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14 May 2012


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Davide Panagia

This is a great post, Catarina. I'd like to know more about this idea of ‘conceptual archeology’. Have you written on this elsewhere?

Catarina Dutilh Novaes

Thanks :) I haven't written that much on the very idea of conceptual archeology, but besides the blog post I mentioned above, there's a bit about it in the conclusion of my forthcoming book:

Other than that, perhaps the best place to see how I conceive of conceptual archeology 'in action' is my paper in the current issue of Synthese, 'Reassessing logical hylomorphism...'

Aldo Antonelli

Frege, of course, was as far from a Kantian as one can be in this respect: he thought that logic was a science and that logical truths were just that -- true.

Catarina Dutilh Novaes

Well, the extent to which Frege is or is not a Kantian is a delicate issue. He does say things like "Laws of logic … are the most general laws, which prescribe universally the way in which one ought to think if one is to think at all" (Grundgesetze), and the notion of epistemic subject underlying the whole thing is very Kantian. But the fundamental disagreement is indeed with the idea that the laws of logic are contentless: for Frege, they are all the way contentful. MacFarlane discusses this difference quite extensively in his dissertation.

Mark Lance

I think it is important here to distinguish three claims, at least two of which are distinct.

One claim is the "logic as umpire" view. Now I take it no one really thinks logic is analogous to an umpire - that is agent-like. Rather, I take it the idea is that logic is the rules of the game - to state a claim as being a logical truth is to make a claim about how the language game is to be played, to propose a governing rule, or some such - where other claims are moves within the game structured by those rules.

A second claim is that those rules - defining the game as they do - are unrevisable, or more specifically not empirically revisable.

A third claim is that logical claims are contentless. (I'm going to largely ignore this one because to address it would require talking about what content is, and that's a big issue for a comment.)

A possible forth is what transcendental philosophy is, whether "the" project of transcendental philosophy requires any of the above etc. I'm going to skip this also because I'm in the midst of writing a paper on this, which I'll report on here in a month or so.

So my main claim is that the first two are independent. One can think, correctly in my view, that logic seeks to define something like rules of the game, where the possibility of meaningful claim-making at all requires us to be bound by some such rules - and at the same time claim that these are thoroughly revisable in the face of empirical challenge. This is the view of Wittgenstein in On Certainty, though he is surely not unique in claiming this. (Putnam at times makes just this claim, Sellars arguably does, Brandom might be claiming this sometimes, though he is not explicitly talking about logic, it is very much the picture in much of Haugeland's work, and there are many others.) Insofar as there is a Kantian mistake, as I see it, it is in equating these. He says, rightly I think, that constraint by logical rules is a precondition on the possibility of thought, and seems to just assume that this means that they are not revisable. But the idea that structuring rules are revisable is already familiar from, say, sports. On this picture, there is indeed an important difference between arguing about what the logical rules should be - in a given context, with a given purpose, under a given interpretation - and arguing about the facts. But this just does not imply that empirical failure - failure to successfully develop an empirically adequate theory within a given practice structured by inferential norms - cannot put rational pressure on us to revise the rules structuring that practice of empirical investigation.

Eric Winsberg

I confess that I have no idea what Williamson took himself to be arguing for. He gives two arguments in the piece, and I don't exactly see what they have in common. One is logic is revisable. Is the idea that players are revisable but umpires aren't? I can't make much sense of this. The second argument is that proofs in logic can be informative. Again, is the idea that players are informative but umpires aren't? Umpires are very informative.

I'm lost by the analogy to players and umpires, and I am lost by the idea that these two arguments are meant to show one overarching thing about logic.

Moris Stern

I don't think the following is accurate. "For Kant, general logic has no substantive content because it pertains to the forms of thought as such, with no connection to objects whatsoever (not even the a priori conditions for the relation of the understanding to objects, which is the domain of transcendental logic."

A few comments.

