Tyke Nunez

What got lost with the advent of the new mathematical logic of Frege and Russell? Although mathematically probably not much—I don’t officially have a view—philosophically, I think quite a bit. I see a tradition in the philosophy of mathematics that ends with Russell, but traces its roots back through Kant to Euclid, Eudoxus, and Aristotle, on which geometry was the preeminent mathematical science, fundamentally grounded in space. With the rejection of space as the foundation of mathematical knowledge, and the attempt to ground it in logic or thought alone, a tectonic transformation within the order of knowledge took place. In many respects, its subtle repercussions for virtually all parts of philosophy would be hard to overstate. Much of my work attempts to peer back through the Fregean looking glass and bring back into focus insights and questions from the earlier tradition that have become occluded or distorted, firmly planted as we now are on the other side of the Fregean revolution.

Because I take Kant to be the apogee of this older tradition, much of my work has examined various dimensions of his thought. In this, I find thinking about the ways in which Kant is picking up on and modifying insights in Leibniz, Aquinas, Cicero, Aristotle, and Plato especially useful. I am also working on a book manuscript on Bertrand Russell’s conception of space in his early, An Essay on the Foundations of Geometry. In it, I argue Russell recognizes and preserves the feature of space that allows it to ground geometry for Kant, and in working through the collapse of the project of Foundations, Russell not only invents mathematical logic, but also incorporates the most basic role space had played for Kant into logic itself.

Publications

“No inference necessary: Kant’s account of the experience of a causal connection.” Australasian Journal of Philosophy. Forthcoming. (abstract)

The near consensus among Kant’s interpreters is that if he holds experience of a causal connection to be possible, then cognition of necessity gets “injected” into it through reason when we infer it from a particular causal law. Kant, however, does not write of such injection. Rather, in its least scientifically developed form, he seems to hold that experience of a causal connection is constituted merely through present perceptions and the categories—especially cause and necessity—in a judgment of the understanding. I present an interpretation where experience of a causal connection is so constituted, and the cognition of necessity in it need not be grounded in cognition of a particular causal law.

“The Formality of Kant's Logic and Consciousness of Logical Laws.” In The Palgrave Handbook for German Idealism and Analytic Philosophy. Ed. by Jonas Held and James Conant. Forthcoming. (abstract)

I examine how Kant understood the formality of pure general logic, which is what distinguishes it from other sciences. This formality is grounded in his conception of the understanding as the faculty for thinking, and as the faculty that contributes the form to cognition. Pure general logic is formal cognition or formal philosophy because it studies the laws of thinking that make thinking what it is, as thinking. I investigate how we should understand this task of pure general logic by proposing two plausible interpretations of it, one that is more, another that is less, Fregean. On the more Fregean proposal, pure general logic makes distinct the concepts <concept>, <judgment>, and <inference>, while on the less Fregean proposal it merely articulates the system of the laws that govern material cognitions in virtue of their form, or what they are as thoughts. Ultimately, I argue that the crux of the difference between these proposals comes down to how they understand Kant’s conception of consciousness or awareness (Bewußtsein), which is “a representation that another representation is in me” (JL, 9:33). According to the more Fregean proposal this is a second-order representation. According to the less Fregean proposal consciousness is formal. It is the form of the original representation and is what makes the representation what it is. I argue that ultimately Kant’s system of logic dissolves on the more Fregean interpretation, and that the less Fregean proposal is truer to Kant.

“The Doctrine of Internal Relations: Russell’s 1897 Rejection.” In Early Analytic Philosophy: Essays on its Origins and Transformation. Ed. by Gilad Nir and James Conant. 2025. Pre-print Version. (abstract)

Bertrand Russell’s rejection of the doctrine of internal relations — the doctrine that all relations are grounded in intrinsic properties of the terms related — was a critical step in his development away from his geometry focused idealist philosophy of mathematics of the 1890s and towards his logic of relations and the logicism of Principles of Mathematics. Although this rejection is usually tied to his 1898 discussions with Moore (Hylton) or reading of Leibniz (Griffin), I argue that in his 1897 An Essay on the Foundations of Geometry Russell rejects the doctrine within geometry. I make this argument by examining his discussion of Hermann Lotze, Carl Stumpf, and William James in resolving what Russell calls “the antinomy of spatial relations.” In this examination I argue that Russell rejects Stumpf’s conception of spatial figures as grounded in an underlying “absolute content” (which is grounded in an acceptance of the doctrine of internal relations) in favor of a conception where spatial figures are merely relations. Russell finds support for this view in James. Even though Russell strives to stay neutral on the metaphysical issue of whether space is real or ideal, his Foundations view of space and the non-spatial atoms that underlie it is closer to Lotze’s interpretation of Kant’s view of phenomena and things in themselves than Lotze’s own, which is grounded in the doctrine of internal relations. Tied to this, in closing I argue that reencountering Lotze’s argument against Kant early in 1898 may have been one catalyst for Russell’s warming to the doctrine of internal relations within geometry, before his rejection of it later that year. On the interpretation I’m offering, then, Russell rejects the doctrine in geometry in Foundations, comes to accept it in 1897 to 1898, before rejecting it again at the end of 1898, and in examining Russell’s “early idealism,” interpreters need to distinguish these fundamentally different positions.

“Not quite yet a hazy limbo of mystery: Intuition in Russell's An Essay on the Foundations of Geometry.” Mind. Volume 134, Issue 533, Pages 107–133, 2025. Pre-print Version. (abstract)

I argue that in Bertrand Russell's An Essay on the Foundations of Geometry (1897) his forms of externality serve the same fundamental role in grounding the possibility of geometry that Immanuel Kant's forms of intuition serve in grounding geometry in his critical philosophy. Specifically, both provide knowledge of bare numerical difference, where we have no concept of this difference. Because on both accounts geometry deals with the composition of such conceptually homogeneous magnitudes, on both accounts the forms of intuition or externality (respectively) are at its foundation.

“Kant on Plants: Self-activity, Representations, and the Analogy with Life.” Philosopher's Imprint. Volume 21, No. 11, May, pages 1-30, 2021. (handout) (abstract)

Do plants represent according to Kant? This is closely connected to the question of whether he held plants are alive, because he explains life in terms of the faculty to act on one’s own representations. He also explains life as having an immaterial principle of self-motion, and as a body’s interaction with a supersensible soul. I argue that because of the way plants move themselves, Kant is committed to their being alive, to their having a supersensible ground of their self-activity, and to their having desires (although these are not conscious). I then spell out the important ramifications of this for Kant’s teleology and philosophy of mind.

“Kant on Vital Forces and the Analogy with Life.” Proceedings of the 13th International Kant Congress ‘The Court of Reason.’ (Oslo, 6-9 August 2019) ed. by Camilla Serck-Hanssen and Beatrix Himmelmann. Vol 2, Pages 961-972. Berlin/Boston: Walter de Gruyter. 2021. Pre-print Version. (abstract)

In this essay I examine Kant's analogy with life from §65 of the Critique of the power of Judgment. I argue that this analogy is central for understanding his notion of a natural end, for his account of the formative power of organisms in the third Critique, and for situating Kant's account of this power in relation to the Lebenskräfte of the Vitalists. (There is overlap between §2-4 of this essay, and §3 of my “Kant on Plants: Self-activity, Representations, and the Analogy with Life.”)

