In my own picture, if one is reading this and knows horses as horses and trees as trees, one knows that horses are not anything but horses, not anything such as trees. If one has concepts, such as the concept horse, then one knows identity, at least a thin identity, and knows classes, whether or not one yet realizes one is dealing in those general patterns identity, class inclusion, and class exclusion. Knowing horses and trees as such, one knows already that horses are necessarily horses and necessarily not anything other than horses, such as trees. Then too, if one is reading this and has the concept horse, one knows validity of the inference from “All horses have blood vessels” and “Bucephalus was a horse” to “Bucephalus had blood vessels.” Also, being a horse, Bucephalus was necessarily not rooted in the soil like a tree.
If one has concepts—even ones held, in early development, according to weighted sums of typical features, not yet according to natures and definitions—I say one has the knowledge grounding recognition of elementary logically valid inference. Where there is knowing things under concepts, there is knowing some what-it-is and what-it-is-not. If equipped with concepts—even before learning to read and before express understanding of grammar—one knows at least dimly that contradiction is false of all things said of the world under concepts, necessarily false.
Rightness and necessity in our later grasp as concepts our concepts of things, things as they are, are inherited rightness and necessity from those earlier concepts of things as they are. Grasping logic requires grasping concepts as concepts. Then my view is that rightness and necessities of logic are heirs ultimately of rightness and necessities in our concepts not as concepts, but merely as of things as they are. My own picture then is a variety of logical ontologism.
Peikoff sets Locke in that broad stream as well. Locke did not have the vantage of our contemporary scientific research into early cognitive development. On his somewhat inconstant model of human cognition and its ontogeny, one has no knowledge which one had not been self-consciously aware of in its acquisition. Moreover, Locke’s tendency towards nominalism in universal concepts sets him to reject possession of universal concepts of things empirical as funding logical necessities such as noncontradiction (or syllogistic inference). Locke would reject the conveyance of empirical necessities to logical necessities by attainment of empirical concepts. Rather, he would have PNC be a generalization of our early notice of particular empirical distinctions and necessities, which were made without knowledge of PNC. Further, in his congeniality towards nominalism, Locke has PNC with its formality and necessity grounded rather more in keeping our reflections on the world straight than in reflecting the world.
Locke rejected the realist theory of universals in both its extreme and moderate forms. Locke understood Aristotle, or anyway the Aristotelianism of his own era, as moderate realism. He argued against our access to any such things as specific, substantial form or real essences. We work with nominal essences, by the lights of Locke, and his own theory of universal concepts has been classified as conceptualism, wherein general words stand for general ideas.
Marco Sgarbi 2013 shows that highly empiricist Aristotelian logic texts flourished in Britain in the 16th and 17th centuries. Frances Bacon criticized the strain therein subordinating the world to the mind and the mind to its concepts. Insofar as Locke took concepts as tightly bound to the mind-independent world, he is located, as Peikoff locates him, in the tradition of logical ontologism, specifically in its Aristotelian wing. Conceptualism is an alternative to realism in theory of universals and in theory of science. Insofar as a variety of conceptualism creates any breach or looseness between what Newton called phenomena (such as orbits of planets) and the mind, it leans away from logical ontologism, I should say.
Peikoff 1964, like Locke 1690, takes Aristotle in the usual way, which is as a moderate realist in which universal concepts, such as horse or tree, derive from particulars in perceptual experience, particulars containing real essences, which are real forms. Aristotelian forms are the definite delimitations joined with fundamental indefinite matter in any actual particular. Unlike Platonic Forms, Aristotle’s forms, even the forms essential to a thing being the kind of thing it is, are not residents of a realm separate from this world of particulars around us. Those essences reside in the particulars around us, and they are accessible to us through appropriation by intellect attending to things sensed. Essential form is of itself never separate from its matter; it is contemplated as separate by the intellect. Contra Plato, essences according to Aristotle do not themselves reside in a realm separately and independently from the realm of sensible particulars, and essences are not accessed by intellect alone.