1) there is a relationship between logic in general and transcendental logic. It is not accidental that there are 12 categories in each. i take it that the transcendental logic is a kind of a reworking of logic in general according to the a priori forms of space, time and schematism.

2) General logic has no substantive content insofar as it does not by itself establish existence of anything. it is, however, a necessary (but not a sufficient) component of cognition that establishes existence (insofar as general logic is appropriated in the transcendental logic).


Kant tried to show that we have a role in engendering knowledge by fusing our infallible logical concepts with intuition. He was clearly right that we bring concepts to judgements; logical formalisms and their rules are great examples. But he was wrong that these concepts were unalterable, as noted in the post, and as demonstrated by myriad scientific, mathematical and logical developments thereafter.

That said, although in this sense we do have to go beyond (rather than ignoring) Kantian principles, it is not fair to say that concepts used in logic represent logic itself, and thus that logic is substantive or alterable. Formal systems of logic obey rules created by people, just like computer programs. What is not clear from logic, and yet central to it, is what it is to be consistent. Consistency does not have any rules, rules rely on consistency for their validity. What makes something logical is not the correct use of any particular set of formalisms, but an appeal to consistency, which is an inexplicable consensus; or, in the last instance an unimpeachable, neutral and indifferent umpire.


I don't endorse the logic-as-umpire view (I'm agnostic on the issue of what exactly logic is supposed to be). However, I think one of the attractions of the logic-as-umpire view is simply that it's very hard to state *what logic is* otherwise. If you think logic is just about truth-preserving inferences, well, physics and math give us truth-preserving inferences. If you think it's about *necessary* truth-preserving inferences, then logic just seems to be a very general branch of metaphysics. And if you try to characterize logic in normative terms, then that opens up a whole other can of worms (MacFarlane and Gilbert Harman talk about this).

Of course, I imagine many people might not be so unsettled by the idea that logic isn't some distinct discipline separate from metaphysics/epistemology/psychology/phil-language/etc. Russell, after all, thought that the laws of logic were just like laws of zoology, but more general.

Catarina Dutilh Novaes

Well, that's sort of what Kant says:

The laws of general logic are “without content and merely formal”; general logic “. . . abstracts from all content of knowledge . . . and . . . treats of the form of thought in general.” (KrV: A152/B19)

Of course general logic will then have this foundational role of providing necessary conditions for (contentful) thinking and perceiving, but one of the reasons why it *can* perform this role is precisely because it pertains to the pure forms of the understanding as such.

I am enough of a historian to know that matters of exegesis tend to be much more complicated than portrayed above, but certainly in terms of how Kant was *read* by those under his influence, this is the gist of the position.

Catarina Dutilh Novaes

Sure, the rules of logic are the rules of the game, but *which* game? (and btw, which *logic*?) Kant took it to be the 'game' of the very conditions of possibility for thought as such, and that is highly problematic in view of points made by e.g. Harman. My dialogical account has it that *classical* logic corresponds to the codification of the rules of certain rather specific and contrived dialogical practices, which emerged in ancient Greece. So the locus for the emergence of logic has nothing to do with mono-agent situations of thinking, as Kant seems to claim.

And I completely agree with you that the move from the claim that some rules are constitutive of certain practices to the claim that they are not revisable is doubtful to say the least. But Kant clearly seemed to think that the rules of logic are unrevisable (e.g. the famous claim that Aristotle had discovered all there was to discover about logic).

Catarina Dutilh Novaes

I don't think that Williamson thought about it in this way, but the Kantian connection also helps clarifying the connection between the two points, namely the neutrality and non-informativeness of logic. If logic deals with the laws of thought as such and thus has no content of itself, then its claims cannot be informative.

But yes, the way it's set up in Williamson's piece is not particularly illuminating.

