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5 hours ago, merjet said:

Thank you for that, Stephen, especially for the distinction between logical necessity and physical necessity. Also, I liked your comments about John Locke. I have began a series on my blog about inference and necessity. Here is the first: Blanshard on Implication and Necessity #1. More to come. 

My integrative and conceptual powers applied to a lifetime of experience still leave me scratching my head.  Is this distinction an academic and historical characterization of what philosophers thought or think or is a first hand distinction of a proper philosophy?

Is the distinction as follows: physical necessity IS metaphysical i.e. identity, and logical necessity IS epistemological i.e. non-contradiction?

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The weed-vine example strikes home to anyone who has tried it. In the example, a flowering vine, in the garden, pole beans, cucumber, to a lesser extent squash and pumpkin. Pulling the weed-vine meant being able to distinguish without being able to see, or where finding a viewing angle was just downright awkward.

I took the physical-logical necessity as a neat example of ontologically based logic.

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50 minutes ago, StrictlyLogical said:

Is the distinction as follows: physical necessity IS metaphysical i.e. identity, and logical necessity IS epistemological i.e. non-contradiction?

The distinction I have in mind is different, but not incompatible with that. Physical necessity is about physical things. Logical necessity is broader, and includes the sort of necessity one can grasp in, say, higher mathematics. For example, this consequence is logically implied by this theorem. For example, this function is differentiable, therefore continuous. The reverse may be true, too, but not always.

Edited by merjet

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I concur with the distinction Merlin draws between physical and formal necessity in the preceding post. That’s a good example from mathematics, and I should note additionally that (i) it is a fact—ascertained in the way one does for mathematics—that there are some continuous functions that are nowhere differentiable, and it remains a fact even if it is the case that there simply is nothing physical to which some such function applies and that (ii) we find great success in technology and in extending comprehension of the physical by applying many functions, each one both continuous and differentiable, to electricity, to fluids, and to solids, yet understanding perfectly well that such things are discontinuous at small enough scales. 

SL, I should not want to equate the physical with the metaphysical. When Rand claims that only living things can have values or when philosophers from time immemorial say nothing comes from nothing, those claims are consonant with modern physical science, but the claims are made in what I’d call a metaphysical perspective, not a scientific one.

In his 1967 essay “The Analytic-Synthetic Dichotomy” Peikoff has a section on the traditional distinction within metaphysics between necessary and contingent facts (and how this feeds into the A-S distinction). The meaning of metaphysical necessary/contingent has changed over the centuries, but there is family-descendant resemblance under the continuing distinction. Peikoff did not think such a distinction is correct to make within metaphysics. However, he there drew a distinction between the metaphysical and the manmade (in tune with Rand’s later elaboration). Human free will is the root fact for this distinction. Unfortunately, Peikoff and Rand thought that the rule of Identity in metaphysics entailed complete determinism throughout metaphysics as contrasted with the realm of free will. Furthermore, Rand thought that such metaphysics rightly constrains (a bit) what physical science might find, but that the reverse flow does not soundly occur. That is, she thought metaphysical fundamentals could not be changed in light of advances in science. So for example, the development of chaos theory in the classical regime of physics (starting in the 1970’s as I recall) and the distinction within physics between a classical system in its regular regime as opposed to being in its chaotic regime could not suggest any reformation of general metaphysics. Really, the total determinism that Rand-Peikoff attached to metaphysics under identity was an inheritance from modern physics (Laplace et al.) and is not properly part of right metaphysics, rather should be left open for physics to settle. In his book OPAR, Peikoff does acknowledge that when it comes to value theory, biology supplies the characterized phenomena, pertinent for philosophical fundamentals concerning value.

In his dissertation, Merlin, Peikoff included Blanshard’s books The Nature of Thoughtand Reason and Analysis. He does not cite the former in his text or notes. He cites and makes specific explicit use of the latter from its pages 252–54 and 271–75. The former stretch lays out the traditional view that necessity (the one, as it happens, to be most often sainted by philosophers traditionally) arises only at the level of universals and essences; discerned at the level of conception, not perception. The latter stretch concerns conventionalist theories of logic.

Merlin, I’ve inclined to the view of logic put forth by Rand (1957) and Branden (c. 1968) and Peikoff (1967, 1991) in their orientation towards logic as tool for successful thinking. (I reject Rand’s definition of logic in its differentia. I expect she was misled by a remark in Aristotle’s Metaphysics, which seems oblivious to his great achievement, theory of the syllogism, in Prior Analytics.) It has seemed plain that on the Objectivist orientation towards logic, material implication should not be incorporated. A lot of other thinkers have thought material implication off the mark for deficiency in the relevance factor, as had Blanshard. They developed Relevance Logic (also called Relevant Logic) as replacement for classical modern logic, and I think that the way to go and a way consonant with Objectivism also. I have books telling the history, concerns, and purposes that brought on material implication, but I’ll have to open them. I’ll let you know on your blog what I find.

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4 minutes ago, Boydstun said:

SL, I should not want to equate the physical with the metaphysical. 

Just to clarify, when I say physical x is metaphysical, I mean it in the sense I would say a crow is an animal.

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I had meant to mention in the preceding post that Peikoff 1964 notes that not all classical philosophers subscribed to a metaphysical distinction between the necessary and the contingent. He helpfully mentions John Scotus Erigena, Spinoza, and Hegel.


Links to the sections of this essay so far:


Aristotle I  II   

Kant I  II  III

Conventionalism I  II  III

Edited by Boydstun

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There are patterns of exclusion for which one knows that no counterexample could be found. Such excluded combinations are not in existence and cannot be in existence. Examples are:

(A) A counting number cannot be both even and odd.

(B) The sum of interior angles of a triangle in a Euclidean plane cannot be any value but 2R.

(C) An oscillation of inconstant period cannot at the same time be both increasing and decreasing in frequency.

(D) There are various things; a thing cannot be both itself and a thing not itself.

All varieties of logical ontologists (excepting the coarse-weaver Mr. Locke) and all their opponents agree that those patterns of exclusion, as necessarily so, can be seen only through work of the intellect, not seen in simply sensory perception. How the mind renders this intellectual seeing and what is the relation of this seeing to sensory perception are the contested matters.

(B) and (C) are facts entirely independently of the existence of mind in the world. (A) is a fact about facility of mind in its engagement with mind-independent numerosity: I’ve got five-fingered hands, but whether a particular finger is even or odd depends on a count and the order in which I include that finger in the count. Unlike in my post of 26 Feb in this thread, I now understand the second clause in (D), which is PNC, to be like (A), not like (B) or [C]. The first clause in (D) is the mind-independent basis of PNC, and it is discerned by the senses as well as by the intellect. PNC requires that mind-independent fact, but also the mind activity of mapping. Counting and mapping have mind-independent facts to cognize, and these cognitions, of course, do not exist in the world without mind, specifically intellect.

I had not been able to return to completing my discussion of Peikoff’s dissertation since last May, until today. I needed to work on some final developments fulltime in my own fundamental metaphysics during those months, but that much completed (which I expect to see print in 12 or 18 months from now), I hope now to be back on the Peikoff 1964 issues (and his 1967 A/S issues) sustained to completion of this tread. 


Edited by dream_weaver
Corrected referenced article date.

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17 hours ago, Boydstun said:

(A) is a fact about facility of mind in its engagement with mind-independent numerosity: I’ve got five-fingered hands, but whether a particular finger is even or odd depends on a count and the order in which I include that finger in the count.

Fascinating. This is not how I think about this at all 

(btw what do you mean by "mind-independent numerosity"?)


Whole numbers for me count quantities of things even when simply "counting" time, places, relationships... etc  and an even quantity of things has the unique quality of being capable of being separated into two groups of equal quantities (without violating the integrity of any of the members).


Counting fingers one way on the hand, 1, 2, 3, 4, 5, counts quantities of fingers while traversing the hand.  If one starts from the left, then there is one leftmost finger, then two leftmost fingers, then three...  If one starts from the right, then there is one rightmost finger, then there are two, then three...

The facts that the grouping of the leftmost and rightmost fingers are not the same is a statement about the relationships of the fingers in reality, they are spaced at various locations along left-right.

Even if we construe the counting as merely LABELING positions from the right or left... the labels are still statements about direction and spatial relationships to the other fingers in reality as well as the quantity of positions/fingers.  The second finger from the right is the fourth finger from the left... I.e. it IS THE finger which is both second from the right and fourth from the left. 

Is the finger itself ODD or EVEN?  Certainly one could label a finger ODD or EVEN (you can label a spoon a fork) but a "finger" is not something which, as such, possesses oddness or evenness.  Now, what about a label "2 and 4"?  Can a label, as such, be odd or even? "2 and 4" is not "a number", in fact no label (qua label) can "BE" a number, it is a label.  Now a label of course can contain concrete symbols representing numbers, like "2" or "4".  Can any "number" which is generally represented by a concrete symbol in a label labeling a finger be odd or even?  well yes... and because that thing IS a number it must be odd or even.


Imagine I decide to call my cat "three" or "four"... it is still true (in everyday English parlance) that I cannot "name it as a number" which is both odd and even... but this says nothing about cats, it is a fact of reality about what numbers refer to in general... and those groups of things in reality, referred to by any single number, cannot be both even and odd.


English is far from a perfect philosophical language... we do not have pronouns to distinguish between real or imaginary or to color terms as referring to reality or mental contents (I so wish we had such pronouns or logical "genders" like the French "un" or "une" and "la" or "le")

Consequently, I find distinguishing between fact (A) on the one hand and (B) and (C) to be fraught with difficulty... to what fact is one actually referring by the string of words in A?


