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Bernard Bolzano – Theory of Science

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“Our ancestors have achieved much, but did not bring it to completion. Much remains still to do, and much will always remain, and someone born a thousand generations hence will not be denied the opportunity to add yet more.”

—Seneca, quoted by Bolzano

 

I shall dive into Bernard Bolzano’s monumental Theory of Science (1837) in the next post. The text of that post will be taken directly from a portion of chapter Six of my own book in progress. The native title of this mature work of Bolzano is Wissenshaftslehre, and I’ll follow the usual convention WL to designate my citations of it. I shall omit my lists of References for these two posts. Contact me through the personal message system of this site if you would like to have them. The following material of this post is background for the post to follow, and is taken from other parts of my book, but this can be skipped for a first reading of that next post, concerning Theory of Science.

 

Unlike moderns such as Leibniz, Baumgarten, Kant, and Rand, Aristotle did not connect a “law of identity,” in so many words, with his principle of noncontradiction.[1] Aristotle additionally did not connect the law of identity that speaks to the distinctive natures of things with a formula such as “A is A” or “A thing is itself.” He would say “A thing is itself” is nearly empty and useless, and he would not connect that proposition to “A thing is something specifically,” which he thought substantive and important.[2] Aristotle was the founder of logic, and his great contribution thereto was his theory of correct inference, which is his theory of the syllogism. Though he did not realize it, the formula “A is A” in the form “Every A is A” can be used to extend the kingdom of the syllogism. By about 1240, Robert Kilwardly was using “Every A is A” to show conversions such as the inference “No A is B” from the premise “No B is A” can be licensed by syllogism.[3]

 

There are places in which Aristotle connects (what we call the law of identity) “A thing is something specifically” or “A thing is what it is” with the principle of noncontradiction: “The same attribute cannot at the same time belong and not belong to the same subject in the same respect” (Metaph. 1005b19–20). Though not given the pride of place given it by Rand, there is some recognition that Existence is identity in Aristotle: “If all contradictories are true of the same subject at the same time, evidently all things will be one . . . . And thus we get the doctrine of Anaxagoras, that all things are mixed together; so that nothing exists” (1007b19–26).[4] Aristotle realized too that any existent not only is, but is a what.[5]

 

Aristotle, Avicenna, Henry of Ghent, John Duns Scotus, Francis Suárez, Spinoza, and Baumgarten also reached principles close to “Existence is identity,” though not the Randian rank of it among other metaphysical principles.[6] The Thomist text Rand read had included: “What exists is that which it is” (Gilson 1937, 253). That is a neighbor of Rand’s “Existence is identity.” Neighbor Baumgarten: “Whatever is entirely undetermined does not exist” (1757, §53).

 

In Rand’s fundamental Existence is identity, the identity of an existent includes its that/which and its what. Rand has the relation of identity to existence as Aristotle had the relation of unity to being, which the schoolmen called a transcendental relation. Existence and unity are convertible; unity follows existence everywhere.[7] In Rand’s metaphysics and in mine, not only is unity convertible with existence, identity is also convertible with existence. Unity is absorbed into Rand’s ample identity. Intelligibility, another traditional “transcendental property” of being, is also absorbed into the transcendental that is identity where (i) existence is identity and (ii) consciousness is identification. The scholastic transcendental property (of being) truth is absorbed into identification, which is not a transcendental property of existence. Rand’s convertibility of identity and existence was most fully seen before her by Avicenna with his addition of the transcendentals “thing and something, meaning definiteness and otherness, respectively” (Kovach 2013, 240). Aquinas folded those into his system of the transcendental properties.[8] Within Rand’s metaphysics and mine, let us call such “properties” merely comprehensive standings with existence. They follow existence everywhere, existence actual and potential.

 

© Stephen C. Boydstun 2015

 

Notes

[1] Leibniz 1678; Baumgarten 1757 (1739), §11; Kant 1755, 1:389; 1764, 2:294.

[2] Aristotle, Metaph. 1041a10–24.

[3] First mood of the second figure; Kneale and Kneale 1962, 235–36; see also Kant 1800, §44n2.

[4] See also Aristotle, Metaph. 1006b26–27, 1007a26–27.

[5] Metaph. 1030a20–24.

