(Falk, 2020)
As Jerrold Katz correctly noted, the philosophy of mathematics is central and indeed essential to philosophy as a whole, even despite its abstractness, formal character, and technicality. The reason for this is that an adequate philosophy of mathematics would explain the nature of truth, necessity, apriority, and categorical (i.e., unconditional, principled) normativity, and how they are essentially connected with one another. In turn, by virtue of explaining the nature of categorical normativity in relation to truth, universality, necessity, and apriority, an adequate philosophy of mathematics would also thereby explain the meaning or purpose of rational human existence. Let’s call this the fundamental significance of mathematics thesis, or “the FSM thesis” for short. In Cognition, Content, and the A Priori, or CCAP for short (Hanna, 2015), Robert Hanna presented and defended an argument for the FSM thesis. In “Mathematics and Human Existence” Hanna recapitulates that line of argument from CCAP and then spells out some further implications of it. If Hanna is correct, then our knowledge of basic arithmetic is not only the foundation of all higher mathematical knowledge, but also the paradigm of all rational human knowledge and rational activity and as such, (i) it’s presupposed by all human rationality and (ii) it clearly and distinctly displays the meaning or purpose of rational human existence, which is freely and wholeheartedly to choose and act according to and for the sake of true, universal, necessary, and a priori categorically normative principles (Hanna, 2018a, 2018b), whether in higher mathematics, logic, natural science, morality, sociopolitics, or philosophy, while also at the same remaining ineluctably “human, all-too-human”: that is, finite, fallible, and thoroughly normatively imperfect in every other way too. If we can do basic arithmetic, then we can do anything that’s really possible for rational human animals.
REFERENCES
(Falk, 2020). Falk, D. “How Mathematics Can Save Your Life.” Undark. 17 January. Available online at URL = <https://undark.org/2020/01/17/math-life-death/>.
(Hanna, 2015). Hanna, R. Cognition, Content, and the A Priori: A Study in the Philosophy of Mind and Knowledge . THE RATIONAL HUMAN CONDITION, Vol. 5. Oxford: Oxford Univ. Press. Available online in preview HERE.
(Hanna, 2018a). Hanna, R. Deep Freedom and Real Persons: A Study in Metaphysics. THE RATIONAL HUMAN CONDITION, Vol. 2. New York: Nova Science. Available online in preview HERE.
(Hanna, 2018b). Hanna, R. Kantian Ethics and Human Existence: A Study in Moral Philosophy. THE RATIONAL HUMAN CONDITION, Vol. 3. New York: Nova Science. Available online in preview HERE.
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