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Page 1761 of Mathematical Reviews Vol. , Issue 93d
[page]
1993
Mathematical Reviews
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Siegfried Gottwald (Leipzig)
03A_ Philosophical and critical
934:03015
93d:03015 03A05 03B65
Orilia, Francesco
Type-free property theory, exemplification and Russell’s paradox. Notre Dame J. ...
By a type-free property theory the author says he means “a multi- sorted second-order language with individual variables and pred- icate variables of different n-adicity” (p. 434), and in particular a ...
Mechanizing Principia Logico-Metaphysica in Functional Type Theory
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1711.06542v2 fatcat:35p656oycbalvgfnmv6adnbktaOther Versions
Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. ...
This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. ...
about relational and functional type theory. ...
arXiv:1711.06542v3
fatcat:bgnkpwutuvaw7jh6r4k5vvrbxm
In Defense of the Law of Non-Contradiction *
[chapter]
2004
The Law of Non-Contradiction
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and the variable 'F ' both have type i, i . The former denotes a property of relations and the latter is a variable ranging over properties of relations. nonwellfounded set theory, etc. ...
Consider, as an example, Priest's analysis of Russell's paradox. ...
doi:10.1093/acprof:oso/9780199265176.003.0024
fatcat:gnksyfx6wnhvll3ptth3acuc2m
Page 6063 of Mathematical Reviews Vol. , Issue 2001I
[page]
2001
Mathematical Reviews
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Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. ...
The paper has the following fourteen sections: (1) Introduction; (2) Formal type-free property theory; (3) Applying RTD [revision theory of definitions] to exemplification; (4) The system P*; (5) Some ...
Russell, His Paradoxes, and Cantor's Theorem: Part I
2010
Philosophy Compass
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These include Russell's paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes ...
) in Bertrand Russell's work. ...
He is currently engaged in a research project regarding the development of Bertrand Russell's philosophical logic. ...
doi:10.1111/j.1747-9991.2009.00270.x
fatcat:k5xx6lvctrhl7ae56fabh6wuby
Worlds and Propositions Set Free
2013
Erkenntnis: An International Journal of Scientific Philosophy
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The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. ...
After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified ...
, which types the relation and argument places of atomic sentences, Russell's classic paradox does not arise: one cannot assert of properties that they can or cannot exemplify themselves, nor formulate ...
doi:10.1007/s10670-013-9565-x
fatcat:at5ltsh4jbaz7gwht2bd36aryu
Wittgenstein's Tractarian Apprenticeship
2003
Russell: the Journal of Bertrand Russell Studies
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Time has produced something of a consensus concerning the nature of the Tractarian criticisms of Russell's philosophy. ...
Recent work on Russell's philosophy of logic reveals, however, that the agreed account of Tractarian criticisms relies upon characterizing Russell with positions he did not hold.</p> ...
recovered in a type-free substitutional theory of propositional structure. ...
doi:10.15173/russell.v23i2.2045
fatcat:lj63uom3m5bq5a7ptoytrb7w3e
"On Denoting" against Denoting
1998
Russell: the Journal of Bertrand Russell Studies
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The process continues as one ascends types. But Russell's paradox is solved. An expression such as "</>(</>)" is inexpressible in the formal grammar of the substitutional theory. ...
His constructions are framed from within a type-free second-order calculus of attributes. ...
doi:10.15173/russell.v18i1.1929
fatcat:hwk2yj5nkze3xbjwfedykcioia
Page 5148 of Mathematical Reviews Vol. , Issue 97H
[page]
1997
Mathematical Reviews
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., Russell’s paradox. ...
This is a first step in applying RTD to the problem of constructing a type-free the- ory of properties, relations and propositions (in short, PRPs). ...
Meinongian Theories and a Russellian Paradox
1978
Noûs
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paradox that arises in the modified theory. ...
To do this, properties must be meaningfully (i.e., truly and falsely) predicable, in some sense, of non-existents. ...
There are three major ways to block the paradox (short of tampering ith the nature of exemplification): The first is to deny that SSC is a property. ...
doi:10.2307/2214690
fatcat:4u2g4i7bvbg2tmzaqvuxyepvsy
Meinongian extensions of predicates
2005
Logic and Logical Philosophy
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This leads to a discussion of the types of properties that can be predicated about objects as belonging to the sets of properties ascribed to them, and such that can be predicated about them only 'externally ...
It is also problematic in which sense nonexistent objects possess the properties ascribed to them. ...
difference in Parsons's theory between two types, or forms of predication, viz., a Meinongian predication of nuclear properties, and a Russellian predication of extranuclear properties and relations. ...
doi:10.12775/llp.2005.011
fatcat:2ybcoddwevfrbc7d4ekirmvjlu
Two Flavors of Curry's Paradox
2013
Journal of Philosophy
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A unified treatment of Curry's paradox thus calls for a unified treatment of both c-Curry and v-Curry. ...
In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn't automatically solved ...
', or both true and false. 3 But while the liar paradox may be blocked via a non-classical theory of negation, Curry's paradox arises even in negation-free languages, and in particular in those theories ...
doi:10.5840/jphil2013110336
fatcat:zp5alyizgbcpxglyuofhyhzdxm
Relations Versus Functions at the Foundations of Logic: Type-Theoretic Considerations
2010
Journal of Logic and Computation
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This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an over-simplification ...
There is an interesting system having a logic that can be properly characterized in relational but not in functional type theory. ...
Anderson 1993 analyzes the intensional logic and discusses the solution to the paradoxes of object theory. ...
doi:10.1093/logcom/exq017
fatcat:gfeghxdyozgljlh6pb5gfbukbi
Object Theory and Modal Meinongianism
2017
Australasian Journal of Philosophy
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In this paper, we examine some of the objections Berto raises for object theory, i.e., the theory of abstract objects defended in Zalta 1983 Zalta , 1988, and elsewhere. ...
We respond to these objections and show how to disarm them. * ...
x & ∀F (xF ≡ φ)), where φ is any formula with no free occurrences of x t That is, for any type t, there is an abstract entity of type t that encodes all and only the properties of type t objects that satisfy ...
doi:10.1080/00048402.2016.1260609
fatcat:wl744hnfmfba7hknse6ddn4elm
How to Say Goodbye to the Third Man
2000
Noûs
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For example, in type theory, one could postulate a 2-place exemplification relation that holds between a property F and an object x, and postulate a 3-place exemplification relation that holds between ...
For example, Plato never worried about formulating his theory of Forms so as to remove the threat of Russell's paradox. ...
doi:10.1111/0029-4624.00207
fatcat:amssxpsqn5boxfdsl57zrjgzuu
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