Monday, 2 May 2011

Logic and external target phenomena

It is a real pleasure to have been invited to contribute to M-phi! As some of you may know, I also contribute to the New APPS blog, where I write about all kinds of things besides logic (feminism, philosophical methodology, current affairs). But from now on, I will be cross-posting my posts on logic and the more ‘formal’ parts of philosophy here; I look forward to debates with the knowledgeable readership of this blog :)

For my first post here, I’d like to discuss the very general question of what logical theories are theories of, if anything at all, and to inquire into the appropriate terminology to be used in such contexts. In a forthcoming JPL paper (co-authored with Edgar Andrade-Lotero), we start with the following remark:

Let us start with a fairly uncontroversial observation. Generally speaking, a logical system can be viewed from (at least) two equally important but fundamentally different angles: i) it can be viewed as a pair formed by a syntax, i.e. a deductive system, and a semantics, i.e. a class of mathematical structures onto which the underlying language is interpreted; or ii) it can be viewed as a triad consisting of a syntax, a semantics and the target phenomenon that the logic is intended to capture. In the first case, both syntax and semantics are viewed as autonomous mathematical structures, not owing anything to external elements. In the second case, both syntax and semantics are accountable towards the primitive target phenomenon, which may be an informally formulated concept, or even phenomena in the ‘real world’ (e.g. logics of action, logics of social interaction, quantum logic etc.). Indeed, in the second case, both syntax and semantics seek to be a ‘model’ in some sense or another of the target phenomenon.

In Chap. 12 of Doubt Truth to be a Liar Graham Priest draws a similar distinction between pure vs. applied logics. As I read him, the distinction is not really intended to differentiate logic systems as such, but rather to outline different attitudes one can have towards a logical system. He then goes on to argue that, from the applied logic point of view, the canonical application of logic is correct reasoning. In a similar vein, Paoli (JPL, 2005) draws on Quine’s distinction between immanent and transcendent predicates, and remarks:

According to Quine, in fact, logical connectives are immanent, not transcendent. There is no pretheoretical fact of the matter a theory of logical constants must account for; rather, the vicissitudes of a connective are wholly internal to a speciﬁed formal language, to a given calculus. There is nothing, in sum, that precedes or transcends formalization, no external data to “get right”.

The issue is very general and does not concern logical connectives in particular. The key opposition is between the internal features of a logical theory, and its potential relation with external phenomena, which the logical theory purports to be a model of. Although Quine (in Philosophy of Logic) seemed to mean something slightly different with his notions of immanent and transcendent predicates, I find Paoli’s appropriation of the terminology quite fitting.

My question now is: whenever there is something transcendent that a logical system is intended to capture, what is the appropriate terminology to refer to these external phenomena? In practice, the adjectives ‘pre-theoretical’ and ‘intuitive’ are often appended to whatever target phenomenon that a given logical system is ‘about’ (the ‘being about’ part is also what needs to be explained). Presumably, the idea is that the phenomenon is conceptually prior to its systematization within the theory, and this seems right according to the 'transcendent' approach, but there are problems.

Elsewhere, I have objected to the qualification of ‘pre-theoretical’ as attributed to the notion(s) of logical consequence which is (are) presumably the target of the familiar technical accounts of logical consequence (proof-theoretic, model-theoretic). The trouble with the terminology is that it suggests a theoretically neutral target phenomenon, emerging from ‘common, everyday’ practices (terms used in Tarski’s seminal 1936 paper). In truth, the notions in question are inherently couched in robust theoretical frameworks –-T. Smiley (1988) and P. Smith (2010) make similar points; the latter specifically criticizes Field’s misconception of what is ‘squeezed’ in a squeezing argument. My general worry is that, by describing these notions as ‘pre-theoretical’ and ‘intuitive’, we seem to be suggesting that they are transparent and unproblematic, whereas what is often required to make philosophical progress in these discussions is precisely a deeper understanding of the target phenomenon as such. (Shapiro’s and Prawitz’s papers in the 2005 Handbook are good attempts in this direction.)