EDIT1:  Even the terms "odd" and "even" are potentially fraught with difficulty.  IF "EVEN" refers to a property of a referent number, i.e. "2" "12", as such,  and it is defined "those references to quantities of things, such that those quantities can be split into two even quantities", then technically no group of things are "even", the numbers which refer to them are even.  BUT IF "EVEN" refers to a property of the quantities of things themselves referred to by the number "2" "12", and it is defined as "a property of a quantity of things which can be split into two even quantities". then technically "numbers" are not "even" as such, the quantities to which they refer are "even", and for shorthand we can label the number as even based upon the kind of quantity to which it refers....


17 hours ago, Boydstun said:

(B) and (C) are facts entirely independently of the existence of mind in the world.

I tend to suspect (and my apologies for the lack of technical rigor.. I am limited by ignorance/innocence of formal philosophy) that all facts are facts entirely independently of the existence of mind in the world.  In fact that seems to be what distinguishes fact from non-fact ("falsehood" is not quite commensurate... as touched on obliquely below).

The fact that I think, is not metaphysically caused by or metaphysically dependent upon my thinking, in the exact same way that the fact that an electron is, is not metaphysically caused by its being... the electron simply is.

So facts about what people think are in that sense independent of their thinking... now they ARE thinking, and that is a metaphysical fact but it is not a fact which has a priori genesis (primacy of consciousness) in the mind... new thoughts spring into reality and those are new facts (independent of mind) which can be identified.

It seems then that all facts, at any one time, are metaphysical absolutes, which are not metaphysically dependent upon the existence of any mind.


EDIT2: Mappings of any kind are relative, but so are relationships in reality.  What is the significance that one can identify those relationships in multiple ways, which is a direct result of the relative nature of reality?  Now arbitrary ordering (random numerals for fingers) seems of a different category because the labels are not meaningfully related to reality.  And finally a relationship of each and every thing to itself ... this does not seem "relative" or "arbitrary" at all... and can such be called a "mapping" when there are no alternatives?


(Sorry for this added complication... but I have never been comfortable with the word "fact".  Does the concept "fact" refer solely to metaphysical existence, or is it used to signify "statements" about the world, which themselves refer to metaphysical existence... I suppose the simple question is can facts be true or false [now that sounds nutty], or is it that facts simply ARE... now that I think of it a fact is a fact it is something metaphysically absolute...)


I do not want to clutter up your thread, but I would like to understand your thoughts a bit better.  Would you be willing to have a brief discussion in a new thread? 

Can you think of a title which succinctly identifies the distinction between facts (A) on the one hand and facts (B) and (C) on the other?

New thread Dream Weaver?


I might be completely off base here... if I am I apologize... and am here for discussion and illumination.


Edited by StrictlyLogical

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PNC Ground Shifts to the Side of the Subject – Conventionalism IV

Leonard Peikoff’s dissertation sets out a developmental conceptual story across the centuries of philosophy. His pages present the story of the theories put forth for the place, character, and origin of PNC and the points on which those theories become untenable, suggesting replacement theories.

That contradictions cannot obtain in reality is a necessary truth. The existence of necessary truths poses a problem for philosophers. “One way of putting the problem is as follows: How can man, who has access to only a very limited portion of a universe whose character is independent of what man thinks about it, nevertheless know with certainty that certain truths will obtain throughout all the regions of space and across the whole course of future time? . . . The conventionalists, in principle, find the solution in denying that necessary truths provide information about any world, real or phenomenal, and in construing them instead as expressive of relations between meanings which men themselves have created; i.e. the conventionalists protect necessary truths from the vagaries of an uncertain world, not by claiming a particular insight into the structure of that world nor legislative power over it, but rather by cutting them off from the world and making them independent of what occurs in it.” (Peikoff 1964, 230)

It is only conventionalism that cuts off necessary truths from the world that was or is provocative. The conventionalists Peikoff mentions were as guilty of equivocation in describing their position as “conventionalist” as were their critics. When they pass off the practicality, convenience, or effectiveness of using PNC and other necessary truths in thinking or communication as showing the “conventionalism” of their position, they are being imprecise (possibly for showiness). Ayer is an example of that, and I’ll look at him in a moment and in the next installment. Firstly, I want to point out that when one takes necessary truths to be tools, having (in our supposed choice of them among supposed alternatives) highest practicality, convenience, or effectiveness, one is certainly not cutting them off from the world and making them independent of what occurs in it, even were one to imagine that is what one is doing. Aristotle pointed out that if one wants an artifact to be effective as a saw, making its teeth of iron is the smart choice. Why? Because of the nature of the world!

It is only certain parts of what conventionalists put forth as conventionalism that actually goes to their position of making necessary truths independent of the structure of the world. Any points at which they are speaking of the practicality, convenience, or effectiveness of necessary truths go against, not to, the provocative part in their pronouncements that conventionality makes necessary truths what they are.

At the end of his dissertation, Peikoff sets out some points on which a new sort of ontologism of PNC would need to diverge from previous ones to block the alternative of conventionalism. This is a highly informed set of constraints—shown to be highly informed by the dissertation—to apply for a viable new ontologism, and Peikoff silently knows that Rand’s epistemology to be issued in a couple of years after his dissertation, along with his own addendum (1967) to that epistemology, will be satisfying those constraints.

Peikoff 1964 does not undertake an exposure of the weaknesses in the conventionalists positions he notes as having displaced ontologism to mid-twentieth century. I shall critique those conventionalist approaches. Conventionalisms too, not only previous ontologisms, had their inadequacies, which by now in philosophy have been exposed, opening the area for reformed ontologisms.

For logical empiricist Ayer, the path to an account of logical and mathematical truths and their necessities is the exclusive and exhaustive division of all truths into either empirical ones or analytic ones, where analyticity is conceived in a very thin way. Like logical empiricists Reichenbach, Schlick, and Carnap before him, Ayer rejected Kant’s synthetic class of necessary, a priori truths. The only necessary, a priori truths Ayer acknowledged were analytic ones. Sebastian Rödl observes that this rejection of the existence of synthetic a priori knowledge is of a piece with rejection of the idea of logic as including general forms of right connection of thought to the world (e.g. Kant’s transcendental logic or Rand’s theory of proper concepts and definitions), leaving only right deductive inference (formal calculii) as logic (Rödl 2012, 3, 22–27, 33–39, 43–45).

In the view of Ayer, analytic propositions “are entirely devoid of factual content. And it is for this reason that no experience can confute them.

“When we say that analytic propositions are devoid of factual content, and consequently that they say nothing, we are not suggesting that they are senseless in the way that metaphysical utterances are senseless. For, although they give us no information about any empirical situation they do enlighten us by illustrating the way in which we use certain symbols. Thus if I say, ‘Nothing can be colored in different ways at the same time with respect to the same part of itself’, I am not saying anything about the properties of any actual thing; but I am not talking nonsense. I am expressing an analytic proposition, which records our determination to call a color expanse which differs in quality from a neighboring color expanse a different part of a given thing. In other words, I am simply calling attention to the implications of a certain linguistic usage. Similarly, in saying  that if all Bretons are Frenchmen, and all Frenchmen Europeans, the further statement that all Bretons are Europeans is implicitly contained. And I am thereby indicating the convention with governs our usage of the words ‘if’ and ‘all’.

“We see, then, that there is a sense in which analytic propositions do give us new knowledge. They call attention to linguistic usages, of which we might otherwise not be conscious, and they reveal unsuspected implications in our assertions and beliefs.” (79–80)

What is an analytic proposition (or analytic truth) according to Ayer? What was his definition of analyticity?

Kant had held that all necessary judgments had to be known a priori. What made an analytic judgment a necessary judgment was that its predicate was conceptually contained in its subject. The concept of a body contains the concept that bodies are extended in space. “Bodies are extended” is necessarily so. Kant’s concept of containment is not entirely determinate. He takes “all bodies are extended” as analytic. What about “all smart women are smart”? Is that a variety of analytic containment? If one denies that all smart women are smart, one plainly has contradicted oneself. Kant required analytic statements to be contradictions upon denial, but it is unclear whether that requirement is a fundamental criterion for analyticity or only a variety of his containment criterion for analyticity (Juhl and Loomis 2010, 4–8).

Bolzano tried to formulate a clearer concept of analyticity, one more centered on logic. If a proposition’s truth value remains constant under any substitution of its terms not belonging to logic itself, it is analytic. Also, the the rules of logic are analytic. Frege took up that concept of analyticity, imported it into his logic wider than subject-predicate logic, and argued that, contra Kant, propositions of arithmetic are analytic, not synthetic a priori. Russell identified an important flaw in that Frege program and made innovations to keep the program afloat (ibid., 11–18; further, Burgess 2005, 34–46; Potter 2000).

Logical empiricists such as Ayer were heirs of this logic-centered concept of analyticity and its proposed undergirding of arithmetic. Then too, they took to heart Wittgenstein’s analysis of logical truths (such as PNC) in Tractatus, a work informed by logical ideas of Frege and Russell, but a work crafting “a single, unified relation between language and the world” (Juhl and Loomis 2010, 19). “Unlike Frege, Wittgenstein did not treat logical truths as statements or propositions at all. Rather, he saw such truths as ‘tautologies’ which, while they might show the ‘logical scaffolding of the world’, do not themselves say anything” (ibid.).