[6] Metaph. 1006b26–27, 1007a26–27, 1007b19–26, 1030a20–24; Kovach 2013, 240; Wippel 2010, 623–34; Vos 2006, 274–79; King 2003, 28–30; Copleston 1963, 186–89; Spinoza 1677, IP25c, 36d; Baumgarten 1757, §§10–11, 20–24, 34–35, 53, 55.

[7] Top. 127a27–28; Metaph. 1003b23–34; cf. Aquinas ST Q.11 A.1.

[8] Kovach 2013, 241.

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Bernard Bolzano – Theory of Science

A translation of his Wissenschaftslehre (1837)

by Paul Rusnock and Rolf George (Oxford 2014)

 

Call comprehensive a true universal proposition reflecting fact at play in every fact. Rand’s selection Existence exists for philosophical primary, comprehensive and fundamental, was evidently a selection of Bernard Bolzano as well. Of the proposition “There is something” he writes that “every other truth which could be thought to be its ground, must itself to be a consequence of it or of others that are its consequences etc.” (WL §214).[1]

 

Rand and I can concur with some of what Bolzano conceives as a ground in his ground-consequence relation. I think, however, and Rand could probably come along, that in place of consequence there should be depending occasion, which is to comprehend consequences, but also weaker yet epistemologically important cohorts of ground. Depending from would be a type of weaker depending occasion, such as when a jewel depends from a necklace or a species from a genus. Another type of weaker depending occasion would be existential instantiation of a mathematical model; not only does the instanced mathematical form depends on the concrete, the instance depends from the mathematical type. Notice that depending occasion is in stronger relation to a ground than simply anything associated in mind with something else that had entered mind.[2] Notice too that in the association of the thought “brass fittings in this room” with the thought “me sitting in this room” there is no relation of ground to depending occasion between those two classes of items, although there are such relations among attributes of the two classes and their aggregation as well as between the two associated thoughts.

 

Bolzano’s ground-consequence relation is not entirely settled and perfectly clear. It is wrapped up with relations of deducibility, but is not to be taken as coincident with the entirety of deductive premise-conclusion relations. His ground-consequence relation centers on valid deducibility from true premises that are explanatory of the conclusion.[3] Cause-effect is not a case of ground-consequence, but has a regular tie to it, in his view. To reach the related ground-consequence relation, Bolzano would overwrite causation of alcohol by fermentation of grapes in this way: The truth of the existence and characteristics of fermentation is ground of the consequent truth of the existence and characteristics of alcohol.[4] Truth in this context is what he calls truth in itself, which is what we hope and strive to possess in our thought truths.[5]

 

Bolzano insists it is only other truths in themselves that can be objective grounds of truths in themselves. He keeps his ground-consequence relation in the mold of axiomatic deductive systems: truths are consequences of their grounding truths, they follow from grounding truths, not from things referred to in truths.[6] Bolzano’s truth in itself is a reversion to the scholastic conception of truth as a transcendental (convertible) property of being.[7] That makes conformance of ground-consequence to cause-effect tight as the conformance of God’s understanding to reality. Decline the notion of truth as transcendental property of being or existence, I say. Keep truth tied necessarily to finite, fallible cognition. That Rand’s full identity—unities, particularities, attributes, kinds, and alterations—is convertible with existence suffices for full adequacy of mind, finite and fallible, to grasp existence.

 

The class of relations subsumed under our alternative—ground and its depending occasions—is a larger class than Bolzano’s class of ground and its consequences. Include under the relation of ground to depending occasion two notable relations Bolzano excludes from his relation of ground to consequence. In our broad class of grounds, include causes, one thing making something happen in another. Include also things, or existents, in their relation to truth, or cognized fact, in our class of grounds.

 

Fact is our own currency for “is the case” as when Wittgenstein follows “The world is everything that is the case” with “The world is the totality of facts” (1918, I, II.I). I shall call corporate facts the facts entrained in our perceptual and action schemata and in our concepts and propositions. I replace Bolzano’s truths in themselves with corporate facts. All facts are susceptible in principle to our corporations of cognition. Every past fact, though most are no longer accessible, was such that it could have been assimilated in conceptual corporations. Bolzano leans towards my rewrite of his truths in themselves as corporate facts when he concurs with Johann Ulrich, who had written in 1792: “Objectively the true is what is in fact so” (quoted in WL §27).[8] Where Bolzano says logic studies laws that hold for truths as such, let us say logic studies laws that hold of corporate facts as such.[9] Under either formula, logic is guidance for correct, productive thought.

