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Tractarian Ontology: Mereology or Set Theory?

100%
Lando G.
Forum Philosophicum
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2007
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vol. 12
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issue 2
EN
I analyze the relations of constituency or „being in" that connect different ontological items in Wittgenstein's Tractatus Logico-Philosophicus. A state of affairs is constituted by atoms, atoms are in a state of affairs. Atoms are also in an atomic fact. Moreover, the world is the totality of facts, thus it is in some sense made of facts. Many other kinds of Tractarian notions -- such as molecular facts, logical space, reality -- seem to be involved in constituency relations. How should these relations be conceived? And how is it possible to formalize them in a convincing way? I draw a comparison between two ways of conceiving and formalizing these relations: through sets and through mereological sums. The comparison shows that the conceptual machinery of set theory is apter to conceive and formalize Tractarian constituency notions than the mereological one.
2

Librationist Closures of the Paradoxes

51%
Bjørdal F.
Logic and Logical Philosophy
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2012
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vol. 21
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issue 4
323-361
EN
We present a semi-formal foundational theory of sorts, akin to sets, named librationism because of its way of dealing with paradoxes. Its semantics is related to Herzberger’s semi inductive approach, it is negation complete and free variables (noemata) name sorts. Librationism deals with paradoxes in a novel way related to paraconsistent dialetheic approaches, but we think of it as bialethic and parasistent. Classical logical theorems are retained, and none contradicted. Novel inferential principles make recourse to theoremhood and failure of theoremhood. Identity is introduced à la Leibniz-Russell, and librationism is highly non-extensional. Π11- comprehension with ordinary Bar-Induction is accounted for (to be lifted). Power sorts are generally paradoxical, and Cantor’s Theorem is blocked as a camouflaged premise is naturally discarded.
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