Logic: Not Overrated March 25, 2008
Posted by Colin in Logic.trackback
Richard asks whether logic is overrated. He argues that, in fact, it often is. His point seems to be this: translating claims of philosophical interest into symbolic representation of the logical form we have been taught they have doesn’t typically suffice to settle the question whether our reasoning about them was good or not. The hard work, Richard says, lies in interpretation so logical formalism is often best dispensed with. I would be inclined to agree with Richard if I shared his narrow conception of what logic is about, but I don’t.
The conception to which I refer takes symbolic logic to be the study of good reasoning and thus insofar as reasoning is a skill, it finds the value in logic to be limited to regimenting our ‘know-how’ about which inferential moves are good ones to make. Once one has become proficient at reasoning, the tool of logic can and should be dispensed with.
This narrow conception of logic is often correlated with acceptance of classical logic as the ‘best’ or ‘correct’ logic. Now I can’t say whether Richard himself accepts the classical logic is best or correct. It is somewhat beside the point. I’m not here to pick on Richard, I want to discuss the value of logic. By my lights, the above conception of logic-as-dispensable-tool largely misses what logic is really about and conflates logic with the distinct subject of reasoning. So let me try to set the record straight.
Logic is the study of valid inference. A set of sentences constitutes an argument and various logics contend that various such arguments are the valid ones. This understanding of logic is not particularly contentious, but it raises some complicated questions. The plurality of pure symbolic logics in itself may be an uninteresting fact, but the plurality of ‘intuitive’ or ‘plausible’ logics makes for a very interesting fact. Several equally plausible logics may conflict with respect to their accounts of the very same phenomenon, say validity of arguments constituted by sentences governed by just the basic logical connectives like negation and conjunction. I take this to be the situation we face regarding classical and intuitionistic propositional logics, and propositional K3, LP, and FDE. It is unclear which, if any, of these five logics is entitled to be considered the best or correct account of validity for the target fragment of language.
There are several interesting things to note about this situation. First, the fact that these logics give equally plausible treatments of the basic logical connectives tells us something about the scope and limitations of our understanding of those connectives. Second, the difficulty of justifying a commitment to one of these logics over the others as best or correct suggests that the epistemology of logic is awfully difficult to pin down (contrary to what some philosophers suppose). Third, it raises the possibility that the truth of the matter about validity may not be simple, that validity may be something of a pluralistic phenomenon. I would contend that proficiency with logics and the subsequent awareness of the kind of complications I have been highlighting serves to make one far more flexible and open-minded as a philosopher, not to mention able and willing to explore options for solving philosophical problems that other people might ignore. For these reasons, I can’t help but think of logic as being of the utmost value.
What logic is not about is reasoning. Even more so, logic is not about rationality. There may be some important connections between logic and reasoning and rationality, but whatever those connections are need to be spelled out carefully. Furthermore, it seems to me that the connections are in some sense extrinsic to the subject matter. Logic may have something to tell us about good reasoning, but that it not its target. I for one do not know what the connections are. Here is an example of some prima facie plausible connection: one should only reason validly. But that is obviously silly. Insofar as inductive and abductive inference are perfectly good ways of reasoning, the suggested connection far overstates the case. Suppose we expand our use of ‘logic’ to include regimented formal theories of non-deductive argument forms. But then the complications I mentioned above about the plurality of logics and the epistemology of logic make it difficult to assess the claimed connection between validity and good reasoning. It just seems to me that the question of good reasoning is separate from the question of which arguments are valid, and thus is not properly in the domain of logic.
At any rate, I hope that others see things the way I do. Logic is a field of study with as rich and compelling a subject matter in its own right as any other branch of philosophy. It is, to that extent, so much more than just a dispensable tool. I also happen to believe that proficiency with logic yields a myriad of benefits. Logic is decidedly not overrated.
Suppose I agree with you about the following claims:
1) The fact that there are multiple logics that give equally plausible treatments of the basic logical connectives tells us something about the scope and limitations of our understanding of those connectives.
2)The difficulty of justifying a commitment to one of these logics over the others as best or correct suggests that the epistemology of logic is awfully difficult to pin down (contrary to what some philosophers suppose).