 

Bolzano conceived philosophy as the science of penetrating contingencies to reach truths in their objective relations of grounds to consequences.[10] I should rather say philosophy is the metascientific discipline reaching for wide grounds, discerning varieties of relation between ground and depending occasion. As exhibited in the block quote below, by the idea of consequence following from ground, Bolzano insinuates a relation leaning towards deducibility of all further truths in part from explanatory first truths.[11] In this his philosophical first-ground would have foundational role in serious excess over the role Rand gives Existence exists. Bolzano is right to include material truth within the purview of logic.[12] But he errs by his shadows of deductive premise-conclusion in the relationship of first truths to all other truths.[13] Rather, first truths, first facts (such as Existence exists and is identity) ground and elucidate such things as deductive inference.[14]

 

Bolzano errs also in his view that we are better acquainted with the events in our inner selves than events outside ourselves.[15] I am better acquainted with the fire in the fireplace than with my reception and processing of the fire’s input to sight, hearing, smell, and sense for heat flow rate across skin surfaces. Attending to whether the burning logs need adjustment is much less labored than attending to and discriminating what are all my sensations from the fire. Notwithstanding any excess of deductive potency implicated in Bolzano’s account, and notwithstanding his erroneous view that our acquaintance with inner events is stronger than acquaintance with outer events, the status of There is something in Bolzano’s philosophy is a forerunner—the closest in modern philosophy—of Rand’s Existence exists in hers.

 

I should notice the fuller statement of the quotation above from Bolzano. Rand-like example again of a ground without further ground: “the proposition that there is something, or (as I think it should be put) that the idea of something has objectuality” (WL §214). With his concept of objectuality and his preferred expression read out of context, Bolzano might be thought to be some sort of post-Kantian taking the subject to be structuring source of the possibility of objects in general. He is not. Unlike Reinhold, Fichte, Schelling, and Hegel, Bolzano is not a post-Kantian, at least not in a positive way. To be sure, he writes after Kant, being born in the year the first Critique was first issued. From age eighteen, he seriously studied that work. He sometimes adopts Kant’s theoretical vocabulary, while specifying his own exact, different meaning of those terms. He opposes Kant’s recourse to an extra-logical power of intuition in pure mathematics, replacing Kant’s account with an alternative conception of conceptual analysis and of deduction. Bolzano is squarely anti-Kantian in theoretical philosophy. He is a complete realist. He rejects the primacy of consciousness, human or divine.[16] Eternal truths and even all the truths in this world that is God’s creation are not true because He conferred truth on them, according to Bolzano.[17]

 

Objectuality of an idea is fundamentally trueness to facts, positive or negative, facts of the one and only reality that is. Bolzano’s contrast for the objectual is the objectless. Nothing and round square and wooden iron poker would be uncontroversial examples of objectless concepts. Bolzano counts some mathematical elements as objectual. Such would be triangle. But he counts others as objectless that I count should count objectual: zero and square root of negative one.[18] I think of all mathematical objects in their net of demonstrated mathematical relations as facets of identity, of intelligibility, in potential physical structure. Adequacy of human mind to reality is at hand in the objectuality of our ideas,[19] or as I prefer to say, in the trueness of our self-consistent concepts of themselves to objects[20] and in the trueness of our concepts’ propositions to facts of existence, including all the depending occasions of existence, such as mind. Take negation and “not anything at all” to depend from existence only by way of depending on mind, a mind knowing analogues of them that depend directly from existence.

 

Bolzano continues:

If it is already a controversial question whether there is even a single truth which has no further ground, it is even more difficult to decide whether there are several. I believe that this should be affirmed, for I cannot understand how from a single truth all others would follow either as consequences, or consequences of consequences, etc. (WL §214)

 

Note. Since Leibniz speaks of vérités primitive in the plural, he must also have held this opinion. When, by contrast, many logicians write that the so-called principle of identity, i.e., the proposition “What is, is” is the highest truth of all, it seems that they thought this to be the only truth which has no further ground of its truth. (WL §215)

 

