Necessity and Form in Truths

[Boydstun]

Necessity and Form in Truths

In this study, I firstly examine the Objectivist account of how Rand’s theory of concepts dissolves the customary distinction of truths into ones true in virtue of meaning and ones true in virtue of experience. Although that particular character of concepts in Rand’s mold of them does dissolve that wrong divide of truths—the analytic-synthetic divide—I advance an additional character of her theory, one more peculiar to hers, that also dissolves the A-S division, at least when her theory is set in my ontology. In that residence, concretes as in the world, as in fact, possess form in their situation, passage, and character, I show that the two sorts of necessity traditionally attached respectively to analytic truths and synthetic truths are rightly dissolved and replaced by a single necessity attending a single compounded formula of truth familiar from Rand. This necessity is not a compound of the two necessities, logical and physical, characterized by supporters of the A-S division. It is, rather, a compound of necessity-for of life and of living mind in grasping fact, the realm of necessity-that. I exhibit this single necessity attending truths in logic, truths in mathematics, and truths of concretes tooled by logical and mathematical truths.

[Boydstun]

Part 1 – Leonard Peikoff*

By truths I mean, as Ayn Rand meant, “recognitions of facts of reality” which is to say “identifications of existents” (ITOE 48). Without living, fallible minds, there are no truths in this sense of the word. The world would have facts, but until some are recognized, no truth would have come into the world.

Truth is sometimes used to mean what here is meant by fact. That is not the way I mean truth here nor the way Rand or Peikoff used it.

Leonard Peikoff’s 1967 essay “The Analytic-Synthetic Dichotomy” (ASD) set out the basics of the contrasting sorts of truths—analytic and synthetic—the way the distinction had been cast up to middle of the 20th century. Analytic truths had been lately taken as true in virtue of their meaning. Rationality and animality would be included in the meaning of the concept man. So the truth “man is a rational animal” would be an analytic truth, a truth made so by definition, which under contemporary nominalism had become a matter of social convention, pretty arbitrary, free of much constraint by facts of the world. Necessity in such a truth would be from the say-so in our definitional prescription.[1]

That choice of convention, I notice, satisfies a necessity of self-consistent, coherent thinking and talking. Such necessity lies among the class of necessities for a purpose, necessities for an end. I call this class necessity-for.

The truth “man has only two eyes” would not be analytic, the story went, because the feature of having only two eyes is not part of the meaning of the concept man. Such a truth is known as synthetic. Unlike analytic truths, which are necessarily true, a synthetic truth is said to be only contingently true.

Peikoff argued this to be a false dichotomy among truths. The historical root of this widespread falsehood in philosophy, Peikoff maintained, is the Platonic theory that only essential characteristics of a thing are part of the form of a thing and its definition. The inessential, which is from the material aspects of a thing, not its formal aspects, are not part of a thing’s definition. 

I concur in Peikoff’s discernment that the false dichotomy in truths between those analytic and those synthetic has a distant ancestor in a false dichotomy in Plato. In Cratylus Plato has Socrates uphold the principle that contrary attributes never belong to a fully real thing simultaneously and the principle that “things have some fixed being or essence of their own. They are not in relation to us and are not made to fluctuate by how they appear to us. They are by themselves, in relation to their own being or essence, which is theirs by nature” (386d–e; see also Euthyphro 6d–e; Phaedo 65d, 75c–d, 78d, 100c; Republic 475e–76d, 479–80). Each thing has attributes such as shape, sound, or color; but in addition, each thing has a being or essence. Indeed, “color or sound each have a being or essence, just like every other thing that we say ‘is’” (Cra. 423d–e). Plato maintained moreover that what each thing essentially is, such as Man, Good, Size, or Strength is not discovered by sight or hearing, but by reason when it is most free from bodily, sensory distractions (Phd. 65, 74–75, 78c–79d, 83, 86, 96–105; Theaetetus 184b–87a).

The character of each thing that is always the same is a kind—call it a Form—that is “a being itself by itself” (Parmenides 135a–c). Sensory perceptions are as shadows and reflections of these intelligible forms, these intrinsic natures, these essences and being of things (Rep. 509d–e). Plato had no notion of ideas or concepts encompassing both visible forms (such as shapes, sounds, or colors) and intelligible forms.[2] Modern notions of concepts or ideas are, in Plato’s frame, only our thoughts grasping intelligible forms.[3]

Peikoff acknowledged, correctly, that Aristotle breathed new life into this Platonic error by bringing essences down from some purely intellectual nether-realm to the material world open to regular senses.[4] Aristotle is the heavy-weight instigator of the necessary-contingent divide and the essence-accident divide. These doctrines constrained Scholastic theories of universals, concepts, and predication, and facilitated the modern A-S divide.

Peikoff observed that Rand’s conception of the concept of a thing, and her conception of the essential in the concept, rules out an A-S partition of the kinds of conceptual truth in our possession. A thing is all the things that it is (ASD 98). I might add that Rand took a thing’s external relationships as part of what a thing is, a blunt contrast with Plato (ITOE 39). And in Rand’s epistemology, we can have a conception of all that a thing is, including all its external relationships and all its potentials, even though we know our present concept of the thing contains only a portion of that totality of its identity.  

In Rand’s conception of right concepts, they are “classifications of observed existents according to their relationships to other observed existents” (ITOE 47).[5] Furthermore: “Concepts stand for specific kinds of existents, including all the characteristics of these existents, observed and not-yet-observed, known and unknown” (ITOE 65). Objectivist epistemology does not regard the essential and the non-essential characteristics of existents as simply given, as if in an intellectual intuition. Rather, that distinction is based on our context of knowledge of the facts of existents (ITOE 52; ASD 107, 101–103).

“To designate a certain characteristic as ‘essential’ or ‘defining’ is to select, from the total content of the concept, the characteristic that best condenses and differentiates that content in a specific cognitive context. Such a selection [in Objectivist epistemology] presupposes the relationship between the concept and its units [its member elements in reality regarded as substitutable for each other under suspension of their particular measure-values of their shared characteristics]: it presupposes that the concept is an integration of units, and that its content consists of its units, including all their characteristics.” (ASD 103)

Nelson Goodman had written 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).

I’ll examine the cases mounted against the A-S distinction by White and by Quine, and compare them to the Objectivist case, in the next two installments.[6]

(To be continued.)

Notes

[1] Brand Blanshard’s book Reason and Analysis appeared in 1962. It was reviewed favorably by Nathaniel Branden the following year. Branden understood that Blanshard was some sort of absolute idealist, but the book offered access to contemporary positivist and analytic philosophy (including the A-S distinction), and it offered criticisms of them, which Objectivists might join. Against say-so free of constraints from conditions of the world being the source of necessity in necessary truths, see Rasmussen 1982. On the nature and need of understanding for truth, see Haugeland 1998.

[2] Cf. Metaphysics 987b1–13; Notomi 2005, 193–201.

[3] See further, Kraut 1992, 7–12; White 1992.

[4] ASD 95. See also Peikoff 1972, 191, on Aristotle’s influential division of the necessary and the contingent. On medieval and early modern roots of the false A-S dichotomy, see Peikoff 1964, 15–16, 45–59.

[5] Concept empiricism is defended and a version of it, thickly informed by pertinent modern science, is formulated in Prinz 2002.

[6] White 1952 appeared originally in Hook 1950. Sidney Hook would a few years later become Peikoff’s dissertation advisor. Recent defense of the A-S distinction against the attack by Quine is Russell 2008. Additional contemporary debate on the issue is Juhl and Loomis 2010. I’ll not undertake assimilation of these in the present study.

References

Aristotle B.C.E. 348–322. Metaphysics. C.D.C. Reeve, translator. Indianapolis: Hackett.

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

Goodman, N. 1953. The New Riddle of Induction. In Fact, Fiction, and Forecast. 4^th edition. 1983. Cambridge, MA: Harvard University Press.

Haugeland, J. 1998. Truth and Rule-Following. In Having Thought. Cambridge, MA: Harvard University Press

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

Juhl, C., and E. Loomis. 2010. Analyticity. New York: Routledge.

Kraut, R. 1992. The Cambridge Companion to Plato. Cambridge.

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

Notomi, N. 2005. Plato’s Metaphysics and Dialectic. In A Companion to Ancient Philosophy. M. L. Gill and P. Pellegrin, editors. Wiley-Blackwell.

Peikoff, L. 1964. The Status of the Law of Contradiction in Classical Logical Ontologism. Ph.D. ProQuest.

——. 1967. The Analytic-Synthetic Dichotomy. In Rand 1990.

——. 1972. Founders of Western Philosophy: Thales to Hume. Lectures by Leonard Peikoff. M. Berliner, editor. 2023. Santa Ana, CA: Ayn Rand Institute Press.

Plato c. 428–348 B.C. Plato – Complete Works. J. M. Cooper, editor. 1997. Indianapolis: Hackett.

Prinz J., 2002. Furnishing the Mind – Concepts and Their Perceptual Basis. Cambridge, MA: MIT Press.

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

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

Russell, G. 2008. Truth in Virtue of Meaning. New York: Oxford University Press.