Catarina Dutilh Novaes

In a 2009 paper on the normativity of logic (in the Proceedings of the Aristotelian Society), Hartry Field puts forward a somewhat similar argument. He takes up on Harman's claim that logic is the science of truth-preserving forms of arguments to argue that, in view of the semantic paradoxes, logic *cannot* be the science of truth-preserving arguments. From that he infers that logic thus must be about the norms of thought as such! Harman in his reply calls it a total non-sequitur, and I agree with him. It rests on the false dichotomy that either logic is about truth-preservation OR it is about the norms of thought, and since it cannot be about the former (or so he claims) then it must be about the latter. Well... (Obviously, one can simply deny the disjunction.)

Your suggestion here is quite different, I know, but I'd rather have no theory of what logic is about at all than to hold on to a theory that I have good reasons to believe is flawed. In fact, I take it that getting rid of well-entrenched (mis)conceptions is an important preliminary step towards making progress here, and that's where conceptual archeology and deconstruction can come in handy.

Lucas Thorpe

Hi Moris: Just a minor point about Kant interpretation. You claim that:
"there is a relationship between logic in general and transcendental logic. It is not accidental that there are 12 categories in each."

Kant obviously thinks that there is a relationship between general logic and transcendental logic, but it is very unclear what the relationship is. Kant claims that general logic "abstracts from all contents.. and has to do with the mere form of thinking."

It is not clear that Kant thinks that there are 12 categories general logic. Kant gives us two tables: a table of judgements and a table of categories (each consisting of four groups with three members) and there are problems with assigning the third judgment/category in group to general logic. kant notes this problem in his discussion immediately after introducing the tables. (and one can also look at his logic lectures).

One interpretation of his discussion the table of judgements (A71-2/B96-7) is that, at least for some of the groups, the third form of judgement does not, strictly speaking, belong to general logic. Thus in his distinction between singular and universal judgements he seems to suggest that this distinction properly belongs to transcendental logic not to general logic. In terms of their from [on this interpretation], "all cats are animals" and "the cat is black" are the same. (they both apply to everything that falls under the subject concept).

Thus Kant claims: "if I consider a singular judgement not only with respect to it's internal validity, but also as cognition in general, with respect to the quantity it has in comparison with other cognitions, then it is surely different from generally valid judgements and deserves a special place in a complete table of moments of thinking in general (though obviously not in that logic that is limited only to the use of judgements with respect to each other)" (A71/B96)

A similar point could be made about his distinction between affirmative, negative and infinite judgements. An infinite judgement is of the form "A is non-B". In terms of it's form (and hence presumably from the perspective of general logic) this is an affirmative judgement. It is only when we when we bring in considerations having to do with content that we can distinguish this from affirmative judgements.

It seems to me that the disjunctive form of judgement also involves considerations involving content. (Kant thinks of disjunction as involving the division of a "logical sphere" or concept into parts (this becomes clearer if one looks at what Kant has to say about disjunction in His logic lectures) - And so presupposes that some content is given.

What to make of all this is not clear. My thought is that, for Kant, transcendental logic is, in some sense, prior to general logic. But these are difficult issues in Kant scholarship.

Lucas Thorpe

I think that this becomes clearer when one considers Kant's account of the distinction between affirmative and infinite judgements:
"Likewise, in a transcendental logic infinite judgements must also be distinguished from affirmative ones, even thought in general logic they are rightly included with the latter and do not constitute a special member of the classification". (A72/B97).

This would suggest that Kant thinks that the categories of Limitation and Totality (which are 'derived' from the infinite and Singular forms of judgement)do no, strictly speaking, belong to general logic.

And I've got to run to class, so this will have to be fairly cryptic: But I think this may help explain why he thinks that arithmetic and geometry are synthetic. Arithmetic is based on totalities, and geometry involves introduces limits.

Catarina Dutilh Novaes

Thanks for the observations, Lucas! Although I keep going around making all kinds of claims concerning Kant and his influence, I am not by any stretch of the imagination sufficiently knowledgeable on Kant to be able to have a discussing on this level of detail.

