42,577 research outputs found
Analogy as Higher-Order Metaphor in Aquinas
At a Thomas Instituut conference in 2000, Otto-Hermann Pesch suggested somewhat enigmatically that the sharp distinction in scholastic Thomism between analogy and metaphor can no longer be maintained since on closer examination analogous statements are in effect instances of a kind of \u27higher-order metaphor\u27. I Pesch intended this qualification primarily to draw attention to the agnostic or negative aspect of analogous speech.2 It is evident from Herwi Rikhof\u27s portrait of \u27Thomas at Utrecht\u27 ,3 that this emphasis on the negative dimension did not introduce anything controversial or novel at the Instituut
Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic
This paper sets out a predicative response to the Russell-Myhill paradox of
propositions within the framework of Church's intensional logic. A predicative
response places restrictions on the full comprehension schema, which asserts
that every formula determines a higher-order entity. In addition to motivating
the restriction on the comprehension schema from intuitions about the stability
of reference, this paper contains a consistency proof for the predicative
response to the Russell-Myhill paradox. The models used to establish this
consistency also model other axioms of Church's intensional logic that have
been criticized by Parsons and Klement: this, it turns out, is due to resources
which also permit an interpretation of a fragment of Gallin's intensional
logic. Finally, the relation between the predicative response to the
Russell-Myhill paradox of propositions and the Russell paradox of sets is
discussed, and it is shown that the predicative conception of set induced by
this predicative intensional logic allows one to respond to the Wehmeier
problem of many non-extensions.Comment: Forthcoming in The Journal of Philosophical Logi
Several types of types in programming languages
Types are an important part of any modern programming language, but we often
forget that the concept of type we understand nowadays is not the same it was
perceived in the sixties. Moreover, we conflate the concept of "type" in
programming languages with the concept of the same name in mathematical logic,
an identification that is only the result of the convergence of two different
paths, which started apart with different aims. The paper will present several
remarks (some historical, some of more conceptual character) on the subject, as
a basis for a further investigation. The thesis we will argue is that there are
three different characters at play in programming languages, all of them now
called types: the technical concept used in language design to guide
implementation; the general abstraction mechanism used as a modelling tool; the
classifying tool inherited from mathematical logic. We will suggest three
possible dates ad quem for their presence in the programming language
literature, suggesting that the emergence of the concept of type in computer
science is relatively independent from the logical tradition, until the
Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC
Heinrich Behmann's 1921 lecture on the decision problem and the algebra of logic
Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in
G\"ottingen in 1921 with a thesis on the decision problem. In his thesis, he
solved-independently of L\"owenheim and Skolem's earlier work-the decision
problem for monadic second-order logic in a framework that combined elements of
the algebra of logic and the newer axiomatic approach to logic then being
developed in G\"ottingen. In a talk given in 1921, he outlined this solution,
but also presented important programmatic remarks on the significance of the
decision problem and of decision procedures more generally. The text of this
talk as well as a partial English translation are included
An Objection to Naturalism and Atheism from Logic
I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism
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