So ‘pre-theoretical’ and ‘intuitive’ are problematic; what could possibly be used instead? I’ve been contemplating using ‘extra-systematic’ or ‘extra-theoretic’, but they don’t sound all the way right either. In a sense, perhaps there is no terminology to be used across the board, precisely because the target phenomena of different logical systems may be widely dissimilar kinds of phenomena. Some of them may come closer to what one could describe as ‘intuitive’ (e.g. the truth predicate as used in everyday language), while others will be grounded in a considerable amount of theorizing (e.g. the validity predicate, extensively discussed in blog posts recently – my general position is that it is a conceptual mistake to treat the truth predicate and the validity predicate on a par, even though there are interesting technical connections). So for the time being, I continue to use the vague and uninformative phrase ‘target phenomenon’, which is more of a place-holder, but this may well be what is required here.

(Alternatively, one may simply maintain that there are no target phenomena that logical systems seek to capture in any interesting way, i.e. that everything in a logical system is an immanent matter. Although frustrating for a variety of reasons, this remains an available move for the theorist.)

1. Hi Catarina,

thanks for the post! Let me try a defence of both "pre-theoretical" and "intuitive".

With "pre-theoretical" one does not need to commit to a target that is neutral to ANY theory, only to the theoretical options that are contextually entertained. Unlike its "absolute" counterpart, this sort of contextual neutrality does not seem out of reach.

Likewise, "intuitive" can be safely applied to something that is PRESUMABLY shared by the parties in a given context. Of course, such a presumption holds if and until a persuasive challenge is raised, in which case it might well turn out to be unwarrented. That is, the candidate "external" constraint was not "intuitive" (or "pre-theoretical") ENOUGH.

Makes sense?

2. First off, I will just (in a rather grouchy, old-fashioned way, but that's just how I think about these things!) point out that I find it completely mysterious why any philosopher who doesn't believe in a target phenomenon of some sort would be interested in logic in the first place (I have met such people, but I don't understand them). Of course, these logics might be mathematically interesting, but that is irrelevant, one would think, to the philosophical issues.

With regard to the target phenomenon itself, I would say that in the simplest case it is just the relation of logical consequence - a relation that holds between statements (or propositions or whatever) in virtue of their logical form (whatever that is!) Calling this relation "pre-theoretic" or "intuitive" seems, to me, to be a kind of category mistake - these terms characterize, at best, our epistemic relationship to the phenomenon in question. But the relation itself is just 'out there' (or, at least, is 'out there' once the language came into existence in the first place), and we use formal logics in an attempt to provide precise mathematical models of that relation.

I suspect that many will find my view of the matter naive or controversial at best. But there it is.

3. It’s a very interesting subject. Here are my 2 cents. I consider logic as the theory of reasoning. So, the target phenomenon is first our capacity, as human beings, to conceive and deduce. This kind of enquiry can be extended to machine and computer. It can be also applied to different fields of knowledge: mathematics, physics, etc. So, the target phenomenon gives for me the definition of logic.
This position is really old fashioned and will be highly suspect, for instance from the point of view of mathematical logic. But I do not agree that the claim 'logic = syntax + semantics' is an uncontroversial observation. This stance has some drawbacks. I agree that it's actually the standard norm when you present a logical system to offer a completeness proof. But what about all the researchers who worked before this modern area (Aristotle, Leibniz, Frege, etc.)? Did they do logic or not? I imagine that technical tools and norms can also evolve. So I don’t think that the technical characterization that you give will survive very long in the future. I prefer to keep the definition of logic as the theory of reasoning, whatever the means employed to work on this subject.

Mathieu

4. Hi Vincenzo,

Thanks for the comments! Regarding pre-theoretical, I usually draw the distinction between being prior to *some* theory (existential reading) and being prior to *any* theory (universal reading). My fear is that people slip very easily between the two. The universal reading is the one I think is completely bonkers (not sure if anyone defends it in all words, but I do think it is sometimes tacitly endorsed). As for the existential reading, it only becomes informative if the theory in question is sufficiently important for there to be a real bite in the concept being prior to it. That’s why I was toying around with the idea of ‘extra-theoretical’, meaning external to the logical system itself (in the ‘transcendent’ sense).

As for ‘intuitive’, it is crucial to be clear on WHOSE intuitions we are talking about. This is of course related to the massive ongoing debate on the role of intuitions in philosophical methodology; my general take on the whole thing is that these intuitions are *precisely* what needs to be looked into, whereas a widespread position is to take them more or less at face-value: you hit rock-bottom, and no reasonable debate is possible anymore. I’ve written a couple of posts on how I see the roles of intuition in philosophy over at New APPS, I can look up the links if people are interested.

