Distributive Terms,Truth, and the Port Royal Logic

The paper shows that in the Art of Thinking (The Port Royal Logic) Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do not require the introduction of a new concept of ‘indefinite’ term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension.     

Functionalism and propositions

Conclusion Some have argued, following Stalnaker, that a plausible functionalist account of belief requires coarse-grained propositions. I have explored a class of functionalist accounts, and my argument has been that, in this class, there is no account which meetsall of the following conditions: it is plausible, noncircular, and allows for the validity of the argument to coarse-grained propositions. In producing this argument, I believe that I have shown that it might be open to a functionalist to adopt fine-grained propositions; thus, one might be a functionalist without holding that all mathematical beliefs are about strings of symbols (and that the belief that all bachelors are unmarried men is a belief about words).My project in this paper has been minimal in the following sense. I havenot argued thatno functionalist account of belief which meets the three conditions can be produced; rather, I have simply explored the inadequacies of certain sorts of accounts. I think that this is useful insofar as it makes clear the challenges to be met by an account of belief which can play the required role in the argument to coarse-grained propositions. It is compatible with my position that such an account is forthcoming, insofar as I have not produced a functionalist theory of belief which is clearly non-circular, plausible, and which yields fine-grained propositions. Of course, it is also compatible with my position that no plausible, non-circular functionalist account of belief of any sort can be produced. My argument has been that,if one construes such mental states as belief as functional states, no convincing argument has yet been produced that they require coarse-grained objects.     

A repair of Frege’s theory of thoughts

Frege’s writings contain arguments for the thesis (i) that a thought expressed by a sentence S is a structured object whose composition pictures the composition of S, and for the thesis (ii) that a thought is an unstructured object. I will argue that Frege’s reasons for both (i) and (ii) are strong. Frege’s explanation of the difference in sense between logically equivalent sentences rests on assumption (i), while Frege’s claim that the same thought can be decomposed differently makes (ii) plausible. Thoughts are supposed to do work that requires that they be structured and work that requires that they be unstructured. But this cannot be! While the standard response to this problem is to reject either (i) or (ii), I propose a charitable repair in the spirit of Frege’s theory that accepts both. The key idea can be found in Frege’s Basic Laws of Arithmetic(BL, GGA). Frege argues that the thought expressed by a sentence is determined by the truth-conditions that can be derived from the semantic axioms for the sentence constituents. The fact that the same axiomatic truth-condition can be derived in different ways from different semantic axioms suggests a Fregean solution of the dilemma: A thought is a type that is instantiated by all sequences of senses (decomposed thoughts) that have the same axiomatic truth-conditions. This allows for multiple decomposability of the same thought (for different decomposed thoughts can have the same axiomatic truth-conditions) and for a notion of containment (the decomposed thought contains those senses whose semantic axioms are needed in the derivation of the truth-conditions). My proposal combines the virtues of (i) and (ii) without inheriting their vices.     

Divine thoughts and Fregean propositional realism

Anderson and Welty have recently advanced an argument for the claim that the laws of logic are ontologically dependent upon a necessarily existent mind, i.e. God. In this paper I argue that a key premise of Anderson and Welty’s argument—viz., a premise which asserts that \(x\) is intrinsically intentional only if \(x\) is mind-dependent—is false, for on a broadly Fregean account of propositions, propositions are intrinsically intentional but not mind-dependent.     

Sense and Simplicity: Wittgenstein's Argument for Simple Objects

This paper puts forward an alternative interpretation of the argument for simple objects advanced in the 2.0s of the Tractatus. In my view, Wittgenstein derives the simplicity of objects directly from his account of possible states, complex objects and senseful propositions. The key to Wittgenstein's argument is the idea that, if there were no simple objects, possible states would not be necessarily possible. If this were the case, however, there would be no senseful language, in Wittgenstein's view. One of the subsidiary aims of this paper is to question the idea that Wittgenstein posits simples because, without them, language would be infinitely analysable. ¹ 1 I am grateful to Malcolm Budd, Jane Heal and Jim Hopkins for their help in the development of this paper.     

Arbitrary reference,numbers, and propositions

Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing what we may call the arbitrary reference strategy. The main claims of such strategy are 2. First, we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Second, our ignorance of which object is picked out as the referent does not entail that no object is referred to by the relevant expression. Different articulations of the strategy are assessed, and a new one is defended.     

If structured propositions are logical procedures then how are procedures individuated?

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode (as opposed to displayed mode). Moreover, procedures are not mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality.

     

Universalism,Vagueness and Supersubstantivalism

Sider has a favourable view of supersubstantivalism (the thesis that all material objects are identical to the regions of spacetime that they occupy). This paper argues that given supersubstantivalism, Sider's argument from vagueness for (mereological) universalism fails. I present Sider's vagueness argument (§§II–III), and explain why – given supersubstantivalism – some but not all regions must be concrete in order for the argument to work (§IV). Given this restriction on what regions can be concrete, I give a reductio of Sider's argument (§V). I conclude with some brief comments on why this is not simply an ad hominem against Sider, and why this incompatibility of supersubstantivalism with the argument from vagueness is of broader interest (§VI).     

Partial Resemblance and Property Immanence

Objects partially resemble when they are alike in some way but not entirely alike. Partial resemblance, then, involves similarity in a respect. It has been observed that talk of “respects” appears to be thinly‐veiled talk of properties. So some theorists take similarity in a respect to require property realism. I will go a step further and argue that similarity in intrinsic respects (partial intrinsic resemblance) requires properties to be immanent in objects. For a property to be immanent in an object is roughly for it to be wholly present in that object. (So understood, immanence does not imply repeatability, and thus tropes count as immanent.) If two objects are intrinsically similar in one way but not another, there must be a difference between the two ways. And if the similarity is between the objects as they are in themselves, then this difference, too, must be within the objects. Partial intrinsic resemblance thus requires internal structure. Without it, there can be no distinctions between ways in which things are intrinsically alike and ways in which they aren't. I will argue, further, that distinctions between properties that transcend objects fail to account for the possibility of partial intrinsic resemblance.     

Radical parochialism about reference

We can use radically different reference-schemes to generate the same truth-conditions for the sentences of a language. In this paper, we do three things. (1) Distinguish two arguments that deploy this observation to derive different conclusions. The first argues that reference is radically indeterminate: there is no fact of the matter what ordinary terms refer to. This threat is taken seriously and most contemporary metasemantic theories come with resources intended to rebut it. The second argues for radical parochialism about reference: it's a reflection of our parochial interests, rather than the nature of the subject matter, that our theorizing about language appeals to reference rather than another relation that generates the same truth-conditions. Rebuttals of the first argument cut no ice against the second, because radical parochialism is compatible with reference being determinate. (2) Argue that radical parochialism, like radical indeterