This paper investigates some classical oppositional categories, like synthetic vs. analytic, posterior vs. prior, imagination vs. grammar, metaphor vs. hermeneutics, metaphysics vs. observation, innovation vs. routine, and image vs. sound, and the role they play in epistemology and philosophy of science. The epistemological framework of objective cognitive constructivism is of special interest in these investigations. Oppositional relations are formally represented using algebraic lattice structures like the cube and the hexagon of opposition, with applications in the contexts of modern color theory, (...) Kantian philosophy, Jungian psychology, and linguistics. (shrink)

This paper sets out to adduce visual evidence for Kroneckerian finitism by making perspicuous some of the insights that buttress Kronecker’s conception of arithmetization as a process aiming at disclosing the arithmetical essence enshrined in analytical formulas, by spotting discrete patterns through algorithmic fine-tuning. In the light of a fairly tractable case study, it is argued that Kronecker’s main tenet in philosophy of mathematics is not so much an ontological as a methodological one, inasmuch as highly demanding requirements regarding mathematical (...) understanding prevail over mere preemptive reductionism to whole numbers. (shrink)

In this paper I address G. C. Rota’s account of mathematical identity and I attempt to relate it with aspects of Frege as well as Husserl’s views on the issue. After a brief presentation of Rota’s distinction among mathematical facts and mathematical proofs, I highlight the phenomenological background of Rota’s claim that mathematical objects retain their identity through different kinds of axiomatization. In particular, I deal with Rota’s interpretation of the ontological status of mathematical objects in terms of ideality. Then (...) I detect certain similarities among Rota’s views and Frege’s account of the constitution of arithmetical identity on the grounds of 1–1 correspondence. I point out an epistemic as well as an ontological aspect of this issue. In the sequel, I attempt to deal with the problem of “mixed identities” in mathematics stated by Benacerraf by taking in account Rota’s use of the phenomenological notion “Fundierung”. (shrink)