“The fact that language, and the world it pictured, possesses certain ‘formal’ features was thought by Wittgenstein to be shown (although not said) in the fact that certain expressions are tautologies. But the Vienna Circle [1926–1938] was dissatisfied with this conception. Wittgenstein’s talk of ‘showing formal properties of the world’ smacked of the metaphysics they, as empiricists, were concerned to avoid. Rather, Circle members (Moritz Schlick and Rudolf Carnap in particular) proposed treating the truths of logic as expressions of the conventions governing a given language. Their role was thus not one of saying anything about the way things—on this point they agreed with Wittgenstein—but rather that of spelling out the relations of implication among statements. And to the extent that mathematics could be reduced to logic following Frege and Russell, a similar account could be given of mathematical truths as well—they too express relations between statements. /There thus emerges a new conception of analytic truths as expressions of the conventions governing language.” (Juhl and Loomis 2010, 20–21)

Ayer’s philosophy tutor at Oxford, beginning in 1929, was Gilbert Ryle. Ryle introduced Ayer to the works of Russell and to Wittgenstein’s Tractatus Logico-Philosophicus. Ayer was captivated by Tractatus. Circumstances converged such that Ayer was given two terms leave of absence from Oxford, and at Ryle’s urging, Ayer headed for Vienna. Carnap was absent from the Circle for that interval, but it was in Vienna that Ayer became impressed with the work of Carnap. In 1933 Ayer lectured at Oxford on Wittgenstein and Carnap. Other influences on Ayer were Popper and C. I. Lewis. Ayer’s Language, Truth and Logic was published in 1936. It was to become one of the most famous English-language philosophy books of the twentieth century.

The edition of it used by Peikoff in his dissertation and in “The Analytic-Synthetic Dichotomy” was the same as ours today: the second edition, 1948.

(Continuation with Ayer in the next installment.)


Ayer, Alfred Jules [1936] 1948. Language, Truth and Logic. New York: Dover.

Burgess, John P. 2005. Fixing Frege. Princeton: Princeton University Press.

Juhl, Cory and Eric Loomis 2010. Analyticity. New York: Routledge.

Peikoff, Leonard 1964. The Status of the Law of Contradiction in Classical Ontologism. Ph.D. dissertation, New York University.

Potter, Michael 2000. Reason’s Nearest Kin – Philosophies of Arithmetic from Kant to Carnap. New York: Oxford University Press.

Rödl, Sebastian 2012. Categories of the Temporal – An Inquiry into the Forms of the Finite Intellect. Translated by Sibylle Salewski. Cambridge, Massachusetts: Harvard University Press.

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And I am thereby indicating the convention with which governs our usage of the words 'if' and 'all'.

. . . saying anything about the way things are---on this point they agreed with Wittgenstein . . .

1948 1946

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PNC Ground Shifts to the Side of the Subject – Conventionalism V

For the second edition of his book (1946), Ayer did not revise the text, but he wrote an Introduction in which he clarified some points and stated his revised positions on other points. Ayer had taken the usual view contra Mill that necessary propositions or necessary truths had to be a priori, not derived from experience (1946, 74–85). That view and Ayer’s view that only analytic propositions were such a priori ones had not changed. He clarified his view that a priori propositions do not describe any facts, saying he means facts that verify those propositions, as empirical propositions can be verified.

“I now think that it is a mistake to say that they [a priori propositions] are themselves linguistic rules. For apart from the fact that they can properly be said to be true, which linguistic rules cannot, they are distinguished also by being necessary, whereas linguistic rules are arbitrary. At the same time, if they are necessary it is only because the relevant linguistic rules are presupposed. Thus it is a contingent, empirical fact that the word ‘earlier’ is used in English to mean earlier, and it is an arbitrary, though convenient, rule of language that words that stand for temporal relations are to be used transitively; but, given this rule, the proposition that, if A is earlier than B and B is earlier than C, A is earlier than C becomes a necessary truth.” (1946, 17)

How in the world could he avoid seeing the feebleness of claiming necessities of transitivity for these propositions comes from acceptance of an arbitrary rule of language? Is it not straightforward to discern that the necessity in the transitivity of these propositions reflects merely a necessity in temporal relations which are topic of these propositions? Ayer had great intellectual sympathy with Hume, and one might wonder if Ayer was at this stage holding on to a view of temporality as contingent, close to Hume’s in the Treatise (which view Kant thoroughly demolished; see Rödl 2012, 111–68; see also Honderich 1987). Be that as it may, it is clear Ayer recognized the conventions taken as source of logical necessity must be arbitrary if they are to serve in maintaining a chasm between logic and empirical facts.

Even if Kant’s reason for thinking arithmetic to be not analytic is off the mark, Ayer did not make a good case that arithmetic is analytic in his sense (expression of convention governing language), thence necessarily true regardless of the constitution of the physical world empirically present. Among Wittgenstein’s scribbles circa 1937–1938, he observed that various sorts of items, such as apples or beans, are such that by counting portions of a collection of those items and counting totals of that collection, one can demonstrate the correctness of summation in arithmetic.

“This is how children learn sums; for one makes them put down three beans and then another three beans and then count what is there. If the result at one time were 5, another 7 (say because, as we should now say, one sometimes got added, and one sometimes vanished of itself), then the first thing we said would be that beans were no good for teaching sums. But if the same thing happened with sticks, fingers, lines and most other things, that would be the end of all sums. / But shouldn’t we then still have 2+2 = 4? —This sentence would have become unusable.” (Wittgenstein 1978, 51–52)

Late in life, Ayer wrote “I am more baffled than enlightened by his [Wittgenstein’s] Remarks on the Foundations of Mathematics. Nevertheless he does make one point of the utmost importance: he calls attention to the dependence of arithmetic upon contingent matters of fact.” Ayer then rehearsed Wittgenstein’s fancy of a world without exemplification of our arithmetic sums, and Ayer asked: “Would the proposition 7+5 = 12 be false in such a world? No. It would still be valid within the framework of standard arithmetic. It would have become not false but useless. . . . it would, says Wittgenstein, be the end of all sums. I am not convinced that this would be so. . . . I do not find it inconceivable that someone would devise an arithmetic which was adapted to such natural facts” (1989, 484–85). Talk of such deliberate adaptedness seems to forget about the supposed chasm between the analytic and the world.

Ayer held out to the end the hope that arithmetic, being not from empirical generalization, is purely analytic (there being no other sort of necessary truths in the view of Ayer and other logical empiricists). It was not a tenable hope. As a contrast to sums among countable things like beans or like words in a sentence, we need not turn to a radical fancy such as Wittgenstein’s. We can turn to contrasting the sorts of sums in the actual world. A positive road grade of 153 yards per mile added to a positive road grade of 153 yards per mile does not sum to a grade of 306 yards per mile, but to 310. 3 yards per mile. Road grades are just as physically real as beans. Different sorts of summations are right for things different in certain of their magnitude-characters. There is no place, I maintain, indifferent to physical reality for pure mathematical summation to abide in “pure analyticity” nor to be based most fundamentally on arbitrary convention.

It was not only of the a priori, necessary principles constituting mathematics, but of such principles constituting logic, Ayer had maintained: “If they are necessary it is only because the relevant linguistic rules are presupposed” (1946, 17). Linguistic rules concerning whether nouns shall have genders with which varieties of definite article must agree (as in German) surely would not be the relevant sort of presupposition—relevant sort of acceptance by one as rule for one’s language—to source the necessity in logic we all put to work in our discursive thought. A linguistic source plausible enough to get off the ground would have to be some deeper aspect of  grammar, an aspect common to all languages.

Recall the picture by Kant that I recorded in Kant I (this picture omitted from the English translation available for Peikoff 1964 and Ayer 1946): “The science which contains these universal and necessary laws [of thought] is simply a science of the form of thought. And we can form a conception of the possibility of such a science, just as a universal grammar which contains nothing beyond the mere form of language, without words, which belong to the matter of language.” That remark engages an analogy in which grammatical form is to grammar-slots filled with particular nouns, verbs, and so forth, as logical form is to its occasions of use in particular topics. Beyond analogy, Sebastian Rödl plumbs deep grammar of thought, along lines of the first Critique (Rödl 2012, 4, 22–25). Deeper plumbs, whether of grammar of language or grammar of thought, pull logical empiricists such as Ayer willy nilly hopelessly far from arbitrary convention as base for logic and its necessities. Wittgenstein evidently suffered that same pull (Ben-Menahem 2006, 265–69). “To collapse correctness into propriety is to obliterate the essential character of thought” (Haugeland 1998, 317; further, 325–43; see also Rasmussen 1982; 2014, 337–41; Rand 1966–67, 47–48; Peikoff 1967, 104; 1991, 143–44).

(To be continued, with Ernest Nagel and Arthur Pap next.)


Ayer, Alfred Jules. [1936] 1948. Language, Truth and Logic. New York: Dover.

——. 1989. Reply to F. Miró Quesada. In Hahn 1992, 478–88.

Ben-Menahem, Yemina. 2006. Conventionalism. Cambridge: Cambridge University Press.

Biondi, Paolo C. and Louis F. Groake, eds. 2014. Shifting the Paradigm – Alternative Perspectives on Induction. Berlin: De Gruyter.

Hahn, Lewis Edwin. 1992. The Philosophy of A.J. Ayer. La Salle, Illinois: Open Court.

Haugeland, John. 1998. Truth and Rule-Following. In Having Thought – Essays in the Metaphysics of Mind. Cambridge, Massachusetts: Harvard University Press.

Honderich, Ted. 1989. Causation: One Thing Just Happens after Another. In Hahn 1992, 243–70.

Peikoff, Leonard 1964. The Status of the Law of Contradiction in Classical Ontologism. Ph.D. dissertation, New York University.

——. 1967. The Analytic-Synthetic Dichotomy. In Rand 1966–67, 88–121.

——. 1991. Objectivism: The Philosophy of Ayn Rand. New York: Dutton.

Rand, Ayn. 1966–67. Introduction to Objectivist Epistemology. Expanded 2nd edition. New York: Meridian.

Rasmussen, Douglas B. 1982. Necessary Truth, the Game Analogy, and the Meaning-Is-Use Thesis. The Thomist 46(3):423–40.

——. 2014. Grounding Necessary Truth in the Nature of Things. In Biondi and Groarke 2014, 323–58.