White, M. G. 1952 [1950]. The Analytic and the Synthetic: An Untenable Dualism. In  Linsky 1952. Included also in White 2004. http://www.thatmarcusfamily.org/.../White%20-%20Analytic... 

——. 2004. From a Philosophical Point of View. Princeton: Princeton University Press.

White, N. 1992. Plato’s Metaphysical Epistemology. In Kraut 1992.

 

Edited February 26 by Boydstun

[Boydstun]

Part 2 – Morton White*

Let me abbreviate the title of White’s 1952 paper by UD (for Untenable Dualism).

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 (1952, 330). He urged rejection of both of these affiliates due to the divisional sharpness falsely maintained for them.

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” (ASD 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” (Ayer 1946, 77; ASD 94, 101, 111–18; Branden 1963, 7).

Whether one were to take analytical truths to be identical with or based on logical truths, I say that the Objectivist view of logic (with which I agree) does not allow the inference of Ayer and others that logical truths are not informed by fact. Logic on our view is a tool we use in identifications of existents. Logical truths are in no way prior to other truths, ones having empirical content. We learn the logical principle of Excluded Middle in an elementary logic course, but that learning is really an explicit articulation of a principle we have already found effective and reliable in thinking about the world we are negotiating.

Either there is a bear sleeping beside the mail box OR there is not. Either I will continue to work on this project non-stop for two more hours from now OR not. Either vampires exist OR not. But there is a limited proper vista on the world within which the principle is sensible if our use of it is in pursuit of identifications of existents. It is nonsense to say that either there are some things existing in the world OR not. The effectiveness and range of sensible employment of the logical principle is learned from experience, and the concept of existence and its totality is learned by experience. The fact that the sensible range of the principle is so wide that it is convenient to indicate its general form as “A or Not-A” does not give us license to suppose there are no limits on sensible “applications” of the Principle of Excluded Middle or to suppose we do not learn that principle by experience.

With that Objectivist view of elementary logic, they can say one thing what Morton White did not say: One’s concept of what is an analytic truth by identifying the analytic with the logical or basing the analytical on the logical does nothing to show that any purported analytical truth is entirely independent of experience, that it bears no information about existence at all, or that a purported analytical truth is made true and derives its necessity of being true by social convention untethered from facts of the empirical world.

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 amounts 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”, by substitution of identicals, we obtain (iii) Every man is a rational animal (UD 319).

So some might propose that analyticity is explicated in terms of logical truth and synonymy, as in the preceding paragraph. White rejects the view that whether “man” and “rational animal” are synonymous is a matter of arbitrarily selected convention. Similarly, that “man” and “animal who can skip” (my example, demonstrated, along with other distinctly human moves here [Tina]) 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).

Could analytic statements be defined instead as those whose denials are self-contradictory? (UD 325–26). White argues that denials of such propositions as “Not every man is a rational animal” are not contradictions, but his concept of contradiction is, in step with dominate contemporary views of logic, too narrow, as I have elaborated above in connection with Ayer.

White did not relate this criterion for analyticity to Kant, but I should do so. One of Kant’s characterizations of analytic judgments is that in them the predicate is “thought through identity” with thought of the subject. Synthetic judgments connect predicate to subject, but not in the relation of identity (KrV A6–8 B10–12), where simple complete identity is meant, not Rand’s more expansive notion of identity as some or other distinctive traits belonging necessarily to anything that exists.[1] According to Kant, all judgments must conform to the principle of self-consistency, but only judgments certifiable by self-contradiction upon denial alone, apart from their truth in experience, are analytic (A151–53 B190–93; 1783, 4:266–70; 1790, 8:228–30, 244–45; Allison 2004, 89–93; Garrett 2008, 204–6).

I object that contradiction upon denial is no genuine grounding of any truth. If we start with a truth and then show that upon denial of it we arrive at a contradiction, well isn’t that cute? But establishment of its truth is elsewhere. 

Morton White found 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 not a skipper,” White responds 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 skipper,” 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). Objectivism can add that there is no qualitative divide in the purported divide analytic/synthetic because elementary logic is based on the widest-frame, worldly facts that existence exists and existence is identity, in Rand’s expansive sense of identity. White did not surmise that the merely-difference-of-degree in our sense of wrongness in “Man is not a rational animal” and in “Man is not a skipper” might be because a thing is everything that it is, as was later underscored by Peikoff in ASD.

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 330). This kinship was also recognized in Peikoff (ASD 95), as I remarked earlier. But Peikoff went further: He observed that essentials of a thing do not exhaust what a thing is. No concepts of a subject are concepts of only what are the essentials in the definition of the subject.

(To be continued.)

Note

[1] Joseph Butler (1692–1752) stated: “Everything is something or other.” Taken as the Principle of Identity, it is expansive. This expansive concept of identity is championed in Oderberg 2007, chap. 5. 

References

Allison, H. 2004 [1983]. Kant’s Transcendental Idealism. Revised and enlarged edition. New Haven: Yale University Press.

Allison, H., and P. Heath, editors, 2002. Immanuel Kant: Theoretical Philosophy after 1781. Cambridge: Cambridge University Press.

Ayer, A. 1946. Language, Truth, and Logic. New York: Dover.

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

Garrett, D. 2008. Should Hume Have Been a Transcendental Idealist? In Kant and the Early Moderns. D. Garber and B. Longuenesse, editors. Princeton: Princeton University Press.

Linsky, L., editor, 1952. Semantics and the Philosophy of Language. Champaign-Urbana: University of Illinois Press.

Kant, I. 1781(A), 1787(B). Critique of Pure Reason. W. Pluhar, translator. 1996. Indianapolis: Hackett.

——. 1783. Prolegomena to Any Future Metaphysics That Will Be Able to Come Forward as Science. G. Hatfield, translator. In Allison and Heath 2002.

——. 1790. On a Discovery Whereby Any New Critique of Pure Reason Is to Be Made Superfluous by an Older One. H. Allison, translator. In Allison and Heath 2002.

Oderberg, D. 2007. Real Essentialism. New York: Routledge.

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

Quine, W. 1951. Two Dogmas of Empiricism. In From a Logical Point of View. 1953. Cambridge, MA: Harvard.

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

White, M. 1952 [1950]. The Analytic and the Synthetic: An Untenable Dualism. In  Linsky 1952. Included also in White 2004.

——. 2004. From a Philosophical Point of View. Princeton.

[Boydstun]

Part 3 – Quine, Objectivism, Resonant Existence – Α

A sharp distinction between analytic and synthetic statements, propositions, and judgments had been important in the modern empiricist philosophy received by Quine. In the present Part and the next, I set out the relation of Quine’s opposition to the distinction in the 1950’s to the Peikoff-Rand opposition to the distinction in the following decade. I emphasize a major problem, tackled earlier by Kant, as reason the dichotomous distinction had been important. That is, I emphasize the problem it had been set to solve in a way not Kant’s.

The characterization and responsibilities of analytic statements in sharp contrast to synthetic statements put forth in Logical Empiricism (also called Logical Positivism) constituted an alternative solution to that old problem, alternative to Kant’s solution. I shall step back in the next Part to more of Carnap and the response of Quine to him, and step back to the epistemological problem that had arisen in Kant. I’ll formulate a new solution, one in some affiliation with Rand’s theoretical philosophy and her theory of value. Form and necessity will enter, and I’ll assess Peikoff’s ASD against my layout.[1]

“[Quine] is perhaps best known for his arguments against Logical Empiricism (in particular, against its use of the analytic-synthetic distinction). This argument, however, should be seen as part of a comprehensive world-view which makes no sharp distinction between philosophy and empirical science, and thus requires a wholesale reorientation of the subject” (Hylton and Kemp 2023)

Quine held that the best science we have garnered is the best ultimate truth at present we have of the world. He did not see logical principles such as the law of excluded middle as arising from ontology, but as a principle of convenience pervasive in knowledge. I should say that dichotomy between those two candidate bases is false. I go with Rand’s picture of elementary logic, as a certain pervasive character of method in successful identifications of reality. Such existence-based logic infuses any higher logic naturally appropriate in attainment of ordinary and scientific knowledge. I add that excluded middle is a tooling formality for a living mind. It is not a formality belonging to concretes in their actuality and independently of the existence of living mind discerning them, by thought, in their concrete identities. Further, in my system (2023), alternatives of any sort do not exist in the universe at all until life enters the scene, and all alternatives, however high in the intellect, are descendants of the fundamental alternative that Rand exposed as uniquely facing the living: continuation of maintaining life or termination of life. 

We have mind, I say, capable of getting knowledge of concretes in part by use of principles of logic and mathematics tooled from formalities that belong to concretes. Identities of concretes—their characters, situations, and passages—can be formalities belonging to concrete existents, where discernment of those formalities is by thought engaged in elementary experience of ordinary objects in the world. Belonging-formalities such as a broad-form principle of identity “Existents have identity, and existence of the latter in full just is the former” can be assimilated and tooled by thought into further formalities tethered to belonging-formalities. The principle of excluded middle, for example, can have a tether to belonging-identities as well as to the high-powered human mind. In other words, we need not begin with logic, then use it in grasping the world, as Quine would have it. No, we begin with the world, including its identities in belonging-formalities, the world in ordinary human experience. When retaking the world in science, we wield formal tools with some tethers, by ancestry, from the world of ordinary experience.

