> 1) we seem to be able to define philosophy in whatever way we want.
    And asserted that this follows from
    >>2) that we cannot say that Derrida is less competent than Dummett

    First: The former does not follow from the latter. Derrida may be as competent as Dummett, but Dennett less competent than both, ‘cos philosophy is however it is.

    But now I see you meant *arbitrary* philosophers X and Y. Your claim was that we cannot say any philosophers are better than any others, so we seem to be able to define philosophy however we want. That makes more sense now. I still don’t see how it follows from what I said though. I said that we use

    >> 3) Rough and ready criteria subject (to my mind) to whims of fashion to some degree

    to assess philosophical competence. I don’t pretend to be able to be clear about what these are; I don’t know exactly what good philosophy is. Isn’t this OK? Moreover, I simply cannot see how 3) entails either 1) or 2) above. I can just about see it if I misinterpret me as saying that it is*purely* fashion, but even then I have to squint my brain a bit.

    Which brings me to the claim that it is “plainly false” that the social/conventional determination of the good and the bad in art/philosophy entails “we” make an arbitrary choice about it. It is plainly false because *nobody can choose what great art is to be*. Although it is a social, conventionally determined matter, that does not mean that anyone (or group) has a choice about it. That’s like saying that because grammar is conventional/social, “we” have a choice about when it is correct to use the present perfect.

    As for misinterpreting you, the comment about social phenomena was my attempt to make sense of 1) and 2), and in particular how you managed to infer them from what I said. If you did not mean by 1) & 2) that good and bad in philosophy was wholly arbitrary, then I am indeed sorry for having misinterpreted you.

  9. Sorry to press the point, but no, not really: in the absence of criteria (“we need to work out the criteria”) there really can be no talk about superior competence (Dummett/Derrida), i.e. the inference firmly holds. It is only when/if we finally get around to agreeing (“social”!) criteria about ‘proper’ philosophy that the inference will/would be false, but that is exactly my point: that it seems unclear (to put it mildly) that/how/when this will be the case, given your comments (“I do not pretend to be clear about this”, “Cos philosophy is however it is”. Well “how” exactly “is” philosophy? That is the question we need to settle and it is not clear from your comments that we are progressing on this, in spite of your original confident claims about “proper” and “genuine” philosophy.

    You are right in the sense that it is clear that we will always be able to find SOME criteria according to which A just happens to be more competent than B, but that is neither here nor there: it seems that those criteria are subject to considerable bias (mostly by those who happen to be salaried members of that self-defined philosophical community), i.e. ‘social’ as you say, in the worst sense of that term.

    As regards your penultimate paragraph, this is where I’m afraid you run the risk of becoming incomprehensible:

    (a) “Although it is a social, conventionally determined matter, that does not mean that anyone (or group) has a choice about it” : why not?! The very definition of “convention” is that we (the group) have a “choice” about it – if we did not it would not be a convention. Given that you admit that it IS, we clearly DO have a choice.

    (b) “It is plainly false because *nobody can choose what great art is to be*”: why not!? Great art is what we end up agreeing to call great art for whatever reasons we call it that. Language is by its very nature conventional: as long as we agree to call something great art then it IS great art: that is what it means to call something great art: agreeing to refer to it as such. You continue to fall into the platonic trap: it seems you assume there REALLY is something that is great art and some people discover what that is and some people do not. What gives you the confidence to say that? What are the criteria that allow you to say that? Where is the argument? A “Form” of Beauty that some of us can perceive if we try long enough and hard enough to perceive it? Surely, …!

    (c) “That’s like saying that because grammar is conventional/social, “we” have a choice about when it is correct to use the present perfect.” No, not really: if grammar is, as you say, (entirely) “conventional”, then it would follow that that small sub-set of grammar (logical inference rules) is conventional as well: I would be very surprised to hear a lover of logic such as you saying that. In other words: something rides on getting grammar right: mistaking the past tense for the present will result in epistemic failures, just as misunderstanding the ‘rules’ of logic will; however, disagreeing on what we call great art or philosophy does not, it merely results in social ‘failure’ when we move in the ‘wrong’ circles. I.e. your analogy does not work. And for the sake of completeness: the fact that English grammar is obviously conventionally different from the Chinese grammar does not change this argument in any way.