Where concepts and propositions, including the propositions that are logical principles, were thought to be bonded to and guided by mind-independent reality through their incorporation of Aristotelian form from particulars, supposed conformity to the world by concepts and propositions and logical principles was at stake should the existence of Aristotelian forms be rejected. They were indeed rejected by moderns not Scholastic, excepting Leibniz. They were rejected, as I have mentioned, by Rand and Peikoff. Rightly so. Locke, as we have seen, rejected Aristotelian accounts of abstraction from perceptual particulars via mental absorption of Aristotelian forms, Aristotelian essence.
Peikoff observes that Aristotle attempted to account for PNC as deriving from our assimilation of essential forms in particulars, yet account for such assimilation being reliant on our knowing PNC and for PNC being foundation of all knowing. (A parallel tension appears in Rand’s proposition Existence exists as most fundamental axiom, yet as conceptually derived from perception.) Locke rejected any need for any of the accounting after the yet. Before the yet, he rejected Aristotle’s forms and essences as existing and as sourcing the necessity of PNC we find in thought or in the world. Locke proposed necessity of PNC is perceived, by sense, in distinct particulars. I agree with Locke that there are directly perceived physical necessities. Peikoff, Kant, and virtually the entire bench of philosophers are right, however, to dismiss Locke’s idea that logical necessity is among the types of necessity perceived directly in sensory perception.
There is another view on the ontogeny of PNC, my own view (supplementing what I wrote in the first three paragraphs of this installment), which is only a stone’s throw from Locke’s. That is the view that impossibility of performative contradictions have metaphysical and epistemological priority with respect to formal PNC. One was getting a grip on incompatibility of one’s alternative physical acts before reaching the one-word stage of language development. Further, one has action- and image-schemata (and working memory) preceding and continually supporting one’s concepts. Furthermore, all defenses of PNC eventually invoke impossibilities in actual performances.
Back to older philosophy. Logical necessity for Aristotle resides in character of concepts, predications, definitions, and inferences. These require abstractions from examination of groups of singulars. In Aristotle’s view, perception of a single object not yet conceptualized will not yet open conceptual necessities, such as PNC logical necessity, even though the basis of PNC stands in the intelligible forms and essences shared by and residing in each perceptible singular.
Aristotle had located the source of logical necessities in active operations of intellect and not in the perceptual, memorial, and imaginative supports of active intellect. This stance of Aristotle, which Locke rejected, would please Leibniz, whom Peikoff places in the Platonic line of logical ontologism. Recall that the Platonic line takes some ideas to be innate. In their view, PNC is an innate guiding principle we posses, not a principle derived from or delivered by sensory perceptions. And they take logical necessities to reflect necessity in relations between essences or essential forms obtaining apart from any participation of concrete existents in those eternally true patterns. I want to indicate Leibniz’ shredding of Locke’s outlook on PNC, along with my display to Peikoff’s diagnosis of the failures of both Platonic and Aristotelian logical ontologism.
Leibniz argued persuasively against Locke’s thesis that we know nothing that was not explicitly known by us at least in its initial appropriation. Locke had rejected the Platonic picture in which there is knowledge of geometry or logic possessed by us implicitly prior to it becoming explicit to us. By way of blocking possibility of innate knowledge, Locke had declined possibility of implicit knowledge. It is implausible, I say (as would most moderns), that we have no implicit knowledge hanging about things known explicitly in their initial acquisition. Yet, contra Leibniz, this is no license for thinking any ideas (as distinct from faculties) to be innate.
Demise of doctrines of the innateness of ideas, including necessary truths, cuts down the Platonic line in their defense of the view that logical truths are grounded in something fixed and independent of our knowing those truths. Likewise in ruins became the Platonic support of PNC ontologism by reification of universals and essences, whether residing in an other-worldly place and whether constituting or inhabiting God’s this-world-independent understanding.
Leibniz challenged Locke’s position that PNC is simply an empirical generalization from particular oppositions in experience such as that bitter is not sweet or that wormwood is not sugarplum or that the nurse is not the cat. Leibniz objects that such oppositions of sense have not the absolute certainty of freedom from illusion or other defect as has PNC. I should say against Leibniz that that is no airtight showing that PNC is not derived by empirical generalization. A triangulated result can be more sure than its individual elements of evidence towards that result; we fare well with Whewell’s consilience of inductions. Be that as it may, Leibniz was correct, I say, to hold that PNC is not derived merely by empirical generalization because ideas of being, possible, and identity intertwined in PNC is at hand in any of our general concepts. Leibniz errs, to be sure, in his rush from that picture to innateness of such ideas and PNC.