Which tooled formalities of logic and mathematics are best suited to which parts of the world is a further intellectual enterprise. Minkowski geometry can be weighed against 4D Euclidean geometry for most faithful and most effective tool for comprehending physical flat spacetime. Aristotle’s syllogistic and second-order logic can be weighed against Quine’s choice.[2] 

Quine aimed to integrate knowledge historical, knowledge scientific, including psychology, and knowledge philosophical. I notice, whole truth be told, he ended up smashing against early-childhood cognitive developmental psychology in the second half of the twentieth century, from his armchair.  Elizabeth Spelke remarked: “Our research provides evidence, counter to the views of Quine (1960) and others, that the organization of the world into objects [in comprehension] precedes the development of language and thus does not depend upon it. I suspect, moreover, that language plays no important role in the spontaneous elaboration of physical knowledge” (Spelke 1989, 181).

The reorientation between science and philosophy sought by Quine is wholesome, I should say. Ayn Rand remained in the old outlook from the philosopher’s chair. She took the sciences, including the modern hard sciences, to be in a one-way need of philosophy, especially in epistemology.[3]

“Philosophy is a necessity for a rational being: philosophy is the foundation of science, the organizer of man’s mind, the integrator of his knowledge, . . .” (Rand 1975, 82; also ITOE 74). “Science was born as a result and consequences of philosophy; it cannot survive without a philosophical (particularly epistemological) base” (Rand 1961, 44; also 26–27). Rand acknowledged that scientific biology informed her concept of the general nature of life that she employed in her theory of ethics. (More generally, on the influence of biology on philosophy, see Smith 2017.) A bit of measurement theory informed Rand’s theory of concepts. A bit of Helmholtz, her thoughts on music.

Rand acknowledges no cases in which science begat or informed philosophy in metaphysics or epistemology. I disagree. Harmonics, geometry, and astronomy existed before Aristotle, before his metaphysics or his theory of science or his organization of logical deduction. Aristotle’s empiricism was a boost to sciences (De Groot 2014), but harmonics, geometry, and astronomy were not inaugurated by systematic explicit philosophy (see e.g. Graham 2013). The idea of a physical law mathematical in expression was not invented by philosophers. Nor the need to look for certain symmetries and symmetry breaking in comprehending parts of physical reality (see Schwichtenberg 2018 [2015]; Healey 2007).

From Plato-Aristotle to the present, where theoretical philosophy flourished, it was shaped by received mathematics and science (Netz 1999; Bochner 1966). Concerning science in our own time, contra Rand, it has not declined in comparison to advances in the nineteenth century, which Rand had maintained in support of the idea that bad strains of modern philosophy have led to a decline in scientific achievements (Rand 1975, 78). Modern hard sciences have continued their stampede to the present time, and cognitive developmental psychology arising in the second half of the twentieth century continues bringing new light to the present. 

To be sure, scientists operate within a general metaphysics they hold, and as Michael Friedman has illustrated, this may be especially useful for resolutions during a time of fundamental innovations in the course of science (2001, chap. 4). Scientists have also been innovators in methods of investigation, theoretical, observational, and experimental. In that we might say they have on a philosophical hat. But I object to the picture that full-tilt philosophers come up with valid methods of rational scientific inquiry independently of existing science, methods not already in the heads and hands of scientists rolling back the darkness.

(To be continued.)

Notes

[1] Recall that “Resonant Existence” is my own philosophy, whose fundamentals in theoretical philosophy are set out in my paper “Existence, We.” The overlap between my philosophy and Rand’s theoretical philosophy and her theory of value are extensive, although, the differences are substantial.

[2] Bivalent, first-order https://plato.stanford.edu/entries/logic-firstorder-emergence/ predicate logic with identity [such has been proven complete]) for best truth-preserving tool in science. I might add, it seems fine tooling-form logical structure of natural-language thought on the world, at least when this much classical logic is bound additionally to existence by relevance logic. https://plato.stanford.edu/entries/logic-relevance/

[3] But consider Sciabarra 2013 [1995], 121–23.

References

Bochner, S. 1966. The Role of Mathematics in the Rise of Science. Princeton: Princeton University Press.

Boydstun, S. 2021. Existence, We. The Journal of Ayn Rand Studies. 21(1):65–104.

Friedman, M. 2001. Dynamics of Reason. Stanford: CSLI.

De Groot, J. 2014. Aristotle’s Empiricism. Las Vegas: Parmenides.

Graham, D.W. 2013. Science before Socrates. New York: Oxford University Press.

Healey, R. 2007. Gauging What’s Real – The Conceptual Foundations of Contemporary Gauge Theories. New York: Oxford University Press.

Hylton, P. and G. Kemp 2023. Willard Van Orman Quine. Online Stanford Encyclopedia of Philosophy.

Netz, R. 1999. The Shaping of Deduction in Greek Mathematics – A Study in Cognitive History. Cambridge: Cambridge University Press.

Rand, A. 1961. For the New Intellectual. New York: Signet.

——. 1975. From the Horse’s Mouth. In Rand 1982.

——. 1982. Philosophy: Who Needs It. New York: Signet.

——. 1990 [1966–67]. Introduction to Objectivist Epistemology. Expanded 2^nd edition. Meridian.  

Schwichtenberg, J. 2018 [2015]. Physics from Symmetry. 2nd edition. Cham, Switzerland: Springer.

Sciabarra, C. 2013 [1995]. Ayn Rand: The Russian Radical. 2nd edition. University Park, PA: Penn State University Press.

Smith, D.L., editor, 2017. How Biology Shapes Philosophy. New York: Cambridge University Press.

Spelke, E. 1989. The Origins of Physical Knowledge. In Weiskrantz 1989.

Weiskrantz, L. editor, 1989. Thought without Language. Oxford: Clarendon Press.

[Boydstun]

INTERLUDE

 

Three handy and highly informative articles pertinent to this present essay:

 

The Analytic/Synthetic Distinction

 

Carnap versus Quine on the Analytic-Synthetic Distinction

 

The Analytic-Synthetic Distinction and the [Quine's] Argument against Logical Empiricism

 

Edited February 26 by Boydstun

[Boydstun]

SIDEBAR

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 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. I'll be digging through the Carnap-Quine briar patch in the next installment of the present study (along with Neo-Kantianism, Logical Empiricism, and of course Kant).

*I stopped posting at that site a year ago, when the owner covertly deleted a post of mine partly critical of Donald Trump.

~References~

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

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

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.

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

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

[monart]

Thank you for your comparisons between Rand-Peikoff's and the others' rejection of the analytic-synthetic dichotomy, the latter of which I knew little about before. I'm just beginning to browse through your prolific work on philosophy llisted on your profile. And I'm looking forward to further postings from you on this topic of necessary truths, and to your explanation of necessity as "a compound of necessity-for of life and of living mind in grasping fact, the realm of necessity-that".

[Boydstun]

Part 3 – Quine, Objectivism, Resonant Existence – Α’

How did Newton (1687) show that the force that causes unsupported objects to fall here on the surface of the earth is the same force that causes earth to orbit the sun? Not as the schoolman Theodoric of Freiberg (d. c.1310), nor as Descartes (1637), scientifically comprehended the formation of rainbows in the sky. Theirs was physical science contributing to understanding in their problem area.

But no, Newton’s effective method for showing expanse of gravitation beyond the earth, his most important problem area, was by bringing geometry and limit-process thought into the service of quantitative representation of force exerted by the sun on its orbiting planets and exact forms of orbits that would result from the various strengths of various candidate central forces specified by their various mathematical forms (Brackenridge 1995 and Harper 2011). Newton’s method on this problem laid the foundation for all subsequent methods of theoretical physics. Newton’s achievement will be the kickoff caught by Kant which, together with Kant’s reception of the old gold of Euclidean geometry, will set in motion a locomotive of thought on to the analytic-synthetic sharp distinction I shall trace and dismantle in §B.

Rand refused the conceptions of science and its relation to philosophy put forth by the early moderns, the rationalists and the empiricists. She maintained that science under the rationalists’ picture of reason and its relation of mind to the world had  “indiscriminate contents of one’s consciousness as the irreducible primary and absolute, to which reality has to conform” (1961, 28). She understood rationalists as maintaining that “man obtains his knowledge of the world by deducing it exclusively from concepts, which come from inside his head and are not derived from the perception of physical facts” (1961, 30; see Descartes’s fourth Meditation).

That is not how Descartes discovered how the rainbow comes about nor how he thought reason should proceed in such an inquiry (Garber 2001, 94–110; Dika 2023). We should notice that Rand did not recommend as remedy for rationalism and its alleged purport for physical science a reintroduction of such things as Aristotle-inspired substantial forms in natural philosophy down from Aquinas and Suarez, against which Descartes had rebelled and had replaced with mechanism (Garber 1992; Garber 2001; Garber and Roux 2013).

From the time of Plato and Aristotle through Descartes and Leibniz, philosophy of nature and physical science were not sharply distinguished as we think of them today. Edward Grant concludes that without the high development of natural philosophy attained between 1200 and 1600, the scientific revolution would not have come about (2007, 329).

