Combining Philosophers

Ideas for Roger Fry, Dale Jacquette and Pierre Gassendi

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10 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic describes inferences between sentences expressing possible properties of objects [Jacquette]
     Full Idea: It is fundamental that logic depends on logical possibilities, in which logically possible properties are predicated of logically possible objects. Logic describes inferential structures among sentences expressing the predication of properties to objects.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: If our imagination is the only tool we have for assessing possibilities, this leaves the domain of logic as being a bit subjective. There is an underlying Platonism to the idea, since inferences would exist even if nothing else did.
The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette]
     Full Idea: Philosophy of logic has (roughly) two camps: extensionalists and intensionalists, with the former view dominant. ...There is a close connection between this and eliminativist or reductivist versus folk psychological and intentionalist philosophy of mind.
     From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4)
     A reaction: Hm. I think I favour intensionalism in the logic, and reductivism about the mind, so I may have a bit of bother here. I'm convinced that this jigsaw can be completed, despite all appearances.
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette]
     Full Idea: Classical logic (of Whitehead, Russell, Gödel, Church) is a two-valued system of propositional and predicate logic, in which all propositions are exclusively true or false, and quantification and predication are over existent objects only.
     From: Dale Jacquette (Intro to I: Classical Logic [2002], p.9)
     A reaction: All of these get challenged at some point, though the existence requirement is the one I find dubious.
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette]
     Full Idea: At one level logic can be regarded as a theory of signs and formal rules, but we cannot neglect the meaning of propositions as they relate to states of affairs, and hence to possible properties and objects... there must be the possibility of truth-values.
     From: Dale Jacquette (Ontology [2002], Ch. 2)
     A reaction: Thus if you define logical connectives by truth tables, you need the concept of T and F. You could, though, regard those too as purely formal (like 1 and 0 in electronics). But how do you decide which propositions are 1, and which are 0?
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette]
     Full Idea: It is infamous that on Russell's analysis the sentences "The winged horse has wings" and "The winged horse is a horse" are false, because in the extant domain of actual existent entities there contingently exist no winged horses
     From: Dale Jacquette (Ontology [2002], Ch. 6)
     A reaction: This is the best objection I have heard to Russell's account of definite descriptions. The connected question is whether 'quantifies over' is really a commitment to existence. See Idea 6067.
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette]
     Full Idea: The substitutional interpretation says the universal quantifier is true just in case it remains true for all substitutions of terms of the same type as that of the universally bound variable.
     From: Dale Jacquette (Intro to III: Quantifiers [2002], p.143)
     A reaction: This doesn't seem to tell us how it gets started with being true.
Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette]
     Full Idea: Some substitutional quantificationists in logic hope to avoid philosophical entanglements about the metaphysics of objects, ..and nominalists can find aid and comfort there.
     From: Dale Jacquette (Intro to III: Quantifiers [2002], p.143)
     A reaction: This has an appeal for me, particularly if it avoids abstract objects, but I don't see much problem with material objects, so we might as well have a view that admits those.
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette]
     Full Idea: Extensionalists hold that quantifiers in predicate logic presuppose the existence of whatever objects can be referred to by constants or bound variables, or enter into true predication of properties.
     From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4)
     A reaction: I have strong sales resistance to this view. Why should a procedure for correctly reasoning from one proposition to another have anything whatever to do with ontology? A false world picture can be interconnected by perfect logic.
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
Intensionalists say meaning is determined by the possession of properties [Jacquette]
     Full Idea: According to intensionalist semantics the meaning of a proposition is determined by the properties an object possesses.
     From: Dale Jacquette (Intro to 'Philosophy of Logic' [2002], §4)
     A reaction: This sounds good to me. Extensionalist don't seem to care what sets they put things in, but if property possession comes first, then things will fall into their own sets without any help for us. We can add silly sets afterwards, if we fancy.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
Can a Barber shave all and only those persons who do not shave themselves? [Jacquette]
     Full Idea: The Barber Paradox refers to the non-existent property of being a barber who shaves all and only those persons who do not shave themselves.
     From: Dale Jacquette (Ontology [2002], Ch. 9)
     A reaction: [Russell spotted this paradox, and it led to his Theory of Types]. This paradox may throw light on the logic of indexicals. What does "you" mean when I say to myself "you idiot!"? If I can behave as two persons, so can the barber.