Rödl, Sebastian. 2012. Categories of the Temporal – An Inquiry into the Forms of the Finite Intellect. Translated by Sibylle Salewski. Cambridge, Massachusetts: Harvard University Press.

Wittgenstein, Ludwig. 1978. Remarks on the Foundations of Mathematics. Edited by G.H. von Wright, R. Rhees, and G.E.M. Anscombe. Translated by G.E.M. Anscombe. Cambridge, Massachusetts: MIT Press.

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PNC Ground Shifts to the Side of the Subject – Conventionalism VI

(Nagel and Pap will not be reached in this installment after all.)

In the Preface to the first edition of his Language, Truth, and Logic (1936), Ayer writes: “Like Hume, I divide all genuine propositions into two classes: those which, in his terminology, concern ‘relations of ideas’, and those which concern ‘matters of fact’” (31). The propositions of logic and mathematics belong to the former, and they are necessarily true, as Hume would have it. That is clear from his texts. But Hume could not concur with Ayer’s further characterization of such propositions as a priori, where an a priori proposition is one known not only independently of this or that perceptual experience, but independently of each and every one of them. Ayer erred, as so many before him and after him, in identifying such a radical sense of the a priori with Hume’s notion of the a priori for propositions of pure mathematics and logic (including PNC) understood as concerning only relations of ideas.

Hume, like Berkeley and Locke before him, was a full-blown empiricist. Ayer’s route to holding forth the logical empiricist view as an empiricist view was to shrink fact to only facts ascertained by the methods of the empirical sciences, to characterize all necessary propositions as radically a priori, which class coincides with a logic-centered analytic, whose truth and necessity are not from relations to the world, but from arbitrary convention hand-waved (in Ayer’s case) from grammar. Then, Ayer proclaims his view as empirical: all knowledge derives from experience because his genre of analytic propositions do not state facts; they are not knowledge. (See also Friedman 1999, 5–6, 9, 18–19, 32–33, 116–18.)

Graciela De Pierris 2015 concludes of Hume:

“The addition in the Enquiry of a seemingly logical criterion for identifying ‘relations of ideas’ does not mean a departure from the sensible phenomenological model of apprehension and ultimate evidence. Hume does not uphold the logical law of non-contradiction in its own right, prior to and independently of phenomenological sensible factors. On the contrary, the status of non-contradiction as a criterion for the acceptance of propositions based on ‘relations of ideas’ depends solely on the phenomenological inspection of intrinsic characteristics of particular items ostensively present before the mind. Necessary a priori methods, in both the Treatise and Enquiry, are ultimately grounded on nothing but the sensible phenomenological model.” (102)

In consistency with their rejection of Kant’s containment-of-predicate-in-subject criterion for seeing which concepts stand in a logically necessary relation each to the other (see Convention IV), the logical empiricists should have spurned Hume’s model of pure relations of ideas (or thoughts). That is to say, they should have spurned his explication of the a priori character of arithmetic, geometry, and logic. Had Ayer understood Hume on this point in Enquiry as harmonious with Hume’s treatment in Treatise, perhaps Ayer would not have set up Hume for worship on analyticity.

In Hume’s picture, discernment of necessary union of items forming a sum or the union of triangularity with the 2R sum of those three angles stands us in high certainty, indeed our highest certainty. We stand on PNC with that highest certainty, and for that reason, PNC can have normative force. “Hume uses his version of the presentational-phenomenological model of apprehension, just as the tradition before him had done, to give a verdict about ultimate evidence” (De Pierris 2015,  228; see also 220–22).

Locke had taken reason as “the discovery of the certainty or probability of such propositions or truths, which the mind arrives at by deduction made from such ideas, which it has got by the use of its natural faculties; viz. by sensation or reflection” (EU IV.xviii.2). Reason investigates ideas and their degrees of certainty or probability of being true, insofar as said ideas are grounded in sensory experience of outer things or in reflection, where reflection means our notice of our own inner, mental operations (EU II.i.3–4, II.v).

I mentioned in Aristotle II that Peikoff argued the unravelling of Platonic logical ontologism into logical conventionalism (as of mid-twentieth century) to have been mediated significantly by Kant. He concluded the unraveling of Aristotelian logical ontologism had been significantly mediated by Locke (Peikoff 1964, 212–35).

I had written in Conventionalism III:

“Logical necessity holds unconditionally and in all contexts. What I’ve called physical necessity is traditionally taken to be necessity under some sort of limiting conditions, and this necessity has been called a contingent connection, reserving necessary connection for logical (and other formal) necessity. . . .

“Peikoff 1964 points out that Locke avoided the contingent/necessary terminology. Locke instead applied probable/certain to the division. We have seen in my section Aristotle II that Locke maintained we have by sensory perception instances of the general fact that different things are not same things and that a thing is never both A and not A at the same time and in the same respect. Philosophers, including Peikoff in 1964, are correct to fault Locke’s blurring under probable/certain a clear understanding that ampliative inductive generalizations over perceived instances do not suffice to land the absolute necessity in general principles of logic or pure mathematics. . . .

“Locke was not really of one mind in this. Peikoff lays out an opposite strand also in An Essay Concerning Human Understanding: IV 3.31, 4.6, 4.8, 9.1, 11.13–14. ‘What is Locke doing in such passages as these? He is now contrasting eternal truths and existential truths. The former are to be discovered only by “the examining of our own ideas,” and “concern not existence” . . .’ (222). . . . For an empiricist such as Locke, . . . [one] joining considerable nominalism (the conceptualist wing of nominalism) concerning universal ideas to the empiricism, the divide between matters of fact and the eternal, formal truths can make conventionalism concerning the ground of logic ‘almost inevitable’ (223).”

(That is not to say, at least in my view, that it makes almost inevitable a root conventionalism that is arbitrary. It need not make almost inevitable a conventionalism making logical principles entirely independent of constraints from the world and from our physical operations in the world.)

I now think, having studied De Pierris 2015, that Locke’s two sorts of distinctions are harmonious. Whether some knowledge is gotten from “examining our own ideas” or from empirical generalization (or from some combination of the two), the knowledge has placement with us as to its certainty or probability. If, as with Descartes before him and Hume after him, degree of certainty is the fundamental index to truth, index to reality won, then Locke was innocent of fundamental severance of formal truths from empirical truths. We of last century and this have been guilty of writing too much of the divides of the logical empiricists back into the distinctions made by Locke and those by Hume.

Locke can be wrong or vague about how we derive PNC from sensory experience, yet right in his view that sensory experience is found to always conform to PNC. That PNC and mathematics are found as well and with highest possible certainty in ‘reflection’ (even reflection “concerning not existence”) need not somehow compete with or belie one’s finding PNC to hold in sensory experience, just as Euclidean geometry is conformed to in carpentry or in Newton’s system of the world (see also Franklin 2014, 95–100). Insofar as Locke is presented with high, highest certainty that PNC is true of the real in every nook and cranny, then PNC can serve as a norm to conform to for correct thinking. Even were the incorrect nominalist leanings of Locke and the incorrect voiding of natural necessitation of Hume not yet diagnosed and dispelled, PNC (and other formal relations) with its mark of certainty and generality can be given to, not cast by, the human faculties envisioned by Locke or by Hume. Then it is not those empiricists who are rightly regarded as intellectual tributaries into logical empiricism, notwithstanding the distant lineage claims declared by the latter. (Further on Locke: chapter VI “Ideas and Psychology” in Yolton 1984.)

What about kinship of the logical empiricists to the classical British empiricist George Berkeley? Kenneth Pearce 2017 argues that for Berkeley words get to be meaningful by being used in pubic discourse, following conventional rules, but for practical ends. The reason a system of language can be effective practically is because with language we capture the grammar of nature as created by God. There is under this conception, I notice, no severance of our minds, including our mathematical minds, from the world due to conventions in language (Pearce 2017, 45–50, 80–83, 112, 151–52, 158–62, 195, 204). Berkeley’s view is contrary the logical empiricist thesis of arbitrariness of linguistic convention sufficiently deep in any formal truths to decouple them from the world.


De Pierris, G. 2015. Ideas, Evidence, & Method – Hume’s Skepticism & Naturalism Concerning Knowledge & Causation. New York: Oxford University Press.

Franklin, J. 2014. An Aristotelian Realist Philosophy of Mathematics – Mathematics as the Science of Quantity and Structure. New York: Palgrave Macmillan.

Friedman, M. 1999. Reconsidering Logical Positivism. New York: Cambridge University Press.

Pearce, K. L. 2017. Language and the Structure of Berkeley’s World. New York: Oxford University Press.

Yolton, J. W. 1984. Perceptual Acquaintance from Descartes to Reid. Minneapolis: University of Minnesota Press.

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On ‎10‎/‎9‎/‎2019 at 1:11 PM, Boydstun said:

Thanks for the ideas, SL. Let's just leave your post right here for coming back to later (I'll try to set it in perches of Rand's ontology), after I've completed this my festschrift for Leonard Peikoff in theoretical philosophy.

Don't want to clutter this thread, but I remain curious! 

