THE LIMITS OF SENSE AND REASON: A Line-By-Line Critical Commentary on Kant’s “Critique of Pure Reason,” #12–The B Preface & Kant’s Notorious Remarks About Logic.

By Robert Hanna

***

[I] was then making plans for a work that might perhaps have the title, “The Limits of Sense and Reason.” I planned to have it consist of two parts, a theoretical and a practical. The first part would have two sections, (1) general phenomenology and (2) metaphysics, but this only with regard to its method. (Letter to Marcus Herz, 21 February 1772 [C 10: 129])

***

***

Previous Installments:

#1: Introduction to The Limits of Sense and Reason

#2: Bii/GW91 The Motto

#3: Aiii/Biii/GW93–97 The Dedication

#4: Avii-ix/GW99 Preface to the First (A) Edition.

#5: Axi note/GW100–101 Preface to the First (A) Edition

#6: Axi note/GW100–101 Preface to the First (A) Edition

#7: Axii-xiv/GW101–102 Preface to the First (A) Edition

#8: Axv-xvi/GW102–103 Preface to the First (A) Edition

#9: Axvi-xvii/GW103 Preface to the First (A) Edition

#10: Axvii-xx/GW103–104 Preface to the First (A) Edition

#11: Axxi-xxii/GW104–105 Preface to the First (A) Edition

A Note on References to Kant’s Works

***

The first five installments in this series followed the 2019–2020 version of THE LIMITS OF SENSE AND REASON, aka LSR.

Starting with installment #6, subsequent installments follow the revised and updated 2021 version of LSR.

In any case, you can read or download a .pdf of the complete text of the 2021 version of LSR HERE.

Because LSR is an ongoing and indeed infinite task, revised and updated .pdfs of the complete text will be uploaded to that URL on a regular basis.

***

CPR TEXT Bviii-ix/GW106–107 Preface to the Second (B) Edition

Bvii Preface to the second editiona

Whether or not the treatment of the cognitions belonging to the concern of reason travels the secure course of a science is something which can soon be judged by its success. If after many preliminaries and preparations are made, a science gets stuck as soon as it approaches its end, or if in order to reach this end it must often go back and set out on a new path; or likewise if it proves impossible for the different co-workers to achieve unanimity as to the way in which they should pursueb their common aim; then we may be sure that such a study is merely groping about, that it is still far from having entered upon the secure course of a science; and it is already a service to reason if we can possibly find that path for it, even ifwe have to give up as futile much of what was included in the end previously formed without deliberation.

Bviii That from the earliest times logic has traveled this secure course can be seen from the fact that since the time of Aristotle it has not had to go a single step backwards, unless we count the abolition of a few dispensable subtleties or the more distinct determination of its presentation, which improvements belong more to the elegance than to the security of that science. What is further remarkable about logic is that until now it has also been unable to take a single step forward, and therefore seems to all appearance to be finished and complete. For if some modems have thought to enlarge it by interpolating psychological chapters about our different cognitive powers (about imagination, wit), or metaphysical chapters about the origin of cognition or the different kinds of certainty in accordance with the diversity of objectsc (about idealism, skepticism, etc.), or anthropological chapters about our prejudice (about their causes and remedies), then this proceeds only from their ignorance of the peculiar nature of this science. It is not an improvement but a deformation of the sciences when their boundaries are allowed to run over into one another; the boundaries of logic, however, are determined quite precisely by the fact that logic is the science Bix that exhaustively presents and strictly proves nothing but the formal

a This new preface, so entitled, replaces the preface from the first edition.

b Kant’s text reads “erfolgt”(result or ensue), which does not make sense here because it is an intransitive verb; we follow Grillo in reading verfolgt.

c Objecte

rules of all thinking (whether this thinking be empirical or a priori, whatever origin or objecta it may have, and whatever contingent or natural obstacles it may meet with in our minds).

a Object

***

COMMENTARY

There’s an important difference between the A and B Prefaces.

The A Preface focused on the historical dialectic between classical metaphysics and especially classical Rationalist metaphysics, and classical Empiricist skepticism, in the 17th and 18th centuries.

But by contrast, the B Preface’s treatment of metaphysics zeroes in on what Kant takes to be three authentic sciences, moving smoothly along in their secure paths, by way of a series of illuminating comparisons and contrasts with metaphysics: logic, mathematics, and natural science — or more precisely, physics.

I’ll come back again to this crucial point shortly.

Reason always concerns itself with cognitions or Erkenntnisse, i.e., conscious objective mental representations or Vorstellungen — and for a hierarchically-ordered table of the different types of Vorstellungen, see the famous or infamous Stufenleiter (which means, roughly: “progression”) text at CPR A320/B376–377 — but not every set of rational cognitions counts as an authentic science.

