This section reproduces a selection of the various handouts Mr. Hydomako prepared for class presentations and distributed to his fellow student who were also present on the day of any particular in-class presentation. While the handouts themselves were not typically graded, we can suppose that the grade earned on the presentation itself was at least in part also based upon these handouts and their relation to the subject discussed.
Fall 2001
PHIL 565.04: Interpretations of Mathematical Structuralism with Elaine Landry.
Final Grade Received: A
Abstract: reviews and presents the main points associated with three structuralist accounts of mathematics: in re, ante rem, and modal; talks about how for all three positions mathematical objects are "positions in structures"; examines the ontologies of each position (or lack of the need for one wrt modal structuralism); distills the essence of each position, namely, relations and coherence; examines the role of isomorphism wrt systems and examines the function that maps the relations of one system onto the next in an 1-1 manner; explores the use of a basic understanding of the word 'coherence'; turns to the idea of "mystical experience" in terms of a "unification of opposites"--the conjunction of A with its negation; uses this idea to show how the conjunction of a thing with its negation in terms of a dualistic pairing is more "sensible" or "intelligible," that is, offers a more coherent scope of understanding; examines the problem of the empty set and the paradox of the set of all sets; asserts that nothing = everything simply due to the fact that either the empty set or the set of all sets is a manifestation of the same paradoxical structure, namely, A & ~A; uses the Principle of Explosion (implicitly) to show how we get something from this conjunction of opposites, namely, the domain of set theoretic objects; shows how such understanding is necessarily "outside" of any single account due to its explicit contradiction--this is the connection to the "mystical experience, that is, insight which transcends the mundane (implicitly); suggests that a modal structuralist account of mathematics is the "mediator of potential" when it comes to the absurdity created qua the conjunction of in re and ante rem structuralist positions; makes reference to a particular work of M.C. Escher's, "Encounter" as representative of the so-called "mystical experience" qua "the union of opposites"; discusses the importance of "internal consistency" wrt either of the terms of the binary pair (in re, ante rem), that is, truth is internal to each account, but the largest scope of truth is necessarily "outside" any singular account, but such "truth" is, itself, an absurdity; reviews MS as the mediator of potential wrt to "truth" of the absurdity qua the Principle of Explosion (implicitly); touches upon the problem of the gap between the potential and the actual; closes making reference to the Buddhist concept of knowing emptiness.
Winter 2002
PMAT 415: Set Theory with Claude Laflamme.
Final Grade Received: B+
Abstract: opens with presenting the Liar Paradox as exemplifying each and every claim made in the presentation to come; examines the logical consequences of claiming "Every statement of this presentation is a lie," and explicitly acknowledges the paradox involved in such a claim (whee!); turns to the concept of "self-referencing" and discusses the problems of self-referencing as manifested in the paradox of "the set of all sets" in terms of what V cannot be; asks the audience to consider themselves as a set and shows the regress involved in the self-referencing of such a consideration; introduces the idea of the I as exemplifying emptiness in terms of some Eastern philosophies and also in Jung's conception of the archetype of the Self; suggests "reality" (of both our own experience and that of "sets") is a relational affair dependent on not only (self, other), but also dependent on awareness; explores the relationship between (self, other) and illustrates not only do the two terms "point to" one and other, but they also self-reference themselves as pointing to one and other; frames the four terms of both ({}, V) and (Self, Other) as fictional entities insofar as each terms is entirely dependent upon the other in each binary pairing in order to have its own seemingly "independent" existence; makes reference to the Buddhist notion of relations in terms of a "interdependent co-arising" within emptiness (technical terms of 'Pratītyasamutpāda' and 'Śūnyatā' left implicit due to the audience's likely unfamiliarity with such terms); closes with a reminder that every claim of the presentation is a lie.
