Kit Fine

The Question of Realism

My aim in this paper is to help lay the conceptual and methodological foundations for the study of realism. I come to two main conclusions: first, that there is a primitive metaphysical concept of reality, one that cannot be understood in fundamentally different terms; and second, that questions of what is real are to be settled upon the basis of considerations of ground. The two conclusions are somewhat in tension with one another, for the lack of a definition of the concept of reality would appear to stand in the way of developing a sound methodology for determining its application; and one of my main concerns has been to show how the tension between the two might be resolved.

In so many possible worlds.

Ordinary modal logic deals with the notion of a proposition being true in at least one possible world. This makes it natural to consider the notion of a proposition being true in n possible worlds for any nonnegative integer n. Such a notion would stand to Tarski’s numerical quantifiers as ordinary possibility stands to the existential quantifier. In this paper I present several logics for numerical possibility. First I give the syntax and semantics for a minimal such logic (sections 1 and 2); then I prove its completeness (sections 3 and 4); and finally I show how to extend this result to other logics (section 5).

THE PURE LOGIC OF GROUND

I lay down a system of structural rules for various notions of ground and establish soundness and completeness. Ground is the relation of one truth holding in virtue of others. This relation is like that of consequence in that a necessary connection must hold between the relata if the relation is to obtain but it differs from consequence in so far as it required that there should also be an explanatory connection between the relata. The grounds must account for what is grounded. Thus even though P is a consequence o fPP but the claim that P is a ground fo rPP they can be assessed for consistency, assigned a semantics, compared for proof-theoretic strength, etc. There are two other, more particular, aspects of my approach. The first lies in its concep- tual basis. Most other philosophers have worked almost exclusively with a concept of strict ground, under which a truth is not capable (or, at least, not normally capable) of being a ground for itself. 2 But I believe that there is also an important concept of weak ground, under which a truth will automatically be a ground for itself. Very roughly, we may say that strict grounds must move us down in the explanatory order while weak grounds must not move us up. Thus P can weakly ground P, bu tP&P cannot weakly ground P given that P strictly grounds P & P.

Plantinga on the Reduction of Possibilist Discourse

Plantinga is what I call a modal actualist. He believes that the idioms of necessity and possibility are to be taken as primitive in preference to talk of possible worlds and that only actuals, as opposed to possibles, arc to be granted ontological status. On these two issues, he and I agree.

Some Puzzles of Ground

In recent years there has been a growing interest in the concept of ground – of one thing holding in virtue of another; and in developing an account of ground, a number of philosophers have laid down principles which they regard as unquestionably true of the concept. The 1 purpose of this note is to show that these principles are in conflict with seemingly impeccable principles of logic. Thus a choice must be made; either one or more of the metaphysical principles or one or more of the logical principles should be given up. Some philosophers – and especially those already unsympathetic to ground – may think that the conflict reveals some underlying defect in the concept. For if acceptance of the concept of ground has such untoward consequences, then this can only be because the concept was no good in the first place. My own view – which I suggest towards the end of the paper – is quite different. It is not that considerations of ground should be ignored or even that the principles of ground should be given up in the light of their conflict with the principles of logic. Rather we need to achieve some kind of reflective equilibrium between the two sets of principles, one that does justice both to our logical intuitions and to our need for some account of their ground. Thus the conflict, far from serving to undermine the concept of ground, serves to show how important it is to arriving at a satisfactory view of what in logic, as in other areas of thought, can properly be taken to be hold. The puzzle to which the conflict of principles gives rise bears some resemblance to the paradoxes of self-reference. It is not itself a paradox of self-reference: the puzzle, on the one side, makes no direct use of self-reference; and the paradox, on the other side, makes no direct appeal to the notion of ground. But considerations of ground are often used to motivate certain solutions to the paradoxes; and the puzzle makes clear the reasoning behind these considerations and brings out the critical role played by the notion of ground. 2 §1 Informal Argument Let me first give an informal presentation of the puzzle and then give a more formal presentation in which the underlying notions and assumptions are made explicit. 0 Here is an especially simple version of the …

Truth-maker semantics for intuitionistic logic

I propose a new semantics for intuitionistic logic, which is a cross between the construction-oriented semantics of Brouwer-Heyting-Kolmogorov and the condition-oriented semantics of Kripke. The new semantics shows how there might be a common semantical underpinning for intuitionistic and classical logic and how intuitionistic logic might thereby be tied to a realist conception of the relationship between language and the world.

Model theory for modal logic part I—The De re/de dicto distinction

It is an oddity of recent work on modality that the philosopher’s main concern has been with quantificational logic whereas the logician’s has been with sentential logic. There have, perhaps, been several reasons for this divergence of interest. One is that the area of sentential modal logic is already rich in logical problems; and another is that the semantics for quantified modal logic has been in an unsettled state. But whatever the reasons have been in the past, the time would now seem ripe for a more fruitful interaction between these two approaches to the study of modality. My aim in these papers has been to bring the methods of model theory closer to certain common philosophical concerns in modal logic. Indeed, most of the results answer questions that arise from some definite philosophical position. In this respect, my approach differs from that of Bowen [I] and others, who attempt to extend the results of classical model theory to modal logic. Although this approach has its attractions, it also suffers from two drawbacks. The first is that most of its results are devoid of philosophical interest; and the second is that many standard results of classical model theory, such as the Interpolation Lemma, do not apply to some standard modal logics, such as quantified S5 (see my paper [S]). The philosophical position that underlies the results of the first two parts of this paper may be called de re scepticism. It is the doctrine that quantification into modal contexts does not, as it stands, make sense. Call a sentence de dicru if, in it, the necessity operator never governs a formula that contains a free variable. Then for the de re sceptic, only de dim sentences, or their equivalents, are legitimate. This position is closely related to another that has been called antiHaecceitism. This states that the identity or non-identity of individuals in distinct possible worlds is a matter of convention. We may regard the class of possible worlds as a model or representation of all that is and is not possible. The position is then that the sameness or difference of individuals

Logics containing K 4. Part II 1

There are two main lacunae in recent work on modal logic: a lack of general results and a lack of negative results. This or that logic is shown to have such and such a desirable property, but very little is known about the scope or bounds of the property. Thus there are numerous particular results on completeness, decidability, finite model property, compactness, etc., but very few general or negative results. In these papers I hope to help fill these lacunae. This first part contains a very general completeness result. Let I n be the axiom that says there are at most n incomparable points related to a given point. Then the result is that any logic containing K4 and I n is complete. The first three sections provide background material for the rest of the papers. The fourth section shows that certain models contain no infinite ascending chains, and the fifth section shows how certain elements can be dropped from the canonical model. The sixth section brings the previous results together to establish completeness, and the seventh and last section establishes compactness, though of a weak kind. All of the results apply to the corresponding intermediate logics.

Semantics for the Logic of Essence

This paper provides a possible worlds semantics for the system of the authors previous paper ‘The Logic of Essence’. The basic idea behind the semantics is that a statement should be taken to be true in virtue of the nature of certain objects just in case it is true in any possible world compatible with the nature of those objects. It is shown that a slight variant of the original system is sound and complete under the proposed semantics.

The RealIty of Tense

I argue for a version of tense-logical realism that privileges tensed facts without privileging any particular temporal standpoint from which they obtain.