Conjoining the first truths There is something with What is, is sets one in the vicinity of Rand’s conjunction Existence exists with Existence is identity, provided the what designates not only an existing item, but acknowledges there is what the existent is. There seems to be such acknowledgment in Bolzano’s predecessor Baumgarten, who writes “Every possible A is A, or a thing is whatever it is . . .” (1757, §11). Bolzano recognizes that for every possible characteristic, a singular thing either possesses it or not.[21] Moreover, he holds that our concept of any concrete thing contains “the idea of something as well as the idea of some attribute which determines it to be” that concept of that concrete (WL §202). Bolzano recognizes the principle of what-identity, though not under that name and as part of the logical principle of identity. Like Aristotle, Bolzano thinks of the principle of identity, or its formula A is A, as meaning only a thing is itself, not also that a thing is what it is. Bolzano recognizes that existence is identity (or that the real is identity), though not in those words, for he writes “That which is indeterminate in itself is simply—nothing” (WL §509).

 

Rand’s notions of fundamentality and grounds weaker than Bolzano’s are right. This is so not only for fundamentality and grounds in the character of philosophic axioms, but in the character of essence in theory of concepts and definitions. Like Rand a century and a quarter later, Bolzano held that whether a conceived attribute of an object is an essential attribute of the object “depends in part upon the object whose attribute it is supposed to represent, and in part upon the concept that we form of the object” (WL §111). Bolzano had proposed that one could approach the objective ground-consequence relation between truths by ordering them such that from the smallest number of truths taken as premises, the largest number of truths as conclusions could be derived.[22] With economy in explanatory power, weaker than economy in deductive power, Rand could conceive of essential characteristics in a concept as most economical set of distinctive characteristics explanatory of the other distinctive characteristics.[23] Bolzano could not come to such a conception for concepts because of the greater strength he was aiming for in his relation of grounds to consequences. That stronger relation does enter into his conception of what is essential in a concept, but only in this: all characteristics within a concept such that were any one of those characteristics removed it would not be the same concept .[24]

 

But now our focus is on Rand’s and my own grounding relations in basic metaphysics and theory of mind. Consciousness stands as depending occasion to a ground: existence. Action and attribute stand as depending occasions to a ground: entity. Identification stands as depending occasion to a ground: identity in its object and the entity that is a mind. Identity does not stand as depending occasion with existence as its ground. Rather, existence is identity and is all, and ground of all wonders within it.

 

© Stephen C. Boydstun 2015

 

Notes

[1] See also WL §§142, 221.

[2] Cf. WL §§277, 300.

[3] WL §§162, 168, 198, 200–204; Rusnock and George 2014, II, xlii–l; Lapointe 2011, 81–90.

[4] WL §201.

[5] Bolzano’s notion that there is an objective, right order of mathematical concepts and premises in proofs enabled some of his contributions to mathematics. See WL §§401, 576–78; Coffa 1991, 27–32; Parsons 2010, 146–47; Friedman 2010, 737n43.

[6] WL §§16, 24–30.

[7] WL §§24, 29.

[8] See also WL §109.

[9] WL §12.

[10] Bolzano 1838.

[11] See further, Betti 2010.

[12] Cf. WL §§9, 12; Lapointe 2012, 26–31; 2014, 305–8.

[13] Bolzano is abetted in such a view by his conception that all attributes of God are deducible “perhaps not by man, but in itself” (WL §110). Further, WL §§111, 113.

[14] Cf. WL §199.

[15] WL §143; Rand, ITOE App. 227; Churchland 1988, 76.

[16] Příhonský 1850, 114.

[17] WL §25.

[18] WL §§29, 55, 67, 70–71, 108.

[19] WL §§49–50, 55 137, 172, 352.

[20] A solid bounded by five equal plane faces, for example, is a false concept. Cf. WL §55.

[21] WL §45.

[22] WL §221.

[23] ITOE 45; cf. WL §114.

[24] WL §§111, 117, 209.

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I had written in #1, “Aristotle, Avicenna, Henry of Ghent, John Duns Scotus, Francis Suárez, Spinoza, and Baumgarten also reached principles close to “Existence is identity,” though not the Randian rank of it among other metaphysical principles.” That list was not up to date with my latest compilation. I was supposed to list also Leibniz and Kant.

 

I think it would be of some interest for readers here to see more of those earlier statements I cite near “Existence is Identity.”

 

Suárez

“Existence is in reality nothing else but the actual essence itself.”

 

Leibniz

“A nonentity has no attributes.”

 

Baumgarten

“Every possible thing is a ground, or nothing lacks a consequence; nothing is without corollary and recompense; nothing is completely sterile, useless, and unfruitful; or, when something is posited, some consequence belonging to it is posited as well.”