Leibniz argues well against Locke’s tendency towards nominalism in universals, essences, definitions, conceptual taxonomies, and logical principles. Leibniz submits their bases to be in the similarity of singular things in reality and in possibilities that are independent of our thinking. But Leibniz’ own realist account, with its Platonic and Aristotelian elements, is upset with the upset of those elements and, as well, of his particular amalgam of them.
Aristotle had written in Physics:
Following out this line of thought, Aquinas thought of being and its opposite nonbeing as contained in some way in any knowledge we might have, however elementary the knowledge.
Aquinas maintained the Aristotelian view that PNC is learned by an integrated employment of sense experience and reason. However, on Aquinas view,
The Aquinas over-writing of Aristotle is a right strand, I say, in an adequate theory of acquisition of PNC and logical ontologism. Aquinas is able to support the theses on both wings of the Aristotelian tension Peikoff highlights across the yet I mentioned in connection with Locke. One does not ascend to grasp of PNC by inductive steps, according to Aquinas. Rather, the more comprehensive precedes the less so, in both sense and intellect.
Aquinas’ utilization of Aristotle in metaphysics and epistemology of logical ontologism land the ship in wreckage for modern thought since the time of Newton and Locke. Aquinas had nous, or reason, as our essentially human capability in cognition, but nous itself as derived from realities transcending nature. Peikoff shows Aristotle’s sayings in that same voice. For Aquinas formal structure among particulars are latched to Aristotle’s hylomorphism, his fundamental metaphysics of prime matter and form, essential and incidental form, which all would be coming to wreckage.
Peikoff argues the unraveling of Platonic logical ontologism into logical conventionalism (as of mid-twentieth century) to have been mediated significantly by Kant. Unraveling of the Aristotelian logical ontologism is mediated significantly by Locke. The Aristotelian moderate realism of universals collapses. Aristotelian Matter, Form, and their join collapse. Concrete particulars, individuated by “matter” nigh well itself “unknowable” apart from form, is a soggy base for any universals, including those entrained in PNC and funding its objectivity. An assembly of super-strong axioms resting ultimately on things unknowable is problematic.
In the next installment, I want to convey and assess Peikoff’s account of Kant’s contribution to the transition to conventionality in philosophy of PNC. I hope to touch on not only conventionalist theories to the time of Peikoff’s dissertation, but on those flourishing today and their historical setting. I plan to add a coda that is an inventory of the elements and works in Peikoff’s dissertation that plainly contributed to things addressed in the early ’60’s in the Rand/Branden journals, points in Rand’s epistemology (1966–67), and points, with morphisms, in Peikoff’s own writings from his “Analytic-Synthetic Dichotomy” (1967) to The DIM Hypothesis (2012).
 Cf. Sullivan 1939, 52–53, 62.
 Boydstun 1990, 34–36.
 Cf. Salmieri 2010, 160n12.
 See also Rasmussen 2014, 337–41.
 Locke 1690, I.1.5, IV.1.9; Peikoff 1964, 87–102.
 Locke 1690, IV.7.8.
 Locke 1690, I.1.15, 25, 3.3, IV.1.4, 2.6, 7.9–10; Peikoff 1964, 103–13.
 Locke 1690, IV.7.4, 10–14, 8.2; Peikoff 1964, 216–26.
 Locke 1690, III.3.11.
 Locke 1690, III.6.23–26, 10.14–15.
 Aaron 1952, a fine work I learned of through Peikoff 1964. Similarly, Salmieri 2008 renders Locke as conceptualist, rather than as realist (51n118). Hobbes is today also argued to be a conceptualist, rather than a nominalist (Sgarbi 2013, 190–92). The conceptualism and empiricism of Locke is presaged in the century before him by the British logicians John Case and Giulio Pace, who were in the lineage of the Paduan Aristotelian Jacopo Zabarello (Sgarbi 2013, 91–97, 101–6). / Binswanger 2014 takes moderate realism most generally as holding there are non-specific properties of things in the world independently of our cognizance of such properties. He argues Locke falls into that general bin in spite of himself (102–4). Binswanger divides theory of universals (Rand’s Objectivist theory aside) into the jointly exhaustive bins of realism and nominalism, as had Armstrong 1978. A conceptualist theory could then belong in either of these bins, depending on the particulars of the conceptualist theory. Salmieri 2008 argues the division of concept theories into realist and nominalist (anti-realist) is not a distinction adequate for classing theories of concepts in accordance with their comparative degrees of similarity and their comparative degrees of difference (52–54).