What is the criterion of authentic sciencehood?

Kant formulates the criterion here in explicitly normative and teleological terms, by providing some negative success-conditions for achieving “the secure path of science” (den sich Gang einer Wissenschaft).

More generally, every aspirational science has both a specific “end” or telos that individuates it and distinguishes it from other sciences, and also a general end or telos aimed at entering the secure path of science, which it shares with all other sciences.

But if an aspirational science

either (i) “gets stuck” before it reaches these ends, presumably by either running into contradictions, or by running out of new cognitions,

or (ii) if it can reach its ends only by “often go[ing] back and set[ting] out on a new path,” presumably by revising its basic principles or by revising its epistemic methods,

or (iii) if its various investigators never form a consensus as to basic principles or epistemic methods, then it’s clear

(iv) that this is a merely aspirational or failed science.

And then, by fully recognizing and frankly accepting the fact of cognitive failure — another example of Socratic self-knowledge — we can begin to make rational progress by re-orienting and indeed revolutionizing that science, which in turn means discarding much of what that science has previously taken as indefeasible knowledge, and at the same time projecting new light onto other claims that science has previously dogmatically rejected or overlooked.

Of course, Kant has the aspirational science of metaphysics primarily in mind here.

As I mentioned above, there’s an important difference between the A and B Prefaces: whereas the A Preface focused on the historical dialectic in the 17th and 18th centuries between classical metaphysics and especially classical Rationalist metaphysics, and classical Empiricist skepticism, by contrast, the B Preface focuses on what Kant takes to be three authentic sciences already chugging along their secure paths — logic, mathematics, and natural science/physics — and then critically compares and contrasts these with metaphysics.

Significantly, in view of what we already know about the The Pure General Logic Assumption — Kant starts with logic, now explicitly designated as the original or Ur-science in relation to all the other authentic sciences.

In the last sentence of the paragraph running from Bviii to Bix, and in the next paragraph at Bix, he says that

[t]he boundaries of logic are determined quite precisely by the fact that logic is the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking (whether this thinking be empirical or a priori, whatever origin or object it may have, and whatever contingent or natural obstacles it may meet with in our minds). For the advantage that has made it so successful logic has solely its own limitation to think, since it is thereby justified in abstracting — is indeed obliged to abstract — from all objects of cognition and all distinctions between them; and in logic , therefore, the understanding has to do with nothing further than itself and its own form. (CPR Bviii-ix)

’Tis a consummation devoutly to be wished, that all readers of these two paragraphs had read those two sentences first, before reading these two sentences at the beginning of the paragraph starting at Bviii:

That from the earliest times logic has traveled this secure path [of authentic science — R.H.] can be seen from the fact that since the time of Aristotle it has not had to go a single step backwards, unless we count the abolition of a few dispensable subtleties or the more distinct determination of its presentation, which improvements belong more to the elegance than to the security of that science. What is further remarkable about logic is that until now it has also been unable to take a single step forward, and is therefore seems to all appearance to be finished and complete. (CPR Bviii, boldfacing in the original)

The two sentences at Bviii-ix tell us that by logic Kant intends, as I spelled it out already in my comments on Axii-iv, to be talking about the categorically normative, strictly universal, law-governed a priori science of the laws of thought — the complete set of rules or principles specifying how rational human animals ought to think, in order to conform to the highest or supreme standards of human reason itself, and even more specifically, to be talking about pure general logic, which, as I also spelled it out in my comments on Axii-xiv, is the absolutely non-empirical, categorically normative, strictly universal, law-governed a priori science of the laws of thought, whether analytic or dialectical, whose consistency/inconsistency, conceptual necessary truth/falsity or illusion, and validity/fallacy does not metaphysically depend on, and therefore is not necessarily determined by, the comprehensions of objects or states of affairs to which logic applies.

Moreover, via The Pure General Logic Assumption, Kant also holds the thesis that logic in this sense lays bare the complete formal structure of human theoretical rationality itself, and is both explanatorily and justificationally presupposed by every other science, including metaphysics, mathematics, natural science or physics, and every other kind of logic.

The two-part thesis, namely,

(i) that logic is the categorically normative science of the laws of thought, and more specifically

(ii) that pure general logic lays bare the complete formal structure of human theoretical rationality itself, and is both explanatorily and justificationally presupposed by every other science, including metaphysics, mathematics, natural science or physics, and every other kind of logic,

is at the very least a deeply important and substantive claim, whether or not it’s true.