 

“Every possible thing is determined with regard to its possibility; hence what is possible in itself is determined with regard to internal possibility. Since internal possibility is essence, every possible thing has an essence, or is determined with regard to essence. Therefore, whatever is entirely undetermined is nothing.”

 

Kant

“A nonentity has no predicates” (A793 B821).

 

Bolzano

“It is absurd to want to ascribe attributes to nothing—hence the well known non entis nullae sunt affectiones [a nonentity has no properties].”

 

“That which is indeterminate in itself is simply—nothing”

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Heidegger’s “Dasein exists, and it alone” coupled with “Dasein is its own disclosedness” resembles somewhat Rand’s couple “Existence exists” with “Existence is identity” (SZ 133). Heidegger, however, was working with a more restricted notion of existence than Rand’s. He crafted Dasein with truncated features distinctive of living existence, even of consciousness and social institution (SZ 11–15, 41–45). And he would not follow Rand in the restriction of being to existence (actual and potential) even though her existence was broader than his. Then too, he hung what she would later call identity, as in Existence is identity, radically from disclosedness and susceptibility to identification, rather than from existence or being. He erred also by disallowing either identity or susceptibility to identification to all being. Lastly, he imported some dynamics into being and truth, a wrong maneuver.

 

I have proposed we should replace Bolzano’s theme of truths in themselves with corporate facts. It seems natural then to likewise replace Heidegger’s notion of ontological truth with corporate facts and keep the notion of truth tethered to knowing subject. Right, but Heidegger had really not done entirely away with that tether due to his tie of truth to Dasein, which is, among other things, existent that is disclosedness and understanding of being (SZ 214–30). There is furthermore something Heidegger, with Aristotle, had gotten quite right in his “ontological” notion of truth, which should not be thrown out with the bathwater. Heidegger’s conception of demonstration of truth by identity of (i) the object thought with (ii) the object is correct and a portion of Rand’s conception of truth as identification of facts of reality (SZ 217–19; ITOE 48). Further with Heidegger: “In accordance with the essential kind of being appropriate to Dasein, all truth is relative to the being of Dasein. Is this relativity tantamount to saying that all truth is ‘subjective’? If one interprets ‘subjective’ to mean ‘left to the arbitrariness of the subject’, then certainly not” (SZ 227).

 

Being and Time (Sein und Zeit, SZ)

Seventh edition, 1953 [1927]

Joan Stambaugh, translator

(SUNY 2010)

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I can now do better than the following paragraph which I had in #1 of this thread.


The following material of this post is background for the post to follow, and is taken from other parts of my book, . . .

 

. . .

In Rand’s fundamental Existence is identity, the identity of an existent includes its that/which and its what. Rand has the relation of identity to existence as Aristotle had the relation of unity to being, which the schoolmen called a transcendental relation. Existence and unity are convertible; unity follows existence everywhere. In Rand’s metaphysics and in mine, not only is unity convertible with existence, identity is also convertible with existence. Unity is absorbed into Rand’s ample identity. Intelligibility, another traditional “transcendental property” of being, is also absorbed into the transcendental that is identity where (i) existence is identity and (ii) consciousness is identification. The scholastic transcendental property (of being) truth is absorbed into identification, which is not a transcendental property of existence. Rand’s convertibility of identity and existence was most fully seen before her by Avicenna with his addition of the transcendentals “thing and something, meaning definiteness and otherness, respectively” (Kovach 2013, 240). Aquinas folded those into his system of the transcendental properties. 

 

© Stephen C. Boydstun 2015

 

 

 

Here is my replacement for that paragraph, with my new learning and further reflection on these concepts and their history:


In Rand’s fundamental Existence is identity, the identity of an existent includes its that/which and its what and perhaps more. She has existence as the fundamental comprehensive reality. That role had been given not to existence, but to being by Aristotelians such as Thomas Aquinas. In its Randian conception, existence is to be taken as all existence, actual and potential, physical or mental. Being in this modern view is reined in to nothing but existence and what is of existence.

