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.