Now back to the two notorious sentences at Bviii, and the sentence immediately following those.

There Kant says:

(i) that pure general logic is the original or Ur-science in relation to all the other authentic sciences,

(ii) that pure general logic has not advanced in any of its basics since Aristotle, although later logicians have added various non-essential psychological, metaphysical, or anthropological details to its corpus of truths, and

(iii) that the very fact that pure general logic since Aristotle has not advanced in any of its basics entails that pure general logic “seems to all appearance to be finished and complete.”

From these three claims it’s all-too-easy to conclude that Kant is saying that pure general logic, the original or Ur-science in relation to all the other authentic sciences,is nothing but, and never will be anything but, Aristotle’s logic or post-Aristotelian Scholastic syllogistic logic.

Yet from a 20th and 21st century standpoint, and indeed even from the standpoint of mid-to-late 19th century mathematical and symbolic logic, as Boole, Peano, and Frege understood it, this is outrageously false.

And certainly, to the extent that Kant does not carefully qualify what he’s saying here, he should be criticized for giving the strong impression that he’s asserting precisely that outrageously false claim.

There is much to be said about this issue, and much that I will say in later parts of LSR, especially in my remarks about the Introduction to the Transcendental Analytic and book I, chapter I of the Analytic (CPR A50–83/B74–116), on book II, chapter II, section I the Analytic (CPR A148–153/B187–193), and on the Introduction to the Transcendental Dialectic (CPR A293–309/B349–366).

For our present purposes, however, two basic points should be made.

First, close readings of Kant’s pre-Critical writings on logic, his logic lectures, and the Jäsche Logic in particular, when taken together with what he says about logic in the first Critique, show that pure general logic in Kant’s sense has been heavily influenced by Stoic logic,[i] and is formally equivalent to a specially restricted version of a consistent, complete, sound, and decidable fragment of first-order classical predicate logic now known as monadic logic,[ii] together with

(i) a second-order component that quantifies over the intensions of first-order one-place predicates,

and also four further intensional commitments:

(ii) existential commitment in the antecedents of univeral affirmative conditional or “A” propositions in the classical Aristotelian-Scholastic Square of Opposition,

(iii) a primary interpretation of “or” as strong or exclusive (aut)disjunction, not weak or inclusive (vel)disjunction ,

(iv) a distinction between

(iva) classical propositional or predicate negation (for example, “not P,” “No Fs are Gs,” etc.) and

(ivb) complement-class negation, aka “infinite” negation (for example, “S is a non-F,” “Fs are non-Gs,” etc.), and

(v) a primary interpretation of conditional propositions as strict or “formal” implication (i.e., logical consequence), not “material” implication.

Clearly, then, what Kant means by pure general logic is not nothing but Aristotle’s logic or post-Aristotelian Scholastic syllogistic logic: far from it.

In fact, Kant’s pure general logic is a Stoic-logic-influenced intensional monadic logic, as we’ve just seen.

Second, as I also indicated just above, Kant’s central claim about pure general logic here, properly understood, is that pure general logic in his sense is the categorically normative rational core or essence of all logic, that is explanatorily and justificationally presupposed by metaphysics, mathematics, natural science or physics, and every other logic.

And whether that claim is true or false, it is certainly not outrageously false.

Indeed, it may even be surprisingly true.[iii]

But in any case, for our current purposes, the upshot is that Kant is not saying that logic is nothing but pure general logic, and far less saying that logic is nothing but Aristotle’s logic or post-Aristotelian Scholastic syllogistic logic.

NOTES

[i] See, e.g., W. Kneale and M. Kneale, The Development of Logic (corrected edn., Oxford: Clarendon/Oxford Univ. Press, 1986), ch. 3.

[ii] See, e.g., G. Boolos and R. Jeffrey, Computability and Logic (3rd edn., Cambridge: Cambridge Univ. Press, 1989), chs. 10, 22, and 25, and esp. pp. 250–255.

[iii] See, e.g., R. Hanna, Cognition, Content, and the A Priori: A Study in the Philosophy of Mind and Knowledge (THE RATIONAL HUMAN CONDITION, Vol. 5) (New York: Nova Science, 2018), ch. 5.

AGAINST PROFESSIONAL PHILOSOPHY REDUX 542

Mr Nemo, W, X, Y, & Z, Monday 5 April 2021

Against Professional Philosophy is a sub-project of the online mega-project Philosophy Without Borders, which is home-based on Patreon here.

Please consider becoming a patron!

Formerly Captain Nemo. A not-so-very-angry, but still unemployed, full-time philosopher-nobody.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store