3) The difficulty of justifying a commitment to one of these logics over the others raises the possibility that the truth of the matter about validity may not be simple, that validity may be something of a pluralistic phenomenon.
4) Proficiency with logics and the subsequent awareness of the kind of complications I have been highlighting serves to make one far more flexible and open-minded as a philosopher, not to mention able and willing to explore options for solving philosophical problems that other people might ignore.
5) What [formal] logic is not about is reasoning. Even more so, [formal] logic is not about rationality.
It seems to me that one can accept all of this and still accept that logic is overrated. The question is: just how highly is it “rated” in the canons of contemporary philosophy? The answer would seem to be very highly indeed, and in fact too highly. One might wonder, for instance, why a course in advanced logic is usually required by grad programs in philosophy, while a course in (for instance) the thought of R.G. Collingwood is not. After all, the thought of R.G. Collingwood is just as likely (more likely, really) to make a person open-minded, and generates insights of much broader interest than the insights into the nature of logical properties and connectives that (no surprise) the study of logic generates.
Moreover, one might complain that the way students are regularly trained in logic, and trained to use logic in philosophy, undermines some of the virtues you ascribe to the study of logic. How many students are trained well enough in multiple systems of logic that they are able to see them as equally plausible, and hence to attain the open-mindedness you mention, or to consider them comparatively in any depth, thereby attaining the desired insights into the complexity of concepts like validity, logical connectives, and so on?
In my experience, this is not the norm. Instead, students learn a little logic under a very limited number of systems, and then are encouraged to use it as the preferred medium for solving philosophical problems.
To this, you might say (a la Timothy Williamson)that the obvious remedy is to require better training in Logic. Perhaps. But if logic isn’t about reasoning or rationality, why bother? If what we’re really interested in as philosophers is getting rational solutions to philosophical problems, and if logic isn’t essential to this task, then why go through the complicated process of mastering competing logical systems? Sure, the nature of validity is intrinsically interesting. But so are issues in the philosophy of mind and the philosophy of religion etc., and, on the face of it, some of these latter questions seem to be more important to human life than questions about how best to formalize certain logical notions.
I’ll close by reminding you of Bertrand Russell’s final estimate of the value of formal logic. As a young man, Russell believed that logic was the best tool available for revealing truths about the world. Under the influence of Wittgenstein, however, he came to believe that logical truths were linguistic and tautologous. (Incidentally, I see this “Wittgensteinian turn” as the crucial move in separating logic not only from reality, but also from reasoning and rationality (as you have observed)). Anyhow, Russell came to believe that logical analyses did not directly reveal truths about the world, nor even about language as such, but about what could be dropped from natural language if, for technical purposes, one wanted to create an artificial ‘language’ using as few symbols as possible. In his mind, this rendered logic trivial, for facts about minimum vocabularies had at best a limited and vague application to the central philosophical task of understanding the world. ‘Minimum vocabularies’, he observed in 1944, ‘are more instructive when they show a certain kind of term to be indispensable than when they show the opposite’ (1944a, 15). Russell illustrated this with the fact that ‘no vocabulary can dispense wholly with words that are more or less of the sort called “universals”, though ‘probably we could be content with one such word, the word ‘similar’. ‘The fact that we need the word ‘similar’’, he says, ‘indicates some fact about the world, and not only about language’, but ‘what fact it indicates about the world, I do not know’ (15). Thus, as Ray Monk observes, ‘the lesson he took from this [i.e., his Wittgensteinian conversion] is not that philosophers should now seek to analyze sentences, but rather that logic did not have, after all, the philosophical significance he had earlier attached to it’ (1996b: 56).
Aaron, thank you for your thoughtful comment. You make a good point about the status of symbolic logic within philosophy curriculums. The present situation, as you describe it, is this:
“students learn a little logic under a very limited number of systems, and then are encouraged to use it as the preferred medium for solving philosophical problems.”
I absolutely agree that this is a problem. I would probably follow Williamson in echoing a call for better training, but I concede that great philosophy has been done, and continues to be done by folks with little to no symbolic logic training. One way or the other, the present situation needs to be remedied, but I would be just as happy to see the current symbolic logic requirement eliminated as to see it expanded to include more comprehensive training. (On the other hand there is something to be said for familiarity with basic symbolic techniques to even follow most contemporary discussions in philosophy of language and metaphysics, but then one might say there is just as much a need for familiarity with the basic vocabulary of ethics to follow those contemporary debates. This is a tough issue to adjudicate.)