“Kant, Frege, and the Normativity of Logic: MacFarlane's Argument for Common Ground” European Journal of Philosophy. Volume 24, Issue 4, December, pages 988-1009. 2021. Pre-print Version. (abstract)

According to what was the standard view (Poincaré Wang, etc.), although Frege endorses, and Kant denies, the claim that arithmetic is reducible to logic, there is not a substantive disagreement between them because their conceptions of logic are too different. In his “Frege, Kant, and the logic in logicism,” John MacFarlane aims to establish that Frege and Kant do share enough of a conception of logic for this to be a substantive, adjudicable dispute. MacFarlane maintains that for both Frege and Kant, the fundamental defining characteristic of logic is “that it provides norms for thought as such” (MacFarlane, 2002, p.57). I defend the standard view. I show that MacFarlane's argument rests on conflating the way that pure general logic is normative as a canon and as a propaedeutic, and that once these are distinguished the argument is blocked.

“Logical Mistakes, Logical Aliens, and the Laws of Kant's Pure General Logic.” Mind. Volume 128, Issue 512, Pages 1149–1180. 2019. Pre-print Version. (abstract)

---Winner of the American Philosophical Association, Routledge, Taylor and Francis Prize (2019).

There are two ways interpreters have tended to understand the nature of the laws of Kant's pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension insofar as the first depends on the possibility of thoughts that violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant's pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternate ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic.

"Modeling Unicorns and Dead Cats: Applying Bressan's ML^ν to the Necessary Properties of Non-existent Objects." Journal of Philosophical Logic. Volume 47, Pages 95–121. 2018. Pre-print version. (abstract)

Should objects count as necessarily having certain properties, despite their not having those properties when they do not exist? For example, should a cat that passes out of existence, and so no longer is a cat, nonetheless count as necessarily being a cat? In this essay I examine different ways of adapting Aldo Bressan's ML^ν so that it can accommodate an affirmative answer to these questions. Anil Gupta, in The Logic of Common Nouns, creates a number of languages that have a kinship with Bressan's ML^ν, three of which are also tailored to affirmatively answering these. After comparing their languages, I argue that metaphysicians and philosophers of language should prefer ML^ν to Gupta's languages because it can accommodate essential properties, like being a cat, while being more uniform and less cumbersome.

“Definitions of Kant’s Categories.” Canadian Journal of Philosophy: Supplemental Volume on Mathematics in Kant’s Critical Philosophy. Volume 44, Issue 5 – 6, Pages 631–657. 2014. Pre-print version. (abstract)

The consensus view in the literature is that, according to Kant, definitions in philosophy are impossible. While this is true prior to the advent of transcendental philosophy, I argue that with Kant’s Copernican Turn definitions of some philosophical concepts, the categories become possible. Along the way I discuss issues like why Kant introduces the ‘Analytic of Concepts’ as an analysis of the understanding, how this faculty, as the faculty for judging, provides the principle for the complete exhibition of the categories, how the pure categories relate to the schematized categories, and how the latter can be used on empirical objects.

Critical Notices

“Robert Sinclair (ed.) Science and Sensibilia, by W. V. Quine: The 1980 Immanuel Kant Lectures.” Journal for the History of Analytical Philosophy. Volume 11, Number 3, pages 11-19. 2023. (abstract)

I give an overview of each of Quine's 1980 Kant lectures, as well as a critical discussion of the six interpretive essays in the volume. I close with a high-level reassessment of the relationship between the philosophical views of Quine, Kant, and Hume.

“Lu-Adler's Kant and the Science of Logic: A Historical and Philosophical Reconstruction.” Journal for the History of Analytical Philosophy, Volume 8, Number 7, pages 17-31. 2020. (abstract)

A critical discussion of Lu-Adler's chapter on Kant's mature view of pure general logic. I sketch an alternative interpretation of its formality on which Kant would hold no deduction is possible of this logic's laws.

Popular Writing

"Dyslexia, Dysgraphia and Academic Philosophy." This is a short blog post on Daily Nous where I discuss what it has been like in academic philosophy as someone with dyslexia and dysgraphia.

"Remarks on the occasion of Kant’s 300th birthday." These are brief remarks about why Kant is still relevant to the world today that I gave to a salon-birthday party on the eve of Kant's 300th.