William A. Wallace (1923–2015) argued that Thomist Aristotelianism in logic and natural philosophy was the best frame fitting the natural world and the advance of modern science. He embedded the scientific advance of Theodoric on theory of the rainbow into Aristotle’s four causes, stressing the continuity between Aristotelian science by qualitative natures and Theodoric’s quantitative methods and conferring absolute certainty of the scientific results by their rendition into Aristotelian demonstrative form of science.

From Rand’s outlook on the relationship of philosophy and physical science, such would be a smothering and hand-maid casting of science by overblown (and faulty) metaphysics (ITOE 273). On the side of consonance with Wallace, however, Rand’s view, in which the import of metaphysics to physics is modest, would not entail a whole dismissiveness up front of Wallace’s 1992 (Chps. 4–6) intellectual archeology of Galileo’s methodological connections, logical and historical, with the Aristotelian epistemological template for science. Rand’s epistemology and metaphysics, to be sure, are in considerable opposition to that template, by her departures from Aristotle on essence, form, causation, universals, and definition. Galileo’s philosophical framework was not Rand’s more modern one, but he famously freed himself of much encumbrance from Aristotelian natural philosophy and got some new and true science crucial for Newton. 

I have noted the radical opposition between, on the one hand, conception of science under Rand’s general metaphysics and epistemology and, on the other hand, what she thought to be the rationalist method for science (see also Rand 1970). One difference between Descartes’ actual method from standard scientific method today, with which latter, Rand’s theoretical philosophy is aligned: for Descartes, observations and experiments serve only to illustrate and reinforce implications of scientific theory bound up with natural philosophy, and first-philosophy, which has already settled that the scientific theory is true. An observation at odds with the rationalist scientific theory would be suspected of error by the rationalist inquirer of those days. Results from the laboratory were not tests against which the theory stands or falls.

Rand saw the classical modern empiricists as “those who claimed that man obtains his knowledge from experience, which was held to mean: by direct perception of immediate facts, with no recourse to concepts” (1961, 30). She saw them as clinging to reality by abandoning their mind. She thought her own theory of concepts filled the large gaps in the rationalist and empiricist theories of knowledge (1970, 89–90), by her tie of concepts (and reason, I might add) to concrete particulars. I hope some day to uncover whether what is distinctive to her theory of concepts—its cast in terms of magnitude structure among particulars subsumed under a concept—solidifies the tie Rand thought she had attained and its rescue of knowledge, ordinary and scientific, from rationalism and empiricism, classical and modern (Logical Empiricism).

Rand maintained that failures of modern philosophy to mount an adequate defense of rational knowledge, including science, against Cartesian and Humean skepticism needed (i) a correct theory of universals and concepts, (ii) a defense of the validity of the deliverances of the senses, and (iii) a validation of inductive inference.[1]

The first as provided by Rand can correct rationalist and empiricist failures in adequately accounting for modern scientific knowledge provided someone yet-to-come can develop further the measurement structure in empirical concepts and show how Rand’s theory of concepts in its true distinctiveness can be extended to mathematical knowledge. Knapp 2014 advertised the latter, but failed to deliver. The second was accomplished in Kelley 1986. The third was attempted within Harriman 2010, which advertised, but failed delivery in the same way as Knapp 2014.

Both the Harriman book and the Knapp one did not make central, deep connection between the nature of modern science and what is Rand’s truly distinctive aspect of concepts in general: its structuring of concepts by measurement ommisions along concepts’ dimensions capturing concretes and their world-given relations. Still, these books are profitable reads as among contemporary realist casts of modern science and mathematics. These two informative Objectivist books, of course, are written in an era in which science and mathematics have become sharply distinct from philosophy and in which much more science and mathematics has been established than at the time of Theodoric, Galileo, Descartes, and Newton. To those Objectivist works should be joined the Objectivist-neighbor realism of Franklin 2014 and Dougherty 2013 from the Aquinas-Aristotelian framework.[2]

In the next installment (§B), we’ll travel the road: Kant, Neo-Kantianism, and Logical Empiricism to Carnap v. Quine on the analytic-synthetic distinction to Peikoff’s tackle of ASD and to my own.

(To be continued.)

Notes

[1] To succeed in accounting for mathematical knowledge, Rand’s theoretical philosophy actually needs a renovation in her general ontology, specifically, a renovation (not possible since Rand is deceased and her philosophy is handily taken as in stasis—identifiably what philosophy she made, just that, as-is) that lands as my own layout of the divisions of Existence (2021). Within my layout, pure mathematics is study of the formalities of situation, some such forms belong to concretes given in perception, and the fundamental contrast of the concrete is not the abstract, but the forms belonging to concretes.

[2] Some additional contemporary work on the relations of metaphysics to science and on realism in science: Maudlin 2007; Chakravarttty 2007; Mumford and Tugby 2013; Morganti 2013; Ross, Ladyman, and Kincaid 2013. 

References

Boydstun, S. 2021. Existence, We. The Journal of Ayn Rand Studies. 21(1):65–104.

Brackenridge, J.B. 1995. The Key to Newton’s Dynamics – The Kepler Problem and the Principia. Berkeley: University of California Press.

Chakravartty, A. 2007. A Metaphysics for Scientific Realism. New York: Cambridge University Press.

Descartes, R. 1637. The World and Other Writings, Appendix 2. S. Gaukroger, translator. 1998. New York: Cambridge University Press. 

Dougherty, J.P. The Nature of Scientific Explanation. Washington D.C.: The Catholic University of America Press.

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

Garber, D. 1992. Descartes’ Metaphysical Physics. Chicago: University of Chicago Press.

——. 2001. Descartes Embodied. New York: Cambridge University Press.

Garber, D. and S. Roux, editors, 2013. The Mechanization of Natural Philosophy. Dordrecht: Springer.

Grant, E. 2007. A History of Natural Philosophy. New York: Cambridge University Press.

Harper, W.L. 2011. Isaac Newton’s Scientific Method. New York: Oxford University Press.

Harriman, D. 2010. The Logical Leap – Induction in Physics. New York: New American Library.

Knapp, R.E. 2014. Mathematics Is about the World. Lexington, KY.

Kelley, D. 1986. The Evidence of the Senses. Baton Rouge: Louisiana State University Press.

Maudlin, T. 2007. The Metaphysics within Physics. New York: Oxford University Press.

Morganti, M. 2013. Combining Science and Metaphysics – Contemporary Physics, Conceptual Revision and Common Sense. New York: Palgrave Macmillan.

Mumford, S. and M. Tugby, editors, 2013. Metaphysics and Science. New York: Oxford University Press.

Newton, I. 1687 (1713, 1725). Mathematical Principles of Natural Philosophy and System of the World. 3rd edition. A. Motte (1729) and F. Cajori (1934), translators. Berkeley: University of California Press.

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

Rand, A. 1961. For the New Intellectual. Title essay. New York: Signet.

——. 1970. Kand versus Sullivan. In Rand 1982.

——. 1982. Philosophy: Who Neds It. New York: Signet.

——. 1990 [1966–67]. Introduction to Objectivist Epistemology (ITOE). Expanded 2^nd edition. New York: Meridian.  

Ross, D.J., J. Ladyman, and H. Kincaid, editors, 2013. Scientific Metaphysics. Oxford: Oxford University Press.

Wallace, W.A. 1959. The Scientific Methodology of Theodoric of Freiberg. Fribourg: Fribourg University Press.

——. 1992. Galileo’s Logic of Discovery and Proof. Dordrecht: Kluwer.

[monart]

Thanks. I can follow much of what you're saying, mainly because of my previous readings of Rand's, Peikoff's, Kelley's, and Harriman's writings, even if I don't have any comments to offer now. And I assume I'm being prepared for your upcoming explanation of "necessity-for' and necessity-that"

[Boydstun]

Correct, Monart.

This got to be a longer road than I had in mind at the beginning, but that is giving it full due weight.

And I'm going to get to each promised component.

[monart]

On 3/21/2024 at 9:10 PM, Boydstun said:

Rand maintained that failures of modern philosophy to mount an adequate defense of rational knowledge, including science, against Cartesian and Humean skepticism needed (i) a correct theory of universals and concepts, (ii) a defense of the validity of the deliverances of the senses, and (iii) a validation of inductive inference.[1]

The first as provided by Rand can correct rationalist and empiricist failures in adequately accounting for modern scientific knowledge provided someone yet-to-come can develop further the measurement structure in empirical concepts and show how Rand’s theory of concepts in its true distinctiveness can be extended to mathematical knowledge. Knapp 2014 advertised the latter, but failed to deliver. The second was accomplished in Kelley 1986. The third was attempted within Harriman 2010, which advertised, but failed delivery in the same way as Knapp 2014.

How close does Harriman's book come to validating induction (for Physics)? How close does it come to validating induction in other fields like Psychology or Ethics? What would be a complete, successful validation of any method of induction?

Do you know of "someone yet-to-come" who could extend Rand's "measurement structure"? Do you yourself have some ideas about how to go about it? Have you written any overview of your philosophy, how it complements or expands Objectivism, or generally the ways in which Objectivism as a philosophy (or as an intellectual movement) could be developed further?