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PNC Ground Shifts to the Side of the Subject – Conventionalism VII

From Gillian Russell’s entry LOGICAL PLURALISM (2019) in the Stanford Encyclopedia of Philosophy:

“There are several issues that someone who wanted to defend Carnap’s [1937] position today would need to address. A first concern about the view is that while we are working within the various languages we invent, we could be missing the ‘correct’ rules—the ones that were out there, in effect, before we invented anything. In the words of Paul Boghossian,

“‘Are we really to suppose that, prior to our stipulating a meaning for the sentence ‘Either snow is white or it isn’t,’ it wasn’t the case that either snow was white or it wasn’t? Isn’t it overwhelmingly obvious that this claim was true before such an act of meaning, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences?’ (Boghossian 1996)

“Carnap would perhaps not have taken this objection seriously, since, like the Wittgenstein of the Tractatus (e.g., §4.26, 4.641–4.465), he does not believe that logical truths and rules are ‘out there’, waiting to be discovered:

“‘The so-called “real” sentences, constitute the core of the science; the mathematico-logical sentences are analytic, with no real content, and are merely formal auxiliaries’. (Carnap 1937, xiv)

“Nonetheless, such a ‘conventionalist’ view of logical truth (and along with it, analytic truth) has been argued against by, for example, Quine, Sober, Yablo and Boghossian, and it no longer enjoys the popularity that it had in Carnap’s time (Quine 1936; Yablo 1992; Boghossian 1996; Sober 2000).”

One of the most noted essays of the twentieth century is Quine’s 1951 “Two Dogmas of Empiricism,” which argues the distinction between analytic and synthetic truths, so dear in logical empiricism, is untenable. Necessary truths we have in logic and mathematics cannot receive their necessity of being true merely in virtue of meaning, which is to say, by being analytic truths. Furthermore, for analytic there is no noncircular and enduring rule establishing its extension. A logical truth such as A is identically A, in Quine’s view, need not get its truth only by our say-so meaning of is identically, but could as well get its truth by its capture of the way the world is (Quine 1954, 113).

In a 1963 lecture “Necessary Truth” which Quine delivered on Voice of America (the lecture was published by that organization the following year as a pamphlet), he concluded: “In principle . . . I see no higher or more austere necessity than natural necessity; and in natural necessity, or our attributions of it, I see only Hume’s regularities, culminating here and there in what passes for an explanatory trait or the promise of it” (76). With that last clause, Quine rather takes back the ribbon he had just given Hume. Moreover, earlier in the lecture, Quine had augmented bare regularity with generality-within-a-domain (71, 74).

When I say “Necessarily, were Little Bo Peep’s sheep to come home of their own accord, they will be wagging their tails behind them” (here I abjure Standley’s wild thought they might come home walking in reverse), I speak in the essential form of natural necessity, according to Quine 1963. My necessity-sentence is a subjunctive resting on the nature of sheep. Quine’s view that logical and mathematical necessity are only wide-domain natural necessities acknowledged in subjunctive statements seem right to me. “Necessarily, were not both p and q true, and p were true, then q would be false.” The Randian 1957 necessities concerning leaf/stone, freeze/burn, and red/green can be put into that p/q form with ease. Where q is simply not-p (very wide domain), we have the bare PNC.

In 1967, four years after Quine’s “Necessary Truth,” Leonard Peikoff’s “The Analytic-Synthetic Dichotomy” appeared in The Objectivist. Roderick Long once remarked, relying on Quine 1951: “Rather than defending the existence of necessary factual truth, Quine had in effect denied that any truths were necessary, even the laws of logic” (2005, 226n3). No, not really. To say “necessarily, not both p and not-p” under a blank condition that its wide domain of application might in the future be shown to be not the widest domain, is not to in effect deny there are necessary truths, only to deny knowing that the presently known widest domain is not but part of a wider domain in which those necessary truths do not everywhere apply. I disagree with Quine—we do know the application of PNC is to the widest possible domain—but that does not alter the value of Quine’s insight that formal necessities (however broad, broad their purview) are natural necessities.

Peikoff 1967 attacks contemporary conventionalism concerning necessary truths, though not along the Quinean lines of attack. Rather, Peikoff attacks by attacking the old distinction, from Plato-Aristotle to the early moderns, that there is a distinction, a knowable distinction, between contingent facts and necessary truths. He takes contemporary conventionalism to merely replace metaphysical bases for necessary truths with “subjective choices.” “Their ‘contribution’ is merely to interpret [the traditional position] in an avowedly subjectivist manner” (1967, 108). (Again I stress that a conventionalism concerning logical truth that is not wholly arbitrary in its conventions and their combinations is not wholly effective in freeing logical truth from facts of the world and of our logical facility with those facts.)

Peikoff 1967 rightly attacks the traditional distinction, with its supernatural prop. He then takes on the embrace of the concept contingent facts by (many among) contemporary analytic philosophers. He would have it, rather, that all natural facts are necessary, and only man-made facts are contingent (106–11). Various divisions of all that is have arisen across the centuries under the same words necessary/contingent. Quine does not conceive of natural necessity, thence logical necessity as applying to everything not man-made. Quine’s necessity does not apply, save elliptically, to particular events or states; it applies properly only to whole conditional connections—“Necessarily, if p then q.”

“We must not suppose that a man is entitled to apply ‘necessarily’ to an assertion so long merely as he thinks there is some general truth that subsumes it” (Quine 1963, 70). Suppose the raccoon Rocky is climbing the tree to reach the bird feeder. Then we can say of every raccoon x without exception that if x is Rocky, then x is climbing the tree to reach the bird feeder. Quine restricts necessity in his intended sense to disallow that because we got Rocky’s deed into that form, in a true report of what is afoot, we may straightly say in Quine’s sense “Necessarily, Rocky being indeed Rocky, he’s climbing the tree to reach the bird feeder.” “This line would allow us to attribute necessity to anything, however casual, that we are prepared to affirm at all” (1963, 71). The relation of Quine’s sense of necessity and the one in play in Peikoff 1967 remains work not yet done by anyone, I gather.

In his Introduction to the collection The Age of Alternative Logics (2009), editor Johan van Benthem writes: “Modern logic shows a wide variety of perspectives, application areas, and formal systems which often go under the heading ‘alternative logics’. . . . Actually, terms like ‘alternative’ or ‘non-classical’ logic can easily be misunderstood . . . . To us, the diversity of logical systems today . . . signals a natural and respectable process of growth of the discipline, not of replacement or competition.” (1) It is a mistake to suppose that because there are alternative logics, such as intuitionist logic or relevance logic, that the choice of their domain of application is unconstrained, in fact arbitrary.

We have noticed that Peikoff 1964 used “conventionalism” concerning fundamental logical principles somewhat broadly. The label was meant to encompass the stances of pragmatist and logical empiricist philosophers in the first half of the twentieth century. Peikoff rightly did not try to sweep Kant’s view of logic into the conventionalist bin.

The term “conventionalism” in Sidelle 1989 is far too inclusive. He used conventionalism to mean any view of necessary truth that does not take that necessity to reside in the mind-independent world. A major innovation in analytic philosophy had occurred by the time of Sidelle's book: Kripke 1972. Without resort to Kant’s proposition-type or truth-type synthetic a priori, Kripke had upheld, from logical analysis of language, credible candidates for necessarily true statements not a priori and not analytic. Sidelle attempts to counter the common understanding that Kripke succeeded in putting some necessary truth into the mind-independent world.

(To be continued.)



Boghossian, P. A. 1996. Analyticity Reconsidered. Noûs 30(3):360–91.

Browne, G. M. 2001. Necessary Factual Truth. Lanham: University Press of America.

Carnap, R. 1937. The Logical Syntax of Language. London: Kegan Paul.

Kripke, S. A. 1972. Naming and Necessity. Cambridge: Harvard University Press.

Long, R. T. Reference and Necessity: A Rand-Kripke Synthesis? – Review of Brown 2001. The Journal of Ayn Rand Studies 7(1):209–28.

Peikoff, Leonard 1964. The Status of the Law of Contradiction in Classical Ontologism. Ph.D. dissertation, New York University.

——. 1967. The Analytic-Synthetic Dichotomy. In Rand 1966–67, 88–121.

Quine, W. V. O. 1936. Truth by Convention. In Quine 1976.

——. 1951. Two Dogmas of Empiricism. In Quine 1980.

——. 1954. Carnap and Logical Truth. In Quine 1976.

——. 1963. Necessary Truth. In Quine 1976.

——. 1976. The Ways of Paradox and Other Essays. Cambridge: Harvard University Press.

——. 1980. From a Logical Point of View. Cambridge: Harvard University Press.

Rand, A. 1957. Atlas Shrugged. New York: Random House.

——. 1966–67. Introduction to Objectivist Epistemology. Expanded 2nd edition. 1990. New York: Meridian.

Sidelle, A. 1989. Necessity, Essence, and Individuation – A Defense of Conventionalism. Ithaca: Cornell University Press.

Sober, E. 2008. Quine. Proceedings of the Aristotelian Society LXXIV:237–80.

Standley, J. 1952. https://www.youtube.com/watch?v=7aExUGQOnI0

Van Benthem, J., Heinzmann, G., Rebuschi, M., and H. Visser, editors, 2009. The Age of Alternative Logics – Assessing Philosophy of Logic and Mathematics Today. Dordrecht: Springer.

Wittgenstein, L. 1922 [1918]. Tractatus Logico-Philosophicus. C. K. Ogden, translator. New York: Routledge.

Yablo, S. 1992. Review of Necessity, Essence, and Individuation: A Defense of Conventionalism by Alan Sidelle. The Philosophical Review 101(4):878–81.

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PNC Ground Shifts to the Side of the Subject – Conventionalism VIII

“I have never asserted that it is inconceivable that water isn’t H2O, but only that it is impossible that it isn’t H2O.” —H. Putnam

In the nineteenth century, Weber & Kohlbrausch, Maxwell, and Hertz established that light is electromagnetic radiation (within a certain range of frequencies). This was established by measurements and by mathematical representation of relationships between various physical, electromagnetic properties in media and in the vacuum. They established as well that radiant heat was electromagnetic radiation. Heat and light from the sun, for example, are electromagnetic radiation. Electromagnetic radiation (of some range of frequencies) is the light allowing the wheat to grow. For short, light = EM rad, where ‘=‘ is here ‘identically the same as’.