In sum, while I think your points make good sense, I’m still suspicious of these notions :)

5. Hi Roy,

Regarding your first point, I of course entirely agree :) As philosophers, what we should be interested in are the connections between logical systems and their target phenomena; otherwise we are just lousy mathematicians :D

As for your second point, I actually disagree with your view that the target phenomenon in question is the relation of logical consequence *as couched in natural languages*. More generally, I disagree with yours and Stewart’s view that formal languages are models of natural languages, but that’s going to be a long story… But let me just try to understand your position better: do you mean to say that the relation of logical consequence exists ‘out there’ in a more or less ontologically independent way (depending only on the existence of the language), or does it also have a bearing on people’s actual inferential practices? If the latter, then it becomes to some extent an empirical issue, and as it turns out, the thus far available evidence strongly suggests that people do NOT reason in ways that resemble what we view as the relation of logical consequence (as necessary truth-preservation).

But maybe we can discuss these issues in more detail at some point; I haven’t seen you in ages!

6. I can't believe you disagree with me and Stewart on modeling! Given how, over the years, Stewart and I seem to agree on less and less, I would think that the fact that it is one of the few things that we still agree on is almost incontrovertible evidence that it is true! Ha!

Seriously, though: Your brief sketch is exactly what I think. Of course, as your comments already make clear, there are important things that must be said about how to connect this essentially metaphysical issue regarding connections between statements (or propositions, or whatever) to issues regarding reasoning. And you are right - people get it wrong a LOT. But that's okay, what we are modeling is not how people actually reason, but how people ought to reason.

Things are of course more complicated than this. First, we have the fact that our best method for accumulating initial intuitions regarding logical consequence is to examine how people do reason, and this seems uncomfortable if we are eventually going to devise a view that suggests that most people are bad reasoners. In addition, we are (in my opinion) still lacking any kind of real account of the connection between the objective facts about logical connections between statement, which may be abstract, but which are decidedly non-normative; and the corresponding claims about how we ought to reason, which are decidedly normative (I feel the ghost of Moore looking down on me as I write this!) I guess this is the real issue, since as these comments make clear, I don't thing we have to choose between your "exists 'out there' in a more or less ontologically independent way" and your "have a bearing on people's actual inferential practices?' - well, at least insofar as fact about rightness and wrongness have a bearing on actual inferential practices. But I agree that if we are going to take this option, a lot more needs to be said.

One last point: It is worth emphasizing that believing that the logical consequence relation is 'out there' to be discovered and modeled does not entail that this relation is completely determinate. In fact, suspicions that it isn't determinate fuel my interest in logical pluralism.

7. Hi Mathieu/anonymous,

I never intended to claim that logic is to be *reduced* to the syntax-semantics perspective. In the context of the paper that I took the quote from, these two concepts play a crucial role in the discussion, but that is certainly not intended to imply that this is the only way to make sense of logic. Actually, if you google me, you will see that most of my published work is on medieval logic, which I don't hesitate to call *logic*, and yet obviously the narrow syntax-semantics perspective isn't in any way appropriate to describe what was going on then.

8. Roy, if your position is the 'metaphysical' one as I sketched above, then I am more sympathetic to it than I would be otherwise :) But what I find problematic in how you and Stewart present the argument is the emphasis on 'natural language' as the medium; it opens the door to all kinds of complications related to contingent properties of a given language, problems with uniqueness of meaning and interpretations etc.

But otherwise, the 'metaphysical' view is basically the view that Corcoran (your professional grand-father! there is really a lineage thing going on here...) attributes to Aristotle, and it seems to me to be a compelling way to think about the relation of logical consequence.

9. Hi Catarina, "all kinds of complications related to contingent properties of a given language".
One can argue that languages have their phonetic, syntactic, semantic, and pragmatic properties essentially. For suppose in w1, the string "wibble" refers in L to cats; suppose in w2, the string "wibble" refers in L* to potatoes. Then L is not identical to L*.
On this view, any change - even the tiniest - of syntax, reference, meaning, etc., is a change of language. So languages are individuated extremely finely.
In all likelihood, the language I "speak" is not identical to the language anyone else "speaks" - they're distinct idiolects. Similar, but not exactly identical. So, languages do not have any contingent properties.
Similarly for ambiguity, etc.. If a string "fnoffle" has, say, 7 meanings in L and 17 meanings in L*, then L and L* are distinct. Or, if languages coincide exactly in their syntax and semantics, but have some, perhaps minor, differences in their assertibility conditions, then again they're distinct.