[Boydstun]

3 hours ago, monart said:

How close does Harriman's book come to validating induction (for Physics)? How close does it come to validating induction in other fields like Psychology or Ethics? What would be a complete, successful validation of any method of induction?

Do you know of "someone yet-to-come" who could extend Rand's "measurement structure"? Do you yourself have some ideas about how to go about it? Have you written any overview of your philosophy, how it complements or expands Objectivism, or generally the ways in which Objectivism as a philosophy (or as an intellectual movement) could be developed further?

The books by John D. Norton on induction look excellent: The Material Theory of Induction (2021) and The Large-Scale Structure of Inductive Inference* (forthcoming, 2024) look to be illuminating. They would not be expressly hooked to Rand's metaphysics or theory of concepts. Upon studying these Norton books, concord and discord with Rand's theoretical philosophy is something most any participant here could do for themselves. A case for basing induction on Rand's Law of Identity is made in my Induction on Identity in the early 1990's (one way to access the text of the paper is to click on bolded text in the Abstract linked here). (I received a complimentary personal note on that paper from Jude Dougherty who was at that time head of the phi department at the Catholic University of America and was editor of the professional journal The Review of Metaphysics.)

For deductive logic, the principle of noncontradiction looms large. It is a powerful tool. (Hilbert used only PNC in making the mathematical proof that was his Ph.D. thesis, for example.) Leibniz, Kant, and others of their eras recognized, as did Rand 1957, that PNC is a normative principle of cognition based on the Law of Identity. In some deductive inferences, we rely directly on identity: "All animals are mortal, you and I are animals, therefore we are mortal."

One sense in which one might try to validate induction would be to try to prove that if PNC is securely based on Identity, then so is induction based on identity. I think that the history of trying to link induction very closely to deduction has been widely deemed unsuccessful, and perhaps that route suggested in the previous sentence would fall prey to those criticisms. Another sense in which one might try to "validate" induction would be to try to elicit it's correctness for cognition as a corollary from Rand's general metaphysics (taken for true), in the way that OPAR elicits "corollaries" (not deductive theorems) from the most elementary theses and concepts of Rand's general metaphysics. I approve, notwithstanding the usual charge of circularity one receives for any attempts to discursively defend inference principles, deductive or inductive. Another way to validate induction might be to point to vegetative "induction" in the activities of organic neural networks in bringing about sensory perception. Having validated the deliverances of the senses, one then might argue for goodness of consciously engaging in induction for tracking reality (but, again a circularity (benign?) because the first validation had to enlist some induction).

Rand suggested in ITOE that induction was intimate with abstraction in her (or other, really) account of concepts. This would be abstractive induction, which I mentioned even in the Abstract of my "Induction on Identity" linked above. That genre of induction was the topic of Peikoff's paper "Aristotle's 'Intuitive Induction'" (1985 The New Scholasticism 59(2):185–99), which was a bit taken from his Ph.D. dissertation. ‘Intuitive Induction’ and ‘Abstractive Induction’ are two traditional names for the same genre of induction.

Harriman’s book is nice in his illustrations from the history of physics on the methods we often call induction. That is the standard and very helpful way in contemporary philosophy of science. Scroll down in the pdf link for Norton to his Table of Contents, Part II. I was thrilled in Harriman’s book when I came to text I recognized as taken from old Harvard case studies by Duane Roller, the volume on electric charge, which I had read in my History of Science course in undergraduate around 1970. Roller had joined our faculty at University of Oklahoma.

(I’m sorry, but I need to break off just now. I’ll try later tonight to come back and finish what else I wanted to reply for you, Monart. For the present, my husband is calling me away, hoping that I’ll get our dessert made for this evening’s meal.)

[Boydstun]

(OK. A sour-cream coffee cake, very fine.)

A child can discern the rotary motion of a top. Later she gets conceptual grasp of angular velocity, torque and so forth. An account of this advance in knowledge is tackled in David Harriman's The Logical Leap – Induction in Physics. Does that account solve The Problem of Induction ? How far was it a well-defined problem? Was solution of that problem what Rand had in mind in calling for a validation of induction in FNI? I imagine it was, as she would know of Hume’s making shallow of induction and causation and the hero worship Hume received by Philosophy of Science instructors (approximately Logical Empiricists) in the 1960’s (such as my instructor). Does Harriman’s book contain a solution to that problem? I rather imagine it does; I’d have to look at it freshly and closely as well as at the problem. But with the link to SEP on that problem, you might do yourself well in a close look at Harriman with that problem in view.

I rather imagine Harriman had a good hold on that because of his portrayal of our modern sure inference to the existence and character of atoms. I told that story also in my “Induction on Identity.” We ended up in somewhat different years on when that thesis could no longer be at all doubted, rationally speaking. Harriman was a bit more liberal on that than I. Can’t recall just now if Harriman gave William Whewell credit for the process of the “concilliance of inductions” that played out in that case after Whewell’s time.

Kant had an answer to Hume’s critique of causality. It would be good to know with exactly whose picture of causality Hume had been arguing against and was that prior picture also wrong from the vista of an Objectivist non-Humean system. Kant pulled the premise-rug out from under Hume by exposing that Hume et al. were empty-handed on what was human experience for which Hume could find no necessary connection from episode to episode. Kant’s own hand on what was human experience such that there were necessary connections between its episodes was fantastical. Classic modern philosophers Locke to Kant on this are getting a good replacement today with all the philosophers of perception, direct realist and representational realist who master and incorporate the pertinent science, neurological and psychological. I’ll be taking care of Kant in the sequel of this paper, with a modern realist replacement, my own, which was aided by Rand’s system.

You asked about yet-to-come extension of Rand’s measurement structure for concepts. I did take a first step on that 20 years ago in my paper Universals and Measurement. I don’t know how far I might get back to developing that further in connection with science within my projects in view for however farther I live. (I have no indications on specific future failures of health, but I’m 75, so reasonably, the final grade I give myself in advance is “incomplete.”)

Within chapter 7 of Harriman’s book, he discusses “Physics as Inherently Mathematical”. He has nothing original to say; and no mention of the many contemporaries of ours imminently qualified who have contributed to further understanding on that circumstance first really solidly seen in Newton (gravity, not optics), and rocketed by Maxwell; and he seemed to not actually know what it was from Galileo that was actually crucial for Newton’s advance; and he seemed ignorant of the middle man Descartes between Galileo and Newton concerning the law of inertia and, additionally, how it was that rotational motion came to be seen as a form of acceleration in the first place*; and he did nothing by way of showing a way (if there is one) that Rand’s measurement-omission analysis of concepts is usefully related to uses of mathematics in modern physics. There are other aspects in Rand’s epistemological ideas that are shown to be at work in the practice of physics, but these aspects are not unique to Rand.

If one is a beginner, this book can introduce some history and techniques of physics. Additional literature on those is vast, and some leads to it are in the endnotes of The Logical Leap.

I don’t recall if Harriman discussed abduction teamed with induction in science methods, but that is part of the full picture.  

Edited March 24 by Boydstun

[monart]

On 3/23/2024 at 1:17 PM, Boydstun said:

The books by John D. Norton on induction look excellent: The Material Theory of Induction (2021) and The Large-Scale Structure of Inductive Inference* (forthcoming, 2024) look to be illuminating. They would not be expressly hooked to Rand's metaphysics or theory of concepts. Upon studying these Norton books, concord and discord with Rand's theoretical philosophy is something most any participant here could do for themselves. A case for basing induction on Rand's Law of Identity is made in my Induction on Identity

 

The local university library has a copy of the Norton 2021 book, so I'll do a reading of it. I'll also read your "Induction on Identity" paper. Thanks.

[monart]

16 hours ago, Boydstun said:

... with the link to SEP on that problem, you might do yourself well in a close look at Harriman with that problem in view.

...

You asked about yet-to-come extension of Rand’s measurement structure for concepts. I did take a first step on that 20 years ago in my paper Universals and Measurement. ...

...

I don’t recall if Harriman discussed abduction teamed with induction in science methods, but that is part of the full picture.  

Thanks. I'll accept your recommendations.

[SocratesJr]

On 2/26/2024 at 2:41 PM, Boydstun said:

Part 1 – Leonard Peikoff*

By truths I mean, as Ayn Rand meant, “recognitions of facts of reality” which is to say “identifications of existents” (ITOE 48). Without living, fallible minds, there are no truths in this sense of the word. The world would have facts, but until some are recognized, no truth would have come into the world.

Truth is sometimes used to mean what here is meant by fact. That is not the way I mean truth here nor the way Rand or Peikoff used it.

Leonard Peikoff’s 1967 essay “The Analytic-Synthetic Dichotomy” (ASD) set out the basics of the contrasting sorts of truths—analytic and synthetic—the way the distinction had been cast up to middle of the 20th century. Analytic truths had been lately taken as true in virtue of their meaning. Rationality and animality would be included in the meaning of the concept man. So the truth “man is a rational animal” would be an analytic truth, a truth made so by definition, which under contemporary nominalism had become a matter of social convention, pretty arbitrary, free of much constraint by facts of the world. Necessity in such a truth would be from the say-so in our definitional prescription.[1]

That choice of convention, I notice, satisfies a necessity of self-consistent, coherent thinking and talking. Such necessity lies among the class of necessities for a purpose, necessities for an end. I call this class necessity-for.