 Sgarbi 2013, 169.
 Conceptualism in which general ideas are thought of as unbound to the world is what Rand meant by Conceptualism in her 1966 and what David Armstrong meant by Concept Nominalism in his 1978.
 The usual view that Aristotle held to moderate realism is disputed by Greg Salmieri (see Gotthelf 2012, 302n19). Salmieri argues in his dissertation that Aristotle thought our concepts of natural kinds, such as horse or tree, stand to their instances not under identity of shared essential, nonaccidental form, identity of a shared kind-form, or identity of a shared real essence resident in each particular instance. Rather, as a relation of determinables to determinates (2008, 44–51, 56–122). (See citation of Johnson, Prior, and Searle in Boydstun 2004n5. Salmieri aligns Aristotle with the Johnson version of the determinable-determinate relation.) Salmieri’s cast of Aristotle’s relation of horse to an instance such as Bucephalus as a complex of determinable-determinate relations incidentally locates Aristotle closer to Rand than traditional moderate realism is close to Rand. Determinable-determinate relations, I should mention, have a realist underlining, for determinable-determinate relations are along dimensions, such as length or material hardness, plainly real and accessible. / Against the traditional interpretation of Aristotle as a moderate realist holding to shared essences of kind by instances of the kind is also Lennox 2001, Chapter 7. For Peikoff 1964, prevailing interpretations of Aristotle across the long arc of the history of philosophy are the pertinent interpretations to his tracing of logical turns in that history.
 Aristotle, Ph. 193a30–94b15, 199a30–33, 209b22–23; Metaph. 1033b24–1034a8, 1036a27–31.
 Peikoff 1964, 212–16.
 Aristotle, APo. 71b10–72b4, 73b17–74a4, 75b21–36, 77a5–35, 81a37–b9, 85b16–23, 87b28–88a17, 99b15–100b17; De An. 429a10–30a26; Metaph. 1005b9–08b27, 1015a20–b15, 1018b30–34, 1035b32–36a11, 1040b25–27, 1061b34–62b11; NE 1143a32–b6; Peikoff 1964, 60-79, 119–20, 124–35, 213–14.
 Lennox 2005.
 Boydstun 1991a, 39; 1991b, 34.
 APo. 71b35–72a6, 87b28–88a11; Metaph. 982a23–25, 1029b1–12; Peikoff 1964, 63–75; Barnes1993, 95–97; McKirahan 1992, 30–33. 127, 219–22; Ferejohn 2013, 76–80; Salmeiri 2010, 158–60.
 On the Platonism of Leibniz, see Mercer 2001, 173–205, 243–52.
 Leibniz 1704, 76–78, 359–61, 411–12.
 Peikoff 1964, 187–200, 205–9.
 Leibniz 1704, 86–87, 101–2, 412.
 See also Zabarella, in Sgarbi 2013, on the perfection of first principles in intellect from received empirical inductions (65–70). On Whewell’s consilience, see Snyder 2017. https://plato.stanford.edu/entries/whewell/
 Leibniz 1704, 286–96.
 Leibniz 1704, 317–19, 343–48.
 Cf. Spinoza: “The first thing that constitutes the actual being of a human mind is nothing but the idea of a singular thing which actually exists” (1677, 2p11).
 Peikoff 1964, 119–23.
 On the separation capability of Form from Matter, greater for Christian Aristotelians such as Aquinas than for Aristotle, see Peikoff 1964, 148–56.
 Peikoff 1964, 212–35.
 Peikoff 1964, 67–68, 126, 214–15; Lewis 2013, 177n4, 185, 251; Reeve 2016, 400–402n691, 428n796. A similar problem is argued in Ferejohn 2013 for Aristotle’s conception of substances as most-primary and as simple beings resisting definition, yet they are to be explanatory grounds of other, complex beings (172–73).
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