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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 ...
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
The Law of Non-Contradiction
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
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 ...
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
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
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
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
., 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). ...
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
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
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
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
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
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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