The truth “man has only two eyes” would not be analytic, the story went, because the feature of having only two eyes is not part of the meaning of the concept man. Such a truth is known as synthetic. Unlike analytic truths, which are necessarily true, a synthetic truth is said to be only contingently true.

Peikoff argued this to be a false dichotomy among truths. The historical root of this widespread falsehood in philosophy, Peikoff maintained, is the Platonic theory that only essential characteristics of a thing are part of the form of a thing and its definition. The inessential, which is from the material aspects of a thing, not its formal aspects, are not part of a thing’s definition. 

I concur in Peikoff’s discernment that the false dichotomy in truths between those analytic and those synthetic has a distant ancestor in a false dichotomy in Plato. In Cratylus Plato has Socrates uphold the principle that contrary attributes never belong to a fully real thing simultaneously and the principle that “things have some fixed being or essence of their own. They are not in relation to us and are not made to fluctuate by how they appear to us. They are by themselves, in relation to their own being or essence, which is theirs by nature” (386d–e; see also Euthyphro 6d–e; Phaedo 65d, 75c–d, 78d, 100c; Republic 475e–76d, 479–80). Each thing has attributes such as shape, sound, or color; but in addition, each thing has a being or essence. Indeed, “color or sound each have a being or essence, just like every other thing that we say ‘is’” (Cra. 423d–e). Plato maintained moreover that what each thing essentially is, such as Man, Good, Size, or Strength is not discovered by sight or hearing, but by reason when it is most free from bodily, sensory distractions (Phd. 65, 74–75, 78c–79d, 83, 86, 96–105; Theaetetus 184b–87a).

The character of each thing that is always the same is a kind—call it a Form—that is “a being itself by itself” (Parmenides 135a–c). Sensory perceptions are as shadows and reflections of these intelligible forms, these intrinsic natures, these essences and being of things (Rep. 509d–e). Plato had no notion of ideas or concepts encompassing both visible forms (such as shapes, sounds, or colors) and intelligible forms.[2] Modern notions of concepts or ideas are, in Plato’s frame, only our thoughts grasping intelligible forms.[3]

Peikoff acknowledged, correctly, that Aristotle breathed new life into this Platonic error by bringing essences down from some purely intellectual nether-realm to the material world open to regular senses.[4] Aristotle is the heavy-weight instigator of the necessary-contingent divide and the essence-accident divide. These doctrines constrained Scholastic theories of universals, concepts, and predication, and facilitated the modern A-S divide.

Peikoff observed that Rand’s conception of the concept of a thing, and her conception of the essential in the concept, rules out an A-S partition of the kinds of conceptual truth in our possession. A thing is all the things that it is (ASD 98). I might add that Rand took a thing’s external relationships as part of what a thing is, a blunt contrast with Plato (ITOE 39). And in Rand’s epistemology, we can have a conception of all that a thing is, including all its external relationships and all its potentials, even though we know our present concept of the thing contains only a portion of that totality of its identity.  

In Rand’s conception of right concepts, they are “classifications of observed existents according to their relationships to other observed existents” (ITOE 47).[5] Furthermore: “Concepts stand for specific kinds of existents, including all the characteristics of these existents, observed and not-yet-observed, known and unknown” (ITOE 65). Objectivist epistemology does not regard the essential and the non-essential characteristics of existents as simply given, as if in an intellectual intuition. Rather, that distinction is based on our context of knowledge of the facts of existents (ITOE 52; ASD 107, 101–103).

“To designate a certain characteristic as ‘essential’ or ‘defining’ is to select, from the total content of the concept, the characteristic that best condenses and differentiates that content in a specific cognitive context. Such a selection [in Objectivist epistemology] presupposes the relationship between the concept and its units [its member elements in reality regarded as substitutable for each other under suspension of their particular measure-values of their shared characteristics]: it presupposes that the concept is an integration of units, and that its content consists of its units, including all their characteristics.” (ASD 103)

Nelson Goodman had written 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).

I’ll examine the cases mounted against the A-S distinction by White and by Quine, and compare them to the Objectivist case, in the next two installments.[6]

(To be continued.)

Notes

[1] Brand Blanshard’s book Reason and Analysis appeared in 1962. It was reviewed favorably by Nathaniel Branden the following year. Branden understood that Blanshard was some sort of absolute idealist, but the book offered access to contemporary positivist and analytic philosophy (including the A-S distinction), and it offered criticisms of them, which Objectivists might join. Against say-so free of constraints from conditions of the world being the source of necessity in necessary truths, see Rasmussen 1982. On the nature and need of understanding for truth, see Haugeland 1998.

[2] Cf. Metaphysics 987b1–13; Notomi 2005, 193–201.

[3] See further, Kraut 1992, 7–12; White 1992.

[4] ASD 95. See also Peikoff 1972, 191, on Aristotle’s influential division of the necessary and the contingent. On medieval and early modern roots of the false A-S dichotomy, see Peikoff 1964, 15–16, 45–59.

[5] Concept empiricism is defended and a version of it, thickly informed by pertinent modern science, is formulated in Prinz 2002.

[6] White 1952 appeared originally in Hook 1950. Sidney Hook would a few years later become Peikoff’s dissertation advisor. Recent defense of the A-S distinction against the attack by Quine is Russell 2008. Additional contemporary debate on the issue is Juhl and Loomis 2010. I’ll not undertake assimilation of these in the present study.

References

Aristotle B.C.E. 348–322. Metaphysics. C.D.C. Reeve, translator. Indianapolis: Hackett.

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

Goodman, N. 1953. The New Riddle of Induction. In Fact, Fiction, and Forecast. 4^th edition. 1983. Cambridge, MA: Harvard University Press.

Haugeland, J. 1998. Truth and Rule-Following. In Having Thought. Cambridge, MA: Harvard University Press

 

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

Juhl, C., and E. Loomis. 2010. Analyticity. New York: Routledge.

Kraut, R. 1992. The Cambridge Companion to Plato. Cambridge.

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

Notomi, N. 2005. Plato’s Metaphysics and Dialectic. In A Companion to Ancient Philosophy. M. L. Gill and P. Pellegrin, editors. Wiley-Blackwell.

Peikoff, L. 1964. The Status of the Law of Contradiction in Classical Logical Ontologism. Ph.D. ProQuest.

——. 1967. The Analytic-Synthetic Dichotomy. In Rand 1990.

——. 1972. Founders of Western Philosophy: Thales to Hume. Lectures by Leonard Peikoff. M. Berliner, editor. 2023. Santa Ana, CA: Ayn Rand Institute Press.

Plato c. 428–348 B.C. Plato – Complete Works. J. M. Cooper, editor. 1997. Indianapolis: Hackett.

Prinz J., 2002. Furnishing the Mind – Concepts and Their Perceptual Basis. Cambridge, MA: MIT Press.

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

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

Russell, G. 2008. Truth in Virtue of Meaning. New York: Oxford University Press.

White, M. G. 1952 [1950]. The Analytic and the Synthetic: An Untenable Dualism. In  Linsky 1952. Included also in White 2004. http://www.thatmarcusfamily.org/.../White%20-%20Analytic... 

——. 2004. From a Philosophical Point of View. Princeton: Princeton University Press.

White, N. 1992. Plato’s Metaphysical Epistemology. In Kraut 1992.

 

"A thing is all the things that it is (ASD 98)." Nobody is denying that. In fact, a thing is the sum-total of all of its attributes.

However, some of these attributes are necessary for it to be what it is. Man is a rational being - analytical and necessary; but, "a man has two eyes" is not definitional. It's easy to see that "Man is a rational being" is a universal because it refers to all men, but "a man has two eyes" is not a universal statement, because it refers only to one man.

The difference between necessary and contingent has its roots in the fact that the former (necessity) refers to a class, a group, that must possess all the same attributes in order to be in that class. But the latter refers to a subset of the group. "Some men have only one eye" is a contingent fact. They are all rational beings by definition, but some of them have only one eye.

In order for the latter to be necessary, we would have to redefine "man" as "a rational being some of whom have only one eye." However, that is nonsensical, because a definition must refer to the attributes shared by all members of the class, without exceptions such as "having one eye."

I need to add a bit more to this. It is possible for an "all" statement to be synthetic/contingent. "All bodies are heavy" is contingent on the presence of gravity. I was dealing with Peikoff's example in ASD of man the rational animal versus man having only one eye or a hundred eyes. I should also have explained why such propositions as "all bodies are heavy" are synthetic "all" statements that refer to a group or class.

Edited April 28 by SocratesJr

[SocratesJr]

I just recalled something from my reading of ASD. Peikoff stated that he can solve the division of "is" (analytic) and "has" (synthetic) statements by stating (using the contingent statement about eyes), "some men are such that they have only one eye." That, however, is not a definition, it is only a rhetorical "solution." Changing the predicate has no effect on the analytic or synthetic nature of the proposition.

[SocratesJr]

On 2/26/2024 at 2:41 PM, Boydstun said:

“Concepts stand for specific kinds of existents, including all the characteristics of these existents, observed and not-yet-observed, known and unknown” (ITOE 65).

I'll stop nitpicking after this. I just want to add that a concept refers to its definition. A concept is an abstraction of the known essential elements of an existent in comparison with other existents.

"Concepts stand for specific kinds of existents." Rand should have stopped there. Because we know what kind of existents they are by classifying them, that is, by grouping them using traits they have in common and which are essential to their identity under that class.

[SocratesJr]

3 hours ago, Boydstun said:

The necessities in the formal disciplines stem ultimately from formalities that are not sourced most fundamentally in mental operations. The necessity-thats of formal disciplines attach to existence and to effective mental operations forged by utility of those formalities. Formalities belonging to situation (mathematics) and to passage and character (logic) are the Ur-springs of necessities in the formal disciplines. The necessity of truths in the formal disciplines—necessity absolute and differing from necessities in empirical generalizations—are inherited from the necessity-that of existence and of the formalities belonging to fundamental categories of existence.

Formal logical systems require self-referential reasoning capacities that may resist full materialization or resolution in physical formalities alone. See Gödel's Incompleteness Theorems published in 1931.

Gödel's incompleteness theorems exposed that any sufficiently expressive formal system will contain true statements about the system's own codifiable operations that cannot be derived by the system's proof procedures alone. There are inherent limitations to what can be captured in a purely formal-syntactic manner. Thus Rand's requirement of using intuition, not reason, to derive axioms. Rand's epistemology, privileging intuition over reason for axioms with the proposed idea that formal systems, require non-formalizable self-referential capacities.

The issue is that while physical formalities can encode and manipulate meaningful symbols according to rules, the full semantic interpretations, referential models and self-reflective capacities that underlie logical reasoning may resist complete materialization or resolution just in those formalized physical symbol games.

There appears to be an irreducible mental or abstract dimension to genuine logical reasoning that goes beyond just shuffling physical tokens according to prescribed rules. Self-referential reasoning seems to require some explicit representational capacities that may not be fully reducible to physical formalities alone.

While formal logic can be abstractly specified and token-manipulations can 'mimic' derivations behaviorally, the full semantic grasp of what logic is, what truth, validity and soundness mean, and the ability to self-reflect on systems, seems to rely on an abstract cognitive dimension that transcends mere physical formalities and symbol pushing.

The human mind, with its capacities for explicit conceptual representation and self-reflective meta-reasoning, appears to underlie logic in a way that cannot be simply reduced to physically instantiating syntax games, no matter how complex. An irreducible abstract dimension of understanding appears indispensable for genuine logical reasoning, as we humans recognize it.

So while logic and mathematics can be partially implemented in physical systems, the contention is that their complete self-referential semantic grasp and soundness may ultimately depend on more than just material symbol manipulation - requiring mental capacities of representation and reflection that fundamentally transcend the physical.

[tadmjones]

Non contradictory identification isn’t as much an art as it is a crucible. In its most physicalist form , the chemical reactions in a crucible do not follow the play of art and the molecules don’t produce any contradictions of identity.

Edited April 29 by tadmjones

[SocratesJr]

The idea that the forms or formalities inherent in the physical world alone determine human knowledge would pose significant challenges to mankind's ability to discover truths that require going beyond direct empirical observation and formulating abstract conceptual models or hypotheses.

If human beings could only passively derive knowledge from the physical formalities present in their immediate empirical experience, without the capacity for active conceptual reasoning and hypothesis formation, then major scientific advances like resolving the heliocentric versus geocentric models of the solar system would have been extremely difficult, if not impossible.

[SocratesJr]

15 minutes ago, tadmjones said:

Non contradictory identification isn’t as much an art as it is a crucible. In its most physicalist form , the chemical reactions in a crucible do not follow the play of art and the molecules don’t produce any contradictions of identity.

There's more involved here than chemical reactions (and the fact that we can identify them). These reactions also appear to be predictable and regular. Observed regularities do not automatically confer certainty or truth. Science's self-correcting progress stems from rational conceptual change that goes beyond mere cataloging of patterns, but also the imposition of rules as conceptual, abstract models.

By restricting science to just collating observed regularities, we potentially rule out entire domains such as theoretical physics, cosmology, evolution, etc., where unobserved processes are central.

The result is Leonard Peikoff declaring that science should be subservient to philosophy (meaning, his philosophy). And that, if quantum physics doesn't seem to obey the laws of observation, and identity breaks down, then something is wrong with QM.

Back in the 1920s, QM physicists would've agreed on principle. But 100 years of experiments have failed to disprove the break down of causality and identity in the realm of quanta.

Edited April 29 by SocratesJr

[SocratesJr]

Come to think of it, somewhere in my reading I found where Ayn Rand asserted that steady-state cosmology is true based on the principle that things cannot come into or go out of existence. If this is a result of her axiomatic, absolute thinking process, then according to Peikoff, cosmologists should give up and accept steady-state based on Rand's axioms.

Edited April 29 by SocratesJr

[SocratesJr]

28 minutes ago, Boydstun said:

Under that good principle, the conception that an elementary particle came from vacuum space while maintaining that such space is nothing is false.

Yes, this is leading to big problems for your metaphysics. Because it's a fact (A is A) that virtual particles come and go from empty space. The Casimir Effect demonstrates a tiny attractive force between two closely spaced metal plates. QFT explains this force arising from the exchange of virtual photons between the plates, even though no real photons are emitted.

The Lamb Shift observed a slight shift in the energy levels of hydrogen atoms. The shift can be explained by the interaction of the electron with the virtual "cloud" of particles surrounding it.

Objectivists should not try to be physicists (and vice versa).

[Boydstun]

Introduction to "Necessity and Form in Truths"

Part 1 – Leonard Peikoff

Part 2 – Morton White

Part 3 – Quine, Objectivism, Resonant Existence – A

Part 3 – Quine, Objectivism, Resonant Existence – A'

 

Part 3 – Quine, Objectivism, Resonant Existence – B

What are the right relationships between metaphysics today and modern science? The Analytic-Synthetic dichotomy of the Logical Empiricists and Quine’s refutation and replacement of their dichotomy are bound up with contemporary skepticism towards metaphysics and differing ideas about the relationships of philosophy to science and of logic to reality.

Rand took metaphysics to be the study of existence as such, which is faithful to a traditional conception of metaphysics as the study of being as being. Metaphysics so conceived pertains to all things. It pertains to all things in ordinary experience or in science, which latter makes available more experience and more subtle targets of knowledge. I propose  that metaphysics can, alongside logic and mathematics, rest on ordinary experience and on information attained in empirical sciences.

Against Kant and others, such as Morganti 2013, I propose that metaphysics need not be a priori to fulfill its distinctive modern functions vis-a-vis other disciplines. Metaphysics can be in important part from reflection on knowledge gotten in those disciplines. Metaphysics can sift for principles to which all rational disciplines and their findings conform or set as norms of performance. Metaphysics can aim for setting the fullest context of knowledge, and that without itself uncovering potentials and limits of concretes as in science. And without itself uncovering possible structure in the formalities of situations as (I say is done) in mathematics. Rather, metaphysics can have the job of forming an explicit widest frame for fuller comprehension of findings in those disciplines. Whether such a metaphysics can also set the reality-base for logic employed in ordinary, scientific, and mathematical thought is yet another criterion for the goodness of the metaphysics.

Metaphysics need not and should not in these activities also propose any new ontological finds deeper than anything found in the sciences, such as substances other than those of chemistry, physics, and science of materials. Metaphysics should not try to cook up some special metaphysical concept of time, but address only the time of physics and ordinary experience. One may and should look, I suggest, in the course of any experience or inquiry, to metaphysics for the integrated whole that one is holding, sourced from all areas of experience.

Rand and Peikoff, however, maintained that the concept existence, as one might enlist it in the assertion that “existence exists” or “there are existents” does not mean specifically physical existence (ITOE App. 245–48). In their view, it means only a “that” exists; it means something exists. If that is all one means by “existence” as such, then I say metaphysics could not be a keeper of widest context and general norms worth employing. 

One does not need to have language and express understanding that existence is what one is taking physical actions with and in or that existence is identity in order to implicitly know “existence” is those things in all one’s early activities and experience (and one doesn’t need to have the concept of experience to be having experiences). Learning of alleged sorts of existence that are not physical existence comes later, after acquiring language. To know that existence is physical existence—to know unsupported objects fall, for example—is prelinguistic. We have scientific developmental cognitive psychology on that now for decades. It is far past time to leave behind our folk conjectures on such early developments supplemented with old psychological conjectures of, say, William James.

When I was teaching adults to fetch a ball I rolled across the floor, I was engaging physical existents, and when I say “existence exists,” I am generalizing from such physical specifics, and I still mean them, such physical things, first and foremost by “existents.” Under explicit assertion, “existence exists” is assertion of some physical existence. If we reject the notion of a physicality-not-yet-committed “existence” in “existence exists,” it is more plausible that a Randian metaphysics can be an integrated unity from all experience and thought and a pertinent constraint-from-the-whole on the various parts of reality for pruning some absences of fact alleged as fact.

