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Single Idea 10253

[filed under theme 5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic ]

Full Idea

Ontology does not depend on language and logic if either one has the objects determining the logic, or the objects are independent of the logic.

Gist of Idea

Either logic determines objects, or objects determine logic, or they are separate

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 6.4)

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.192


A Reaction

I favour the first option. I think we should seek an account of how logic grows from our understanding of the physical world. If this cannot be established, I shall invent a new Mad Logic, and use it for all my future reasoning, with (I trust) impunity.


The 22 ideas with the same theme [overview of what must exist to enable logic]:

Our research always hopes that reality embodies the logic we are employing [Peirce]
Logic is a fiction, which invents the view that one thought causes another [Nietzsche]
Logicians presuppose a world, and ignore logic/world connections, so their logic is impure [Husserl, by Velarde-Mayol]
Phenomenology grounds logic in subjective experience [Husserl, by Velarde-Mayol]
Logic is concerned with the real world just as truly as zoology [Russell]
Logic can be known a priori, without study of the actual world [Russell]
Logic can only assert hypothetical existence [Russell]
Logic is highly general truths abstracted from reality [Russell, by Glock]
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
The only classes are things, predicates and relations [Russell]
The propositions of logic are analytic tautologies [Wittgenstein]
Whether a modal claim is true depends on how the object is described [Quine, by Fine,K]
Logical languages are rooted in ordinary language, and that connection must be kept [Quine]
Unfashionably, I think logic has an empirical foundation [Putnam]
Logicians like their entities to exhibit a maximum degree of purity [Kaplan]
Logical space is abstracted from the actual world [Stalnaker]
Logic is a mathematical account of a universe of relations [Badiou]
A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
In first-order we can't just assert existence, and it is very hard to deny something's existence [Bach]
Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
Maybe mathematical logic rests on information-processing [Ladyman/Ross]
We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]