 

Rand has the relation of identity to existence near Aristotle’s relation of unity to being, which relation to (old-width) being the schoolmen called transcendental. Unity follows existence everywhere, to every category whatever, to every particularity. Unity is not apart from existence; only in thought are they separable. In Rand’s metaphysics, unity is absorbed into an ample identity. Unity is not convertible with existence in the full-fledged way it is convertible with being, once we have begun to see unity as only a portion of identity and have confined being to existence and what is of existence. Being is one, and existence is one. One is being, but one is not existence. The oneness of an existent is only an “of existence” where oneness is taken in isolation of other aspects of an existent. Identity, Rand’s ample identity, follows existence everywhere and is moderately convertible with existence in the following disjunctive way: Existence is identity, and identity is existence or is of existence. A floor is nothing but which and what and where and when it is. That is all there is to a floor’s existence if we are thinking by those the total containing all its specifics and particularities. Were one to use a notion of identity so broad as to contain all of those, one could say of the existing floor Identity is existence. A designer’s plan for a floor is also a type of existent, though in relation to its object, it is of a potential floor. Part of the identity of the plan is its being of existence. Existence of the plan is identity, and identity of the plan is existence or of existence.

 

Intelligibility, another traditional “transcendental property” of being, should also be absorbed into identity. The scholastic transcendental property truth is absorbed into identification, which is not convertible with existence nor with “of existence,” for although identification is “of existence,” existence is not identification. Rand’s marriage of identity and existence was seen in fair part before her firstly by Avicenna with his addition of the being-attachments “thing and something, meaning definiteness and otherness, respectively” (Kovach 2013, 240). Aquinas folded those into his system of the transcendental properties. In chapter Seven, I shall add . . . and . . . to Rand’s identity as comprehensive standings with existence. They follow existence everywhere, concrete existence actual and potential. Together these standings with existence, these aspects of existence, are existence. Together they are each existent, whether the existent is in Rand’s categories entity or attribute or action or in any other category of concrete existence.

 

© Stephen C. Boydstun 2015

 

Notes

[1] AS 1016–17, 1035–37, 1040–41, 1054; ITOE 56, 82, App. 240.

[2] Top. 127a27–28; Metaph. 1003b23–34; cf. Aquinas, ST Q11 A1.

[3] Francisco Suárez would rather absorb some aspects of Rand’s ample identity into unity and some into being, absorb as merely synonymous with unity and being, leaving any convertibility of being with Rand’s identity already covered by convertibility of being with a capacious unity; see Aertsen 2012, 609–10.

[4] Cf. Rouse 2013, xviii–xix; Haugeland 2013, 147–51, 191–93.

[5] Cf. Aristotle in Aertsen 2013, 64–67. Cf. Aquinas, DV Q1 A1 Reply, A2 Reply.

[6] Further on Avicenna’s innovation, Aertsen 2012, 86–90, 96–100.

[7] Aquinas DV Q1 A1 Reply; Kovach 2013, 241. On scholastic assimilation of Avicenna’s comprehensive identity-attachments of being into their theories of transcendental properties of being, see Aertsen 2012: on Aquinas 219–20, 222–30, 682–83; on Henry of Ghent, 286–97; on Peter Auriol, 435–36, 439–43, 447–52, 454–56; on Francis of Meyeronnes, 463; on Francis of Marchia, 502–9; on Lorenzo Valla, 570–72; on Suárez, 608–11, 633–34.

 

 

 

The following has been invaluable:

Aertsen, J. A. 2012. Medieval Philosophy as Transcendental Thought. Leiden: Brill.

 

The transcendental under scrutiny in the scope of Aertsen’s book refers (i) to things spanning, or transcending, categories of being and (ii) to nobility of being. My concern has been only with thought about the first of these two senses. Kant would later appropriate the long-standing term transcendental in metaphysics as name for his form of idealism, and his usage in the setting of his “Copernican” inversion has some thin ties to his medieval and modern predecessors mining in transcendental traditions.

 

Aquinas had innovated a distinction between (a) absolute transcendentals of being such as unity and thing and (b ) relative transcendentals of being such as something-distinct-from-others and truth.* Take away all intellect, human and divine, and no convertible with being called truth remains. Kant’s system in effect tries to mold all transcendentals of being into ones relative to intellect. If there are absolute transcendentals, they would have to lie beyond our ways of rational theoretical comprehension. Where Aquinas had the divine intellect as the measure of nature (in the way that a human plan for an artifact is a measure of the artifact) and had nature as the measure of the human intellect, Kant cast off such rational theology and set human intellect as the measure of nature in its fundamental aspects (though not by way of deliberate designing).

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