Indicative conditionals, restricted quantification, and naive truth

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory

The Power of Naive Truth

While non-classical theories of truth that take truth to be transparent have some obvious advantages over any classical theory that evidently must take it as non-transparent, several authors have recently argued that there's also a big disadvantage of non-classical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories should seem preferable to their external counterparts

제 80 차 Saving the Truth Schema from paradox

「Q인 경우 오직 그 경우만 -T()」인 Q가 존재함을 보이는 여러 방법들이 있다. 자기 자신이 참이 아님을 주장하는 역설적 문장이 이러한 Q의 대표적인 예이다. 이에 덧붙여, 만약 우리가 고전적인 참 이론을 받아들이면, 「Tr()인 경우 오직 그 경우만 Q」(참 도식)도 받아들여야 하는데, 그럼 결국 「Q인 경우 오직 그 경우만 -Q」를 받아들여야 한다. 그러나, 이는 고적적인 논리학에서는 모순이다. 자 이제 우리에게는 세 가지 선택지가 있는데, 이러한 Q가 존재하지 않도록 하는 해결책과 고전적인 참 이론을 포기하는 해결책은 별로 설득력이 없다. 따라서, 나는 고적전인 논리학을 포기하고 새로운 논리학을 받아들이는 해결책을 제시하겠다

Prospects for a Naive Theory of Classes

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak

Meaning, Truth, and Physics

A physical theory is a partially interpreted axiomatic formal system (L,S), where L is a formal language with some logical, mathematical and physical axioms, and with some derivation rules, and the semantics S is a relationship between the formulas of L and some states of affairs in the physical world. In our ordinary discourse, the formal system L is regarded as an abstract object or structure, the semantics S as something which involves the mental/conceptual realm. This view is of course incompatible with physicalism. How can physical theory be accommodated in a purely physical ontology? The aim of this paper is to outline an account for meaning and truth of physical theory, within the philosophical framework spanned by three doctrines: physicalism, empiricism, and the formalist philosophy of mathematics

Meaning, Truth, and Physics

A physical theory is a partially interpreted axiomatic formal system (L,S), where L is a formal language with some logical, mathematical and physical axioms, and with some derivation rules, and the semantics S is a relationship between the formulas of L and some states of affairs in the physical world. In our ordinary discourse, the formal system L is regarded as an abstract object or structure, the semantics S as something which involves the mental/conceptual realm. This view is of course incompatible with physicalism. How can physical theory be accommodated in a purely physical ontology? The aim of this paper is to outline an account for meaning and truth of physical theory, within the philosophical framework spanned by three doctrines: physicalism, empiricism, and the formalist philosophy of mathematics