    Anyway: what really are those criteria for competence? Or is just it like Martin said in the Epistemology seminar: “Philosophy is whatever question anyone fancies asking and thinking about because they enjoy doing so”? It’s certainly beginning to look that way!

  10. 1) logic is not grammar (definitely)
    2) convention need not be arbitrary or dependent on choice (possibly, my own view)
    3) the desire for completely precise criteria in every domain is the short road to skepticism (definitely)

  11. With respect 2) I shouldn’t have posted it: I have arguments but no time. Perhaps I’ll return to this in a few days, or do another post on my thoughts on convention. If you would like to post anything, do get in touch. My e-mail is cscambler@gmail.com

    BW
    C

    • I do not like to repeat myself but this really is sophistry, rhetoric, bad philosophy … i.e. avoiding the core original question – so one last time, please: what do YOU think are mutually agreeable criteria for what YOU called “proper” and “genuine” philosophy? No-one asked for “completely precise” criteria (although that would be a good target objective: the fact that ‘complete precision’ may not be achievable does not mean we should not aim for it…). And it may well be the short road to scepticism but that is not really saying much: most of us are perfectly fine with scepticism if that turns out to be the right answer: Socrates was, Descartes was, Nietzsche was: why aren’t you?

      Furthermore:

      – you say: “1) logic is not grammar (definitely)”: again, one last time: WHERE is the argument?! And where did I say that ‘logic is grammar’? I said that grammar and logic are epistemically relevant, and conventional agreement about great art is not.

      – you say: “2) convention need not be arbitrary or dependent on choice (possibly, my own view)”: yes, it NEED not, but more often than not it IS: convention is different from agreement: see Galbraith who coined the (ironic) term “conventional wisdom”, i.e. wisdom that is only called wisdom because a particular social group decided that it would be convenient for them to agree to call that wisdom, i.e. to extend the semantic valence that (conventionally) attaches to he word “wisdom” to include whatever that group agreed, because they think that serves their interests.

      Allow me to reiterate one last time: what ARE those criteria for what you call “proper” and “genuine” in philosophy? If there are not any, please just say so and we can drop the debate.

  12. With respect 1, you said that logic was a “subset” of grammar, implying that grammar = logic + other things. Quine’s “truth by convention” is a good place to start if you want to see why this must be false. (Rare are there such certain philsophical conclusions! The essential core of the paper is that if logic was a part of grammar (and so conventional), we should need consistent rules for applying the conventions we had arrived at. But such consistent rules for application are essentially themselves just the rules of logic, so the view cannot get off the ground.)

    I misunderstood you with 3), I’m sorry about that. I can give what *I think* to be the criteria, but I might well be wrong. I doubt anyone could give you criteria in full confidence, as with what makes good art, literature, math, science even. But I don’t think that the fact that neither myself nor anyone else has their hand on objective criteria doesn’t mean there aren’t any. Similarly with art. No-one can give you a point-wise list of the criteria that make great art (I think). Still some art is great, and some art is better than other art. Likewise, Dummett was a much better philosopher than I ever will be, even if I can’t list the features that make it so. I’d even stretch this to scientific theories, but that’s another debate.

    Let’s indeed drop this one. I’m sorry if I was short at times.

  13. Let me be so bold as to say I think Quine is wrong (assuming he said what you mentioned above (I will read the paper on another occasion)): logic = statements that obey strict (so-called logical) rules that most grammatical statements do not (need to) obey, but they are still grammatical statements, i.e. governed by grammar. The fact that (grammatical) statements of logic have additional constraints do not preclude them from the being part of the set of all grammatical(ly correct) statements, i.e. of being a subset of grammar. And as you pointed out before: a convention (grammar, logic(al grammar)) need not be arbitrary. I rest my case.

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