10. Catarina,

Your comments about Corcoran are more on the mark than you think. I spent a few years writing my dissertation on this logic-as-modeling stuff with Stu, and we were both thinking of the project as one that developed some original ideas in a paper of Stu's. It was embarassingly late in the process that Stu and I re-read some of Corcoran's stuff, and we both realized that we had really gotten it from Corcoran (me, filtered through Stu, and Stu had forgotten how much of it was essentially already in Corcoran's writings on the topic).

11. Jeff and Roy (I think I can reply to you both in one goal),

Roy, I'm not really surprised to hear about Corcoran's (tacit) influence here. Stewart told me at some point that he realizes more and more how much he seems to have absorbed from Corcoran's ideas (btw, in the JPL paper I mentioned in the post we talk a lot about Corcoran and his interpretation of syllogistic -- full circle!).

But let me see if I manage to articulate more clearly the worries I have with taking logical consequence couched in natural language as the target phenomenon. I am prepared to see the point of a 'metaphysical' understanding of the relation of logical consequence, but only once the relata have a determined meaning. But as we all know, expressions in natural language need us people in many cases to acquire a determined meaning (given that they often allow for multiple readings). So they are too 'volatile' to serve as the relata here, people need to get involved for the meaning to be established, and then the relation is no longer purely metaphysical, in this sense. I am not entirely comfortable with taking propositions or other abstract entities as relata either, but at least in that case the metaphysical position would be more tenable.

I guess what's underlying my position is a staunch commitment to a 'meaning is use' approach to language. I am happy to concede that, given a certain formal system with clear formation and transformation rules a la Carnap, whether something follows from something else is a 'metaphysical' matter in that the actual deeds of agents have no role to play. But I don't see how a story like that could fly with so-called 'natural languages' (don't like the phrase either...)

12. I am not sure this is going to be helpful, but I see the situation as one analogous to the following observation about apriority. After telling students that a priori truths are truths that can be known independent of experience, some clever student will point out that this means there can't be any a priori truths, since we need to learn the meanings of the expressions involved, and this is always empirical. We then point out that what we meant was that a priori truths can be known independently of any empirical investigation other than that required to learn the meanings of the expressions involved .

Similarly, I am willing to grant much of what you say about meaning: The meanings of words are influenced by our behavior in complex ways, and thus the determination of the meaning of a particular expression will almost always involve some empirical and psychological 'stuff'. But on my view consequence is posterior to meanings - first the meanings are determined, and then once meanings are fixed, we ask about what follows from what. And my view is that this second task is independent of empirical or psychological 'stuff' (other than whatever is required to determine what the expressions mean in the first place, along similar lines to the story for apriority above). In short, meaning determination might be empirical, but once those facts are fixed, consequence isn't.

13. In that case, I understand your position much better, and if it is indeed close to Corcoran's view of Aristotle's logic, then I think there's lots to recommend about it.

But I'd still like to emphasize that the 'fixing the meaning' part is highly non-trivial. I know you are in principle not really interested in how people 'really' reason (not with respect to this issue, in any case), but in their work on reasoning, Stenning & van Lambalgen draw a distinction between reasoning TO an interpretation and reasoning FROM an interpretation: the first one would be the 'fix the meaning' part of the whole thing, and that's where a lot of the complication arises.

14. Yep. If I needed a cartoon slogan it would be: How people DO reason fixes the meaning, which then determines the facts regarding how they OUGHT to reason (which could be very different from how they do reason, in spite of the role of the one has in determining the other).

15. Trouble is, how people DO reason doesn't really fix the meaning the way you'd like it to, as there is a significant amount of interpersonal variation. Check this out:

Stenning, K., Cox, R. and Oberlander, J. (1995b). Attitudes to logical independence:
traits in quantifier interpretation. Proceedings of Seventeenth Meeting of the Cognitive
Science Society, Pittsburgh 1995. pps. 742–747.