An example of such pruning would be from the ancient metaphysical principle “nothing comes from nothing.” Under that good principle, the conception that an elementary particle came from vacuum space while maintaining that such space is nothing is false. Again, that all mass-energy of the universe came into existence from nothing preceding it can be pruned as false. Ex nihilo creation of the world by an intelligent being is quashed by good metaphysics.

Yet metaphysics can still have things to learn from advancing physics. When physics explicated and experimentally set up situations of chaos in the classical regime in the last three decades of the twentieth century, philosophy could wake up to the aspect that fully deterministic situations do not always allow of realistic in-principle predictability and that ability to control the chaotic action did not require significant predictability. 

From our widest-world assessment of advances in science for their import for metaphysics, however, we must understand the science for ourselves, or at least get report of the science by a qualified authority. One should not just take on board the pronouncements of others about the import for metaphysics.

In Rand’s metaphysics, existents as such have broad subdivisions such as actual or potential, current or past or future, entity or its attribute or activity (animate or inanimate), individual or collection or assembly, natural or man-made, causal (often scientifically lawful) determinations of entities or of their attributes or activities. In Rand’s metaphysics also, existents have magnitude structures we implicitly capture in perceptual-level similarities and in our concepts, concepts in her analysis, being a type of set implicitly structured by suspension of particular measure values within characteristic ranges along dimensions common among collections of particular existents.

Right metaphysics can set a science in right relations to other sciences and set out its right relations to reality. A metaphysics such as Rand’s can be a protector of science by defending realism in science and by refuting mystical and skeptical degradations of science. Metaphysics can tackle integration of the specific findings of all the different sciences, assimilating them into a comprehensive network of conceptual dependencies. Then too, general metaphysics can offer integration across and guidance to detailed philosophies of each science.

Kant would have metaphysics be conceived as “nothing other than the philosophy of the fundamental principles of our cognition” (1763 2:283). Furthermore, two dozen years later: “Metaphysics is a speculative cognition by reason that . . . rises entirely above being instructed by experience. It is cognition through mere concepts (not, like mathematics, cognition through the application of concepts to intuitions)” (KrV Bxiv).

Rand, and I also, and many moderns deny there is any such thing as a priori knowledge, knowledge entirely independent of any experience. Rather, I say, any knowledge we have derives ultimately from our interactions with the physical world and coordinations with other people in the world. That is the source of our knowledge in the physical sciences as well as in mathematics and logic. This is not to deny that some of our rational thinking is intimately tied to the capacity for thought; it is only to say that that thinking, such as deductive inference, is not entirely unentangled with physical experience in its emergence and continuance (contra Ichikawa and Jarvis 2013 and Casullo 2012).

Kant had logic as a priori and as analytic. Logic, in his view, provides the way to make previous knowledge distinct (Lu-Adler 2018, 90). That is the facility of logic as analytic. Kant stressed that logic (i.e., deduction) does not have for its function or power the gaining of new knowledge, and logic does its job of rendering distinctness without rendering new content.

I notice that the notion of logic providing only improvement in old knowledge does not in fact entail that logic is a priori. Contrary to Kant’s view, analyticity might obtain even were that skill to have issued from interactions with the world, not from dictates and organization of Kantian faculties of reason and understanding. I should mention too that right philosophical analyses of conceptual dependencies, which is so much a task for philosophy, is more than being analytic in the sense of drawing out implications of whatever stipulations. Conceptual dependencies of concepts won through ordinary experience, science, and mathematics trace reality in our grasp.

Kant’s reason for thinking that pure logic and pure mathematics must be a priori is because the only way he imagines they could issue from empirical interactions is as empirical generalizations, whose character cannot yield the manifest absolute impossibility-of-exception universality had by logical and mathematical principles. Aristotle might enter the friendly point: “To accept as a sufficient starting point that something always either is or happens in a certain way, is not to take things up in the right way.” (Phys. 252a32–33).

“If we now put aside all cognition that we have to borrow from objects, and merely reflect on the use just of the understanding in general, we discover those rules which are necessary without qualification, for every purpose and without regard to any particular objects of thought, because without them we would not think at all. Thus we can have insight into these rules a priori, i.e., independently of all experience, because they contain merely the conditions of the use of the understanding in general, whether pure or empirical, without distinction among its objects. And from this it follows at the same time that the universal and necessary rules of thought in general can concern merely its form and not in any way its matter.” (Kant/Jäsche 1800, 12; cf. KrV A52–55 B76–79)

“The boundary of logic is determined quite precisely by the fact that logic is a science that provides nothing but a comprehensive exposition and strict proof of the formal rules of all thought [including discursive thought not entirely independent of the senses]” (KrV Bix). “This science of the necessary laws of the understanding and of reason in general, or what is one and the same, of the mere form of thought as such, we call logic.” (Kant/Jäsche 1800, 13). Logic is a canon “and as a canon of the understanding and of reason it may not borrow any principles either from any science or from any experience; it must contain nothing but laws a priori . . . ” (ibid.).

“Logic is a science of reason, not as mere form, but also as to matter; a science a priori of the necessary laws of thought, not in regard to particular objects, however, but to all objects in general; – hence a science of the correct use of the understanding and of reason in general, not subjectively, however, i.e., not according to empirical (psychological) principles for how the understanding does think, but objectively, i.e., according to principles a priori for how it ought to think.” (Kant/Jäsche 1800, 16)

Judgments might fail to adhere to logic set down from the faculty of reason, Kant thought, because of unrecognized spoiling influences from the senses on judgment (Kant/Jäsche 1800, 37; see also KrV A293–94 B350–51). The sensory inputs themselves are not erroneous, in Kant’s view, for only judgments can be true or false. Kant is here staying near Descartes’ view that errors all arise from allowing our will to outrun our understanding.

One might think it a bit odd that logic should be among the norms for right judgments without its principles having arisen from interactions with the world. More basically, one should question, as did Bolzano, how logic can be normative for cognition if logic is not for the purpose of attaining truth.

Kant took some experience to be necessary in order that reason get going in logic. This is analogous to the old Leibniz thought that some sensory experience is needed to trigger access to innate ideas. Not natural or popular logic, but “only artificial or scientific logic [not natural or popular logic] deserves this name [logic], then, as a science of the necessary and universal rules of thought, which can and must be cognized a priori, independently of the natural use of the understanding and of reason in concreto, although these rules can first be found only through observation of that natural use.” (Kant/Jäsche 1800, 17)

Our contemporary students of elementary logic may add to Bolzano: right deductions aid in the pursuit of truth only by giving the rules for preserving truth of premises to truth of conclusions. Necessity in deductive logic, I should clarify, is not that we necessarily follow the rules of valid inference. No, necessity in deductive logic is otherwise in two ways: (i) If we want to preserve truth of premisses to conclusions, we must follow the rules of logical deduction. That is a necessity-for, a necessity for attaining an end. That has nothing to do with the other necessity in deductive logic: (ii) Rules of deductive inference are necessarily right. Rand could say, and I do say, that this necessity, a necessity-that, is from the obdurate everywhere fact that existence exists and is identity and logic is conformed to that circumstance, the widest necessity-that. That first-figure syllogisms are necessarily right is due to the fact that identity (here, particular-to-classed collection character) is a formal feature belonging to concrete existents (once collections are rendered classes and particulars their members).

I say contra Kant: The necessities in the formal disciplines stem ultimately from formalities that are not sourced most fundamentally in mental operations. The necessity-thats of formal disciplines attach to existence and to effective mental operations forged by utility of those formalities. Formalities belonging to situation (mathematics) and to passage and character (logic) are the Ur-springs of necessities in the formal disciplines. The necessity of truths in the formal disciplines—necessity absolute and differing from necessities in empirical generalizations—are inherited from the necessity-that of existence and of the formalities belonging to fundamental categories of existence.

That Existence exists, I should add, is true because it states a fact. It is not true only because any item of thought can be mapped onto itself. That is to say: That Existence exists is not true due to it being a tautology. Rather, that things are susceptible to our mapping them onto themselves is because Existence exists and is identity and part of that identity is the affordance (by highly intelligent animals) of having itself mapped onto itself. 

(To be continued.)

References

Aristotle c. 348–322 B.C.E. Physics. J. Sachs, translator. 2011. In Aristotle’s Physics – A Guided Study. New Brunswick: Rutgers University Press.

Casullo, A. 2012. Essays on A Priori Knowledge and Justification. New York: Oxford University Press.

Ichikawa, J.J. and B.W. Jarvis 2013. The Rules of Thought. New York: Oxford University Press.

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

Kant, I. 1763. Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality. In Immanuel Kant – Theoretical Philosophy 1755–1770. D. Walford and R. Meerbote, translators. Cambridge: Cambridge University Press.

——. 1781(A), 1787(B). Critique of Pure Reason. W. Pluhar, translator. 1996. Indianapolis: Hackett.

——. 1800. Jäsche Logic. J.M. Young, translator. 1992. In Immanual Kant – Lectures on Logic. Cambridge: Cambridge University Press.

Morganti, M. 2013. Combining Science and Metaphysics – Contemporary Physics, Conceptual Revision and Common Sense. New York: Palgrave Macmillan.