Insofar as my original target was to clarify what I take to be the subject matter of logic and value to the logician of the study of symbolic logic, we seem to agree with respect to the main points of my post. However, you do raise some interesting challenges.
“if logic isn’t about reasoning or rationality, why bother… what we’re really interested in as philosophers is getting rational solutions to philosophical problems”
That looks like a pretty fair criticism of symbolic logic, but I think it needs to be tempered with a metaphilosophical discussion that I am not entirely prepared to engage in. Just to gesture at what I’d like to say, I think it is extreme over-simplification to claim (as you do implicitly) that the only thing we are interested in is rational solutions to philosophical problems. Another thing I think we want are solutions which are internally coherent according to the canons of logical consequence relevant to the theoretical language in which we are working. We also want, so far as this is possible, to have an explicit awareness of the commitments, the consequences, of our theory. These, as with the rationality requirement, are not the only or most important desiderata of a philosophical theory, but they are amongst the desiderata, and we cannot begin to explore the internal coherence or the commitments of our theory without a grasp on the appropriate logic.
On Russell: “he came to believe that logical truths were linguistic and tautologous… Russell came to believe that logical analyses did not directly reveal truths about the world, nor even about language as such, but about what could be dropped from natural language if, for technical purposes, one wanted to create an artificial ‘language’ using as few symbols as possible. In his mind, this rendered logic trivial, for facts about minimum vocabularies had at best a limited and vague application to the central philosophical task of understanding the world.”
Well this is a truly enormous topic. My initial reaction is this: so what if logical truths are artefacts of language? How does that separate them from “truths about the world”? I don’t tend to place much of a significance on this distinction between linguistic and other ‘in the world’ facts. If it is true that modus ponens in valid, that seems enough to make it a fact, and thus worth investigating, no? Your concluding thoughts about the nature of symbolic logics as representative of minimal vocabularies and the value that these have to philosophy is tantalizing, but unfortunately something about which I have little to say (mostly just because I am unfamiliar with what Russell meant by this or how he arrived at this view, whether it is the right view to have, etc.)
At any rate, thanks again for a very thoughtful comment.
Hi Colin,
Thanks for these interesting remarks. Let me focus on one of them:
“I think it is extreme over-simplification to claim (as you do implicitly) that the only thing we are interested in is rational solutions to philosophical problems. Another thing I think we want are solutions which are internally coherent according to the canons of logical consequence relevant to the theoretical language in which we are working. We also want, so far as this is possible, to have an explicit awareness of the commitments, the consequences, of our theory.”
Fair enough, but I worry that some of your addenda count as desiderata only if we accept certain assumptions about the nature of logic itself, and its relation to philosophical inquiry. For example, its being desireable to have “solutions which are internally coherent according to the canons of logical consequence relevant to the theoretical language in which we are working” assumes that, in doing philosophy, we most certainly *will* be working in a theoretical language (by which I take you to mean the formal language of some system of logic), that it will have (formalizable?) canons of logical consequence. But I don’t see why this would have to be the case–I mean, maybe the later Witgenstein was correct to think that ordinary language is not reducible to any formalized language. In any case, if we can do philosophy without using a “theoretical language”, but only a natural language, then maybe some of your desiderata are superfluous.
Anyhow, these are good questions. Do you know the early Husserl’s work on formal logic and its relation to reasoning? I think you may find it interesting. One of Husserl’s English translators, Dallas Willard, has done a lot in his own writings to make Husserl’s ideas intelligible. See, for instance:
http://www.dwillard.org/articles/artview.asp?artID=35
http://www.dwillard.org/articles/artview.asp?artID=24
Best wishes,
Aaron
Well, I guess I was thinking that we work in a natural language that has, as you put it, formalizable canons of logic consequence. No doubt this is a questionable assumption, I’ve never thought too carefully about it and I wouldn’t know how to defend this assumption off the top of my head. But if our natural language is such, then it seems fair to say that internal coherence according to such canons is a desiderata for our philosophical theory. I don’t really know anything about Husserl, but I’ll be sure to check out those translations, thanks for the recommendation!