Lucas Thorpe

Hi Catarina,

I've thought quite a bit about how the distinction between general logic and transcendental logic is supposed to work in Kant. And I'm not sure I've got a satisfactory interpretation. I suspect that it is probably not possible to consistently combine all of his claims about this distinction.

If you haven't read it already you might be interested in having a look at the chapter "Kant: From general to transcendental logic" by Mary Tiles in the Handbook of the History of Logic. I think you'd enjoy it. (

[But it is published by Elsevier- so personally I believe that the moral thing to do would be to find a pirated pdf].

We had an interesting couple of talks here at Bogazici a few weeks ago by Brendan Larvor. He is influenced by Lakatos's (Hegelian) philosophy of Maths. And argues that many proofs in maths (and other types of reasoning) are often essentially informal [I would prefer 'material' here] rather than 'formal'. One of the interesting points he made was about how a change in symbolism can make certain proofs possible - so for example the introduction of brackets into mathematics in the generation before Descartes allowed us to recognise certain valid inferences that we were unable to recognise prior to the introduction of this symbolism. I think that diagrams in mathematical proofs can also play such a role.

I guess my suggestion that for Kant transcendental logic is somehow prior to general logic (with general logic somehow being abstracted from transcendental logic) might push Kant into a more Hegelian direction.

One of our former students (Ozge Ekin) is finishing up her phd in Berlin on the role of diagrams in Kant's account of mathematical and logical reasoning - and I guess she might want to push Kant in this direction too. but I'd have to ask her.

Bill W

I'm not a scholar of German Idealism by any stretch of the imagination, but I'm wodering whether splitting Mark Lance's 1 and 2 is a Hegelian kind of move here. (Jon Cogburn - any thoughts?)

Catarina Dutilh Novaes

Thanks for the pointer to the Mary Tiles article, will check it out. (As it turns out, I also have a chapter in the Handbook of the History of Logic (vol. 2), my one and only publication with Elsevier...)

Yes, I share Branden Larvor's interest in notations and formalization (and absence thereof) in mathematical practice; his work is very interesting.

Lucas Thorpe

Hi Bill: I guess that splitting (1) and (2) pushes you into the direction of something like Reichenbach's relativized a priori. The vaguely Hegelian idea I was suggesting is that, for Kant, much of our 'logical' reasoning is not purely formal, and that the idea of purely formal reasoning (general logic) is parasitic upon a more fundamental type of material reasoning (transcendental logic), which presupposes some sort of determinate content.

Hi Catarina: Hope you like the Tiles article. It has some interesting stuff about Kant's relationship to the Wolffian tradition. Your student Leon might find it interesting too if he hasn't read it.


ad comment 11.): `` *classical* logic corresponds to the codification of the rules of certain rather specific and contrived dialogical practices, which emerged in ancient Greece.''
If classical logic is the logic codified by Frege, then I don't see the relation to ancient Greece; it was presumably the mathematics of the 19th century which Frege used as the model for the construction of his ideography; and that mathematics was certainly not a contrived practice.

Catarina Dutilh Novaes

Exactly, and where does 19th century mathematics come from? Ultimately, it all goes back to the development of mathematics and the deductive method in Ancient Greece. The claim is that the notion of a mathematical deductive proof is originally a dialogical notion (see e.g. R. Netz's The Shaping of Deduction).


Ok, so the claim concerns the so-called deductive or axiomatic method, and not classical logic? (For certainly these are independent notions.)


I think the reason logic (the logic of Frege hence) must be ontologically neutral is based on the crucial nature of the conditional hook, and not so much on the nature of deductive entailment itself (which of course can be expressed by the hook). Since the hook is defined negatively as true if any condition other than T-F obtains, then the hook is neutral on the specific nature of dependencies of any sort except as ascertained as false by some real means. (And of course the formalism of logic is silent on those means.) Equivalences to the hook such as "not-p or q" are not relevant here as they do not address dependencies as such--only logical equivalences truth-functionally, and by means of operations that do not (and cannot) embrace entailment. The hook alone as an operator stands for some real relationship that is not itself trivially defined (the hook is defined as not the conjunction of the true antecedent and false consequent). But its negative derivation from any real world dependencies guarantees its lack of information about any such dependencies. The hook is a minimal arbiter, but necessarily a neutral and important one as excluding what cannot (determined by some means) be the case.