At least one, probably more, of the characteristics of the single thing that is light/EM rad is an essential characteristic of it. But light and EM radiation being the same thing is nothing essential about that thing. Rather, this being-the-same is total identity of the object investigated in optics and an object investigated in EM science. A is not a characteristic of A, though A is A.

In her 2017 paper on Kripkean necessity of identity, García-Encinas argues the identity discovered (my example) by Weber & Kohlbrausch, Maxwell, and Hertz subtly exhibits “how identity belongs to the inner and to the most profound structure of cognition and language” (52). That much having been argued, she suggests: “Despite the general tendency to the contrary, it could be the case that even logical truths, or truths that are usually believed to be necessary but devoid of metaphysical content, like x = x are finally grounded in metaphysics (and aesthetics). x = x could be a logical form of our intuition of Identity” (68). The indefinite article of “a logical form” would be the right choice of article in Rand’s lights, since “x is identically x” as the identity added to first-order predicate calculus with quantification (see Quine 1982, chapter 43) is only a proper part of the full A is A of logic employed in the discovery of the light/EM rad identity.

The single self-same thing light/EM rad exhibits wave-particle duality; has a wavelength inversely proportional to its momentum; has a definite role not only in electrodynamics, but in general kinematics of modern mechanics; has no rest-mass of its particle, the photon; has polarization character; and shows universal characteristic atomic and molecular spectra from matter throughout the observed universe. Whether any one or more of these characteristics is essential to light/EM rad being what it is, Objectivist metaphysics and epistemology takes them all as being necessary to what it is. They have a necessity transcending the necessity of an essential characteristic. This transcending necessity is a necessity merely denying cognitive validity of imagination-criteria for whether something is “contingent.” That I can imagine, without manifest contradiction, that the atoms and molecules naturally present here in the solar system are nonexistent elsewhere in the galaxy or that light and electromagnetic radiation are not (in any range of frequencies) the same thing is no insight into metaphysical or physical character. Such imaginings, since Descartes and until this day, so beloved by many philosophers (e.g. Sidelle 2002), are valuable only for entertainment, and they exhibit only what playfulness I can have over past ignorance and inquiry (cf. Peikoff 1967, 114–16).

Necessities in a posteriori truths as well as all logical necessities whatever are not the offspring of linguistic convention in stipulative definitions. That much, many contemporary philosophers have concluded. Those necessities are the offspring of existence in its identities, an assertion that needs to be fleshed out (see Long 2005, 213, on that need).

I should like to add (my own original connection) that the insusceptibility to trisection of angles in complete generality by straight-edge and compass constructions alone is not shown to be an absolutely necessary insusceptibility by stipulative definitions joined with their contradiction upon supposition of such trisection. The absolute necessity of that insusceptibility was shown by creative discovery of whole new areas of mathematics and their connection to Euclidean geometry (within which workers had failed repeatedly to produce general angle trisection using only straight-edge construction together with compass construction, and within which could not prove its absolute impossibility).


In his 2016, Greg Salmieri notes that it is curious that Peikoff 1967 does not mention Quine’s “Two Dogmas.” Salmeiri points out some ways the Rand-Peikoff diagnoses of and remedies for the errors in analytic-versus-synthetic doctrines differ from Quine’s. Salmieri understands the later challenge of AvS from Kripke and Putnam to have more in common with the Objectivist challenge, though Putnam differs importantly from Rand on definitions and essences, which looms large in the Objectivist challenge (2016, 304n34, 311n87). Salmieri points to the book-review article, in JARS in 2005, by Roderick Long for thoughts on some relations between Randian theory of meaning and those of Kripke and Putnam.

Long’s 2005 review of Greg Browne’s book Necessary Factual Truth was followed a year later by a substantial reply from Browne and rejoinder by Long (JARS V7N1). From May to September of 2007, Prof. Browne engaged in a very generous exchange (his own words coming to about 19,000) in a thread at Objectivist Living defending the rejection by Peikoff of AvS and defending his own kindred rejection of AvS. Browne had in his arsenal the Kripke-Putnam developments that had been savaging AvS in the years since Peikoff 1967. Browne vigorously countered, in that thread, devotees of Logical Empiricism (and of Popper) who criticized (and poorly understood the revolution afoot, such as in) Peikoff 1967.

Late in that thread, Robert Campbell entered it only to ask Browne if he had any thoughts on why Peikoff had not addressed the famous Quine paper in his Peikoff’s dissertation, which Campbell had lately acquired. Browne had not seen the dissertation and had not much to conjecture on that peculiarity. (Remember, Peikoff 1964 is not written as a champion of Ayn Rand’s philosophic views, but, in an even-handed way, by an author acknowledging his background preference for some rehabilitated sort of logical ontologism and pointing near the end of the dissertation to some of that rehabilitation, such as fresh thinking on the nature of definitions and essence; distance between Quine’s views on logic and on AvS and Randian Peikoff views would not be the reason for no Quine in Peikoff 1964.) I should suggest that Quine, Carnap, Russell, and Wittgenstein raise such a briar patch of technicalities that it was better (and enough for deserving a Ph.D.) to stick with the more accessible and manageable Ayer, Nagel, Dewey, and Lewis to get the dissertation (already more than an armful in history assimilated) finally completed.


Near the close of “Two Dogmas of Empiricism,” after saying once more that he rejects the distinction between the analytic and the synthetic, Quine enters a footnote directing the reader to a paper by Morton White “for an effective expression of further misgivings over this distinction” (1953, 46). That paper is “The Analytic and the Synthetic: An Untenable Dualism” (UD).[1] It appeared originally in Hook 1950, then again, in Linsky 1952. My page references are from the latter.

Morton White noted two kinds of statements that had lately been regarded as analytic. The first are purely formal logical truths such as “A is A” and “A or not-A.” The second are cases of “what is traditionally known as essential predication” (UD 318). He ponders especially the example “All men are rational animals.” That statement is logically the same as “Any man is a rational animal” or “A man is a rational animal.” This last expression of the proposition is one of Leonard Peikoff’s examples of a purportedly analytic statement in “The Analytic-Synthetic Dichotomy” ([A-S] 1967, 90).

White did not pursue in this paper whether it is correct to characterize logical truths as analytic (UD 318–19). It will be recalled that Peikoff held forth Rand’s conception of logical truth against that of A. J. Ayer, who had maintained: “The principles of logic and mathematics are true universally simply because we never allow them to be anything else. . . . In other words, the truths of logic and mathematics are analytic propositions or tautologies” (1946, 77; Branden 1963, 7; A-S 94, 101, 111–18).

As with Quine’s “Two Dogmas,” White undermined the distinction between the analytic and the synthetic by finding fault with various explications of what analyticity amount to. They concluded there is no durable articulate way of classifying propositions and truths as analytic in sharp contrast to synthetic.

One way of conceiving an analytic statement is as expressing a proposition deducible from a logical truth by substitution of a synonym of one of its terms. (i) Every A is A. Therefore, (ii) Every man is a man. With rational animal as synonym for man, we obtain (iii) Every man is a rational animal (UD 319).

Thence analyticity is explicated in terms of logical truth and synonymy. White rejects the view that whether man and rational animal are synonymous is a matter of arbitrarily selected convention. Similarly, that man and featherless biped are not synonymous is not a matter of arbitrarily selected convention. Natural language is not like an artificial logical language in which meanings of terms are set entirely by stipulation (UD 321–24).

White allows we certainly have some sort of working distinction between propositions such as, on the one hand, “Man is an animal” and “Man is a rational animal” and, on the other hand, “Man is a featherless biped” and “Man has two eyes” (Peikoff’s example, A-S 90). White concludes that distinction between those two classes of statement is not that statements in the first class are analytic, the latter not, where the analytic is defined as consequence of a logical truth under substitution of a synonym and we are given no objective criterion for synonymy (UD 318–24).

Could analytic statements be defined instead as those whose denials are self-contradictory? White queries how it is that “Man is not a rational animal” leads to “Man is not man,” yet “Man is a quadruped” does not lead to “Man is not man.” He again notes that appealing to synonymies in the language is not illuminating in the absence of objective criteria for synonymy (UD 324). If it is said that one’s sense of wrongness in “Man is not a rational animal” differs from one’s sense of wrongness in “Man is a quadruped,” White replies that that is surely only a matter of degree, not a sharp difference in kind. Between one’s response to contradiction of “Man is a rational animal” and contradiction of “Man is a biped,” there is not a sharp difference in kind. If self-contradiction upon denial of a proposition is the criterion for analyticity of the proposition, then there is no sharp divide between the analytic and the synthetic (UD 325–26).

Suppose we adopt the following criterion for analyticity. Were we to come across an animal we determine to be not a rational animal, we would dismiss it instantly as being a man. By contrast, were we to come across an animal we see is not a featherless biped (it is, say, a quadruped), but whose rationality is not yet confirmed or disconfirmed, we hesitate over whether this animal is a man. We know that we might give up the proposition “All men are featherless bipeds” if we learn this animal is rational (UD 326–28). White responds: “Now I suspect that this criterion will be workable but it will not allow us to distinguish what we think in advance are the analytic equivalences. It will result in our finding that many firmly believed ‘synthetic’ equivalences are analytic on this criterion” (UD 328).

White gives no example, but I think his point is illustrated by an analytic-synthetic pair of judgments, favorites with Kant: “All bodies are extended” (analytic) and “All bodies have weight” (synthetic). By the latter, given his knowledge of Newtonian physics, I think Kant rightly understands “All bodies not in gravitational orbit have weight.” Be that as it may, Kant and his contemporaneous intellectuals would dismiss as body just as quickly an entity lacking weight (in the appropriate setting) as they would dismiss as body an entity lacking extension.[2] The criterion of speed of dismissal upon counterfactual encounter fails to always sort what is taken for analytic from what is taken for synthetic.

