Command and consequence

Philosophical Studies - An argument is usually said to be valid iff it is truth-preserving—iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is...     

Lehrer and the consequence argument

The consequence argument of van Inwagen is widely regarded as the best argument for incompatibilism. Lewis??s response is praised by van Inwagen as the best compatibilist??s strategy but Lewis himself acknowledges that his strategy resembles that of Lehrer. A comparison will show that one can speak about Lehrer?CLewis strategy, although I think that Lewis??s variation is dialectically slightly stronger. The paper provides a response to some standard objections of incompatibilists to the Lehrer?CLewis reply.     

Relevant consequence and empirical inquiry

A criterion of adequacy is proposed for theories of relevant consequence. According to the criterion, scientists whose deductive reasoning is limited to some proposed subset of the standard consequence relation must not thereby suffer a reduction in scientific competence. A simple theory of relevant consequence is introduced and shown to satisfy the criterion with respect to a formally defined paradigm of empirical inquiry.Research support was provided by the Office of Naval Research under contract No. N00014-89-J-1725 to Osherson and Weinstein, Swiss National Science Foundation under contract No. 21-32399.91 and by a Siemens Corporation grant to Osherson.     

Epistemic modals and informational consequence

Recently, Yalcin (Epistemic modals. Mind, 116, 983–1026, 2007) put forward a novel account of epistemic modals. It is based on the observation that sentences of the form ‘\({\phi}\) &; Might \({\neg\phi}\) ’ do not embed under ‘suppose’ and ‘if’. Yalcin concludes that such sentences must be contradictory and develops a notion of informational consequence which validates this idea. I will show that informational consequence is inadequate as an account of the logic of epistemic modals: it cannot deal with reasoning from uncertain premises. Finally, I offer an alternative way of explaining the relevant linguistic data.     

Logical matrices and non-structural consequence operators

In the present paper, we study some properties of matrices for non-structural consequence operators. These matrices were introduced in a former work (see [3]). In sections 1. and 2., general definitions and theorems are recalled; in section 3. a correspondence is studied, among our matrices and Wójcicki's ones for structural operators. In section 4. a theorem is given about operators, induced by submatrices or epimorphic images, or quotient matrices of a given one. Such matrices are used to characterize lattices of non-structural consequence operators, by constructing lattices, antiisomorphic to them (see section 5.). In the last section, a sufficient condition is given for a non-structural operator to be finite.     

Formal analyticity

In this paper, I introduce and defend a notion of analyticity for formal languages. I first uncover a crucial flaw in Timothy Williamson’s famous argument template against analyticity, when it is applied to sentences of formal mathematical languages. Williamson’s argument targets the popular idea that a necessary condition for analyticity is that whoever understands an analytic sentence assents to it. Williamson argues that for any given candidate analytic sentence, there can be people who understand that sentence and yet who fail to assent to it. I argue that, on the most natural understanding of the notion of assent when it is applied to sentences of formal mathematical languages, Williamson’s argument fails. Formal analyticity is the notion of analyticity that is based on this natural understanding of assent. I go on to develop the notion of formal analyticity and defend the claim that there are formally analytic sentences and rules of inference. I conclude by showing the potential payoffs of recognizing formal analyticity.     

Assertion, inference, and consequence

In this paper the informativeness account of assertion (Pagin in Assertion. Oxford University Press, Oxford, 2011) is extended to account for inference. I characterize the conclusion of an inference as asserted conditionally on the assertion of the premises. This gives a notion of conditional assertion (distinct from the standard notion related to the affirmation of conditionals). Validity and logical validity of an inference is characterized in terms of the application of method that preserves informativeness, and contrasted with consequence and logical consequence, that is defined in terms of truth preservation. The proposed account is compared with that of Prawitz (Logica yearbook 2008. pp. 175?C192. College Publications, London, 2009).     

Bolzano's deducibility and tarski's logical consequence

In this paper I argue that Bolzano's concept of deducibility and Tarski's concept of logical consequence differ with respect to their philosophical intent. I distinguish between epistemic and ontic approaches to logic, and argue that Bolzano's deducibility presupposes an epistemic approach, while Tarski's logical consequence presupposes an ontic approach.     

On decidable consequence operators

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.     

The consequence argument ungrounded

Peter van Inwagen’s original formulation of the Consequence Argument employed an inference rule (rule beta) that was shown to be invalid given van Inwagen’s interpretation of the modal operators in the Consequence Argument (McKay and Johnson in Philos Top 24:113–122, 1996). In response, van Inwagen (Metaphysics. The big questions, Blackwell, Oxford, 2008a, Harv Rev Philos 22:16–30, 2015) recently suggested a revised interpretation of his modal operators. Following up on a debate between Blum (Dialectica 57:423–429, 2003) and Schnieder (Synthese 162:101–115, 2008), I analyze van Inwagen’s revised interpretation in terms of explanatory notions and I argue that van Inwagen faces a dilemma: he either has to admit that beta entails fatalism, or he has to admit that a new counterexample invalidates beta. Either way, it seems reasonable to reject beta and to conclude that the Consequence Argument fails. Further, I argue that Widerker’s (Analysis 47:37–41, 1987) well-known substitute for rule beta is faced with a similar dilemma and, therefore, is bound to fail as well. I conclude that, if the modal operators are interpreted in terms of explanatory notions, neither van Inwagen’s nor Widerker’s rule of inference turns out to be valid.     

Formal Ontologies and Coherent Spaces

The paper contains a short summary – oriented by a logical point of view – of a joint work on Formal Ontologies. We shall show how Formal Ontologies correspond to Coherent Spaces, and operations on Formal Ontologies correspond to operations on corresponding Coherent Spaces. So, we are offering a new way to establish the semantics of Formal Ontologies. Surely, we are giving a contribution towards a geometrical treatment of Formal Ontologies (as decidable organizations of digital data).     

Formal operations and simulated thought

For reasons internal to the concepts of thought and causality, a series of representations must be semantics-driven if that series is to add up to a single, unified thought. Where semantics is not operative, there is at most a series of disjoint representations that add up to nothing true or false, and therefore do not constitute a thought at all. There is necessarily a gulf between simulating thought, on the one hand, and actually thinking, on the other. It doesn't matter how perfect the simulation is; nor does it matter how reliable the causal mechanism involved is. Where semantics is inert, there is no thought. In connection with this, this paper also argues that a popular doctrine—the so-called ‘computational theory of mind’ (CTM)—is based on a confusion. CTM is the view that thought-processes consist in ‘computations’, where a computation is defined as a ‘form-driven’ operation on symbols. The expression ‘form-driven operation’ is ambiguous, and may refer either to syntax-driven operations or to morphology-driven operations. Syntax-driven operations presuppose the existence of operations that are driven by semantic and extra-semantic knowledge. So CTM is false if the terms ‘computation’ and ‘form-driven operation’ are taken to refer to syntax-driven operations. So if CTM is to work, those expressions must be taken to refer to morphology-driven operations. But, as previously stated, an operation must be semantics-driven if it is to qualify as a thought. Thus CTM fails on every disambiguation of the expressions ‘formal operation’ and ‘computation’.