Catarina Dutilh Novaes

Close enough, no? What else is classical logic if not a codification of deductive practices in mathematics? One can disagree on what counts as correct reasoning practices in mathematics (say, the intuitionist), but classical logic represents one, quite widespread, account. By insisting on the 'classical' qualification, what I have in mind is mostly to distinguish what I am talking about from the defeasible logics I was talking about last week. Ultimately, any logic that has necessary truth preservation as a *necessary* (even if not sufficient) condition for validity fits into my account.

Moris Stern

it seems that with regard to the origins of logic, at least three contenders have been brought up:

1) transcendental logic of experience(Kantian, and, perhaps, even Newtonian)
2) dialogical practices
3) mathematics

I wonder if what (by Catrina, I believe)is meant by "dialogical practices" is broad enough to cover 1) and 3)? I am as excited as I am perplexed by this term "dialogical practices." What did you have in mind,Catrina?

and what would Kant himself say, I wonder? that (general) logic is just the structure of thinking, period? and not in any way derivative from, or secondary to, any kind of specialized thinking (such as mathematics)?

Lucas Thorpe

Hi Morris,

I'm not exactly sure what is meant by a 'transcendental logic' of experience. But I take it that Kant's logic primarily has to do with the capacities that are necessary to possess conceptual capacities (and the possession of such conceptual capacities are in their turn necessary fro conceptual experience). This is, I think, the point he is making in the quote given by Catarina in her original post, when she claims that for Kant (general) logic deals with “absolutely necessary rules of thought without which there can be no employment whatsoever of the understanding.”
To possess concepts involves the capacity to make certain types of judgement. So, for example, for Kant one aspect of our mastery of concepts is our capacity to specify and this capacity involves the capacity to make disjunctive judgements (which for Kant is the capacity to 'divide the sphere of a concept' - so, for example, dividing the sphere of the concept animal into rational and non-rational animals).

So, for Kant, logic does not primarily, or at least initially, have to do with our capacity to make inferences. The transcendental analytic has to do with the understanding (concepts and judgements) not inferences. The dialectic is concerned with reason, which involves (or perhaps is) our capacity to make inferences.

Catarina: when you claim in your original post that: "Similarly, since the laws of logic determine the very conditions of thought as such, no rational debate can be had about them, as they are presupposed in any rational debate." Are you thinking of these laws of logic as laws governing inference? I think Kant does think that there are laws governing inferences - but I don't think this is his primary understanding of the nature of logic. As I take it he is far more interested in (the rules governing) concept construction. As the understanding is the faculty of concepts, then to give an account of the possibility of concepts is to give an account of the "“absolutely necessary rules of thought without which there can be no employment whatsoever of the understanding.” For some of the things you've said I think you might be reading these 'absolutely necessary rules of thought' as laws governing inferences. And, at the very least, I think that many of these 'rule' do not immediately have to do with inferences. (I guess this depends on to what degree one thinks that Kant is committed to some sort of inferential role semantics).

Moris Stern

Hi Lucas,

I take it that the categories of the transcendental logic are specifically to make possible the understanding and experience of the specific sensible nature that we encounter, live and have experiences within. It is almost as if transcendental logic is really a physics - and so involves not inferences and judgments in general, but those specifically involving the sensible nature that we live and experience in. And Kant thinks of this nature as Newtonian. From what I understand, Cassirer asked and attempted to show what transcendental analytic would look like if one uses Einsteinian physics. But I don't know Cassirer's work to really say much about it - other than to say that my hunch would be that we depart further away from experience if we think about it in Einsteinian rather than Newtonian ways (which is not to say that Einsteinian framework would not be needed in order to do natural sciences).

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