White observes that the obscurity of proposed criteria for distinguishing analytic from synthetic statements, propositions, and judgments, is not fixed by incorporating the sound Millian point that what is synonymous with man, for example, varies with discursive context. In a biological discourse, “mammiferous animal having two hands” (Mill’s example) might be synonym for man. It remains that analyticity is not illuminated by proposing logical truth and synonymy as its base, not illuminated so as to yield a sharp divide, rather than a gradual divide, between the analytic and the synthetic. The arguments run against such an explication of the analyticity of “Man is a rational animal” will rerun for “Man is a mammiferous animal with two hands” (UD 329–30).

White saw the myth of a sharp divide between the analytic and the synthetic as affiliate of an older mythically sharp division: the Aristotelian division between essential and accidental predication (UD 319, 325, 330). This kinship was also recognized in Peikoff 1967 (A-S 95).

(To be continued.)


1. Nelson Goodman writes in a 1953 footnote: “Perhaps I should explain for the sake of some unusually sheltered reader that the notion of a necessary connection of ideas, or of an absolutely analytic statement, is no longer sacrosanct. Some, like Quine and White, have forthrightly attacked the notion; others, like myself, have simply discarded it; and still others have begun to feel acutely uncomfortable about it” (60).

2. Notice also that in modern physics of elementary particles, we take electrons and the other leptons to be bodies (matter) because they have weight (because of nonzero rest mass), yet they have no extension. The feature Kant took for analytic, we eventually took as dispensable, whereas the feature he took for synthetic, we have retained.


Ayer, A. J. 1946. Language, Truth and Logic. Dover.

Branden, N. 1963. Review of Brand Blanshard’s Reason and Analysis. The Objectivist Newsletter 2(2):7–8.

Browne, G. M. 2001. Necessary Factual Truth. Lanham: University Press of America.

García-Encinas, M. J. 2017. The Discovery that Phosphorus is Hesperus: A Follow-Up to Kripke on the Necessity of Identity. Analysis and Metaphysics 16:52–69.

Gendler, T. S., and J. Hawthorne, editors, 2002. Conceivability and Possibility. Oxford.

Goodman, N. 1953. The New Riddle of Induction. In Fact, Fiction, and Forecast. 4th edition. 1983. Harvard.

Gotthelf, A. and G. Salmieri, editors, 2016. A Companion to Ayn Rand. Wiley Blackwell.

Hook, S., editor, 1950. John Dewey: Philosopher of Science and Freedom. Dial.

Linsky, L., editor, 1952. Semantics and the Philosophy of Language. Illinois.

Peikoff, L. 1967. The Analytic-Synthetic Dichotomy. In Rand 1990.

Long, R. T. 2005. Reference and Necessity: A Rand-Kripke Synthesis? —Review of Brown 2001. The Journal of Ayn Rand Studies 7(1):209–28.

Quine, W. V. O. 1951. Two Dogmas of Empiricism. In From a Logical Point of View. 1953. Harvard.

——. 1982. Methods of Logic. 4th ed. Harvard.

Rand, A. 1990 [1966–67]. Introduction to Objectivist Epistemology. Expanded 2nd edition. Meridian.

Salmieri, G. 2016. The Objectivist Epistemology. In Gotthelf and Salmieri 2016.

Sidelle, A. 2002. On the Metaphysical Contingency of Laws of Nature. In Gendler and Hawthorne 2002.

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PNC Ground Shifts to the Side of the Subject – Kant IV-a

I made a mistake concerning Kant’s doctrines on logic. Relying on a smaller pool of Kant material in English, Peikoff 1964 had also made this mistake.

I asked of Kant in the Prep thread (2009 paper) as well as in this Dissertation thread: How can logic be rules necessary for correct operation of the understanding and reason if they simply are rules given by the understanding and reason, and they are rules descriptive and necessarily operative in all understanding and reason? “I concur with the conclusion of Peikoff and others he cites that once Kant had the constitution of the subject the sole source of the purely formal and purely a priori, he was not able to stably maintain an absolute necessity of PNC and other principles of logic together with their normativity, which latter entails our ability to not adhere to such principles. I add that this same irresolvable mess arises for every other sort of cognition purely formal and purely a priori, whether analytic or synthetic, once Kant has squarely located their source purely in the constitution of mind, in its fundamental dynamics, not at all in the constitution of the world.” (Kant III)

The world according to Kant—the empirical and the mathematical—cannot be found with structure contrary to the formal structure of logic provided by human mind. The source of form had moved indoors. Conformance of the world to logic is assured in Kant’s scheme; there is absolute rightness of PNC (and its cohort, identity) for the world we take up, even though PNC is ultimately sourced in pure mind. Objects of any sort can be given to us as objects only upon actuation of our conceptual, logical faculties. The portion of mind trying to discern the world beyond the world’s bare, mind-given logical form is able to commit contradictions, within Kant’s scheme. The pure understanding gives some laws, but the impure understanding may fail to always conform to them in its pursuit of specific empirical and mathematical knowledge.

We can still fault Kant in his view that we possess any “pure a priori” knowledge of any thing at all, in Kant’s radical senses of the a priori and the pure; we can deny that PNC or any other formal principle is such knowledge as that (on purity, see Chance 2018). But it is not the case that Kant’s scheme falters over the fact that humans make logical errors. (Notice Kant’s stress on human logical fallibility in lectures already from the early 1770’s; Lu-Adler 2018, 108.)

Peikoff quotes from the Abbott translation (1885) of the Introduction of Kant’s Logic (the Jäsche Logic) :How error is possible, since in the formal sense of the word, that is, how a form of thought inconsistent with the understanding is possible; this is hard to comprehend; as indeed in general we cannot comprehend how any faculty can deviate from its own essential laws” (44). But Peikoff and I failed to notice or anyway failed to address Jäsche’s words, reflecting Kant’s notes for his logic lectures, on how this problem is to be resolved (here staying with the Abbott translation): “Besides the understanding there is in us another indispensable source of knowledge. This is the sensibility, which supplies the material for thought, and besides works according to different laws from the understanding. From the senses, however, considered in and by itself, error cannot arise, since the senses do not judge. / Hence the origin of all error must be sought solely in the unobserved influence of the sensibility on the understanding, or, to speak more exactly, on the judgment. It is owing to this influence that in our judgements we mistake merely subjective reasons for objective, and consequently confound the mere semblance of truth with truth itself.” (ibid.)

Thinkers following on the heels of Kant then need not “return to an ontological interpretation of logic, thereby preserving absolutism in logic by founding it on facts of reality independent of the variable workings of human minds” else plunk for conventional choice of logical rules such as PNC, the fork proposed in Peikoff 1964. For instance Robert Hanna’s 2006 neo-Kantian, subject-sided, anti-conventionalist account of the nature of formal logic crafts a third way.


Peikoff’s reliance on Henry Mansel’s infirm understanding and adulterated representation of Kant was unfortunate. I refer specifically to Mansel’s Prolegomena Logica: An Inquiry into the Psychological Character of Logical Processes (1860). Mansel insists an empirical psychology must be put to work to “vindicate” logic. Mansel and others Mansel cites who took this post-Kantian turn were trying to keep a foot in the school of Kant (and touting themselves as significantly Kantian) while kicking that foot with the other, empiricist, Kant-undone foot. “To Psychlogy we must look for the explanation and justification of the peculiar features of Logic” (1860, 6). Not by the lights of Kant! For Kant all successful reasoning and understanding requires formal logic as a necessary presumed norm; psychology cannot attain and justify psychology’s special knowledge without thoroughly conforming itself to the general norms of formal logic, which are already presumed (further, Hatfield 1990).

When Kant was four years old, Christian Wolff was writing: “In order to demonstrate the rules of logic, principles must be taken from ontology. Furthermore, . . . we must learn from psychology what the cognitive faculty is and what its operations are. Hence it is also clear that, in order to demonstrate the rules of logic, principles must be taken from psychology. . . . Therefore, ontology and psychology should precede logic if everything in logic is to be rigorously demonstrated and if its rules are to be genuinely known.” (quoted in Lu-Adler 2018, 92)

In Wolff’s view, we have a natural aptitude to follow the prescriptions that are the principles of logic, but to cultivate that aptitude into a habit of their correct use requires learning explicitly what those rules are. The correct logical rules having become explicit are to be followed for knowledge in general, and they are discernible as the correct rules by their enablement of the complete demonstrations in mathematics, particularly in geometry (Lu-Adler 2018, 90–97).

Kant took under consideration the ancient and medieval views on logic as well as moderns such as F. Bacon, Locke, Leibniz, Wolff, and of course Baumgarten and Meier (Wolffian variants). Meier followed Wolff in taking logic-as-a-science (what Kant would later call pure general logic) to be based in part on principles of psychology. Kant was rejecting this already in the pre-Critical period of the Bloomberg logic lecture notes from the early 1770’s (Lu-Adler 2018, 110–11).

Kant regarded pure general logic as a science in his strong sense of science, in which the object of the science is treated “wholly according to a priori principles” (1786, 4:468). A science is termed proper science by Kant if it not treated only according to laws of experience and has more than mere empirical certainty. Proper science has apodictic certainty. Science more generally is “a system, that is, a whole of cognition ordered according to principles,” and “such principles may be either principles of empirical or of rational connection of cognitions into a whole” (4:467). In proper science, the connecting principles are not empirical, but the rational connection of ground to consequence. The empirical connections in chemistry do not possess the necessity that yields apodictic certainty, according to Kant. Proper science of nature has only as much apodictic certainty as there is in it a priori knowledge and application of mathematics. Empirical psychology is even farther from being a proper natural science than chemistry (4:469–71).

“A rational doctrine of nature . . . deserves the name of a natural science, only in case the fundamental natural laws therein are cognized a priori, and are not mere laws of experience. One calls a cognition of nature of the first kind pure, but that of the second kind is called applied rational cognition” (4:468, my underscore). That distinction under the terms pure and applied resembles the distinction under those same terms in Kant’s treatment of logic, although the two sorts of laws of nature, unlike principles of logic, are not norms.

(To be continued.)


Abbott, Thomas Kingsmill, trans. 1885. Kant’s Introduction to Logic. London: Longmans Green.

Allison, Henry and Peter Heath, eds. 2002. Immanuel Kant – Theoretical Philosophy after 1781. Cambridge: Cambridge University Press.

Chance, Brian A. 2018. Wolff’s Empirical Psychology and the Structure of the Transcendental Logic. In Dyck and Wunderlich 2018.

Dyck, Corey W. and Falk Wunderlich, 2018. Kant and His German Contemporaries. Vol. 1. Cambridge: Cambridge University Press.

Hanna, Robert. 2006. Rationality and Logic. Cambridge, Massachusetts: MIT Press.

Hatfield, Gary. 1990. The Natural and the Normative – Theories of Spatial Perception from Kant to Helmholtz. Cambridge, Massachusetts: MIT Press.

Kant, Immanuel. 1786. Metaphysical Foundations of Natural Science. Michael Friedman, translator. In Allison and Heath 2002.

Lu-Adler, Huaping. 2018. Kant and the Science of Logic. New York: Oxford University Press.

Mansel, Henry Longuevill. 1860. Prolegomena Logica – An Inquiry into the Psychological Character of Logical Processes. London: Oxford University Press.

Peikoff, Leonard. 1964. The Status of the Law of Contradiction in Classical Logical Ontologism. Ph.D. dissertation. New York University.

Edited by Boydstun

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PNC Ground Shifts to the Side of the Subject – Kant IV-b

Bernard Bolzano’s masterwork Theory of Science issued in 1837. In this work, we find him objecting to Kant’s definition of logic as conveyed by Jäsche: “The science of the necessary laws of understanding and reason in general, or of the mere form of thinking, is logic.” Bolzano named seven writers of logic texts since Kant who had followed Kant in that definition of logic as a science. Taking thinking in its usual wide sense, Bolzano objected to that definition. It is not a plausible characterization of logic to say logic is merely the law-governed use of reason and understanding. One could then be regarded as engaging logic when thinking fallaciously or with an aim to evasion or when thinking in a whimsical entertainment. Quite better, in Bolzano’s assessment, were several writers who had required that such laws be restricted to those serving the chosen purpose of recognizing truth (the purpose of identification, in Rand’s vocabulary and explication) to warrant the title logic.

We have seen Kant’s view that “general logic . . . abstracts from all content of cognition, i.e., from all reference of cognition to its object” (KrV A55 B79). Bolzano’s own conception of logic was as the set of rules for dividing truths into perspicacious domains of specific sciences, for their cultivation, and for their perspicacious presentation. Logic so understood is itself a science as well. We use some of these rules before turning to isolate what they are. “Once these rules are known, every science, including the theory of science itself can be further elaborated and presented in writing. This amounts to no more than arranging certain known truths in an order and connection that they themselves prescribe” (§2).

Bolzano thought the ultimate goal of logic the discovery of truth (§7). In that ambition, one is reminded of the expansion of logic envisioned in Francis Bacon’s New Organon (although Bolzano, contra Bacon, did not regard Aristotle’s syllogistic as useless). It seemed to Bolzano that “one of Kant’s literary sins was that he attempted to deprive us of a wholesome faith in the perfectibility of logic through an assertion very welcome to human indolence, namely, that logic is a science which has been complete and closed since the time of Aristotle” (§9).  Bolzano 1837 looked forward to future developments of logic that would be a boon to all the sciences. It turned out that, after Bolzano, there were advances in deductive logic. However, these did nothing to advance or clarify knowledge in empirical science. They did illuminate mathematics and its connections to logic, and they illuminated and extended the Aristotelian (and Stoic) logic of old.

Bolzano criticized the Germans such as Kant, Jakob (1791), Hoffbauer (1794), and Maimon (1794) for their slippage from the topic-neutrality of a syllogism form presented as “all A are B, all B are C, therefore all A are C” to taking the objects A, B, and C for indeterminate as to all their characteristics. That is, they erred in taking A, B, and C as empty of absolutely all content. “If we think of an object as altogether indeterminate, then we cannot claim anything about it” (§7). The signs A, B, and C need the determination that B can be rightly predicated of A, and so forth. Logical form in Bolzano’s view was not fundamentally about thoughts, but relations of truths. Bolzano correctly objected as well to contemporaries trying to make logic into some kind of empirical science of the mind.

Today when we say science, we usually mean empirical science. The term science had been used more broadly until recent times, such that science encompassed also the organized disciplines of mathematics, ethics, and logic, especially when considered in their allegedly pure, necessary, nonempirical, and applications-suspended mode.

I said in “Kant IV-a” that Kant proposed to get out of a bind—the bind of holding logical rules to be absolutely necessary rules of human mind given a priori by human mind, yet rules capable of being transgressed in operations of human mind—by a distinction of pure general logic from its application, a distinction between pure and applied logic, and  by a dissection of the latter in terms of posited cognitive powers. I want to press on the soundness of Kant’s distinction of pure and applied logic (and whether problems for Kant in this area also bear against Hanna). I also want to press on Kant’s conception that necessity in empirical science is a function of application of mathematics and of basic (Kantian) metaphysics in the empirical science.

Aristotle had noted the import of necessity by import of geometry into his account of the gross form of the rainbow.* Although, that sort of geometry application was a tidbit compared to the use of geometry by Descartes in theory of the rainbow, let alone the use of geometry by Newton in remaking the world. It was amid these modern roles for geometry that Kant did his thinking, of course.

Kant knew of Aristotle’s general doctrines on science. And via Leibniz, Kant was still hankering after them and to some extent resisting the scheme for making science brought on by Newton.

Aristotle had appealed to a mental faculty in describing how a logical principle, specifically PNC, is ascertained. That, as we have seen, was what in our time has been known as a power of intuitive induction or abstractive induction. That posit of faculty was quite opaque, and its (fallible) attachment to formal character in the world by the human mind’s proposed assimilation of said form—mind itself becoming external formalities—and Aristotle’s form-matter aspect of metaphysics were pretty roundly judged false in the modern era of philosophy (outside the preservation of Scholasticism by Catholic scholars).

I’ll close this installment by getting before us Kant’s basic treatment of the pure/applied distinction in logic.

“A logic that is general but also pure deals with nothing but a priori principles. Such a logic is a canon of understanding and of reason, but only as regards what is formal in our use of then—i.e., we disregard what the content may be (whether is is empirical or transcendental). A general logic is called applied, on the other hand, if it is concerned with the rules of the understanding as used under the subjective empirical conditions taught us by psychology. Hence such a logic empirical principles, although it is general insofar as it deals with our use of the understanding without distinguishing the understanding’s objects. . . . In general logic, therefore, the part that is to constitute the pure doctrine of reason must be separated entirely from the part that is to constitute applied (though still general) logic. Only the first of these parts is, properly speaking, a science . . . . In such pure general logic, therefore, the logicians must always have in mind two rules:

  1. As general logic, it abstracts from all content of the cognition of understanding and from the difference among the objects of that cognition, and deals with nothing but the mere form of thought.
  2. As pure logic, it has no empirical principles. Hence it does not (as people have sometimes come to be persuaded) take anything from psychology; and therefore psychology has no influence whatever on the canon of the understanding. Pure general logic is demonstrated doctrine, and everything in it must be certain completely a priori.

“What I call applied logic is a presentation of the understanding and of the rules governing its necessary use in concreto, viz., its use under the contingent conditions attaching to the subject {the mind–SB}, conditions that can impede or promote this use and that are, one and all, given only empirically. . . . Pure general logic relates to applied general logic as pure morality relates to the doctrine proper of virtue. Pure morality contains merely the moral laws of a free will as such; the doctrine of virtue examines these laws as impeded by the feelings, inclinations, and passions to which human beings are more or less subject. The doctrine of virtue can never serve as true and demonstrated science; for, just like applied logic, it requires empirical and psychological principles.” (KrV A53–55 B77–79 – Werner Pluhar translation).

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Kant IV-a  -- "A science is termed proper science by Kant if it is not treated only . . . ."

Kant IV-b -- ". . . but only as regards what is formal in our use of them . . ." / "Hence such a logic has empirical principles . . . ."

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On 3/17/2017 at 2:43 PM, Boydstun said:

The last three decades, Graham Priest and others have argued specific exceptions to the law. These exceptions seem to be such that from them no possibility of observable, concrete true contradictions can be licensed. The debate over these circumscribed candidates for true contradictions continues. I shall in this study fence them off, without disposition, from our still very wide purview of PNC.

To show that contradictions don't exists, does one have to go through the history of philosophy? (this is a serious question). I have met some people that will argue Graham Priest's case and I can't briefly counter it. I was wondering if there is such a summary that takes care of it convincingly.

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ET, if one is interested in that contemporary rarified controversy, I suggest study of the book The Law of Non-Contradiction (2004), edited by Priest, Beall, and Armour-Garb. The fourth Part of the book contains the papers countering Priest et al. One of those papers in defense of PNC, the one by Edward Zalta, is available online here. I do not personally expect to become competent in that controversy, as I’ve far more of greater interest to me than can be explored in the remainder of my life, even were I to keep cranking another twenty years (I’m seventy-one). I take PNC as universally correct in my meaning of the principle and take it correct for any philosophy I make. I do have an original dissection of PNC in terms of subject and object components, which is included in a paper to be published in several months, but that has no implications for those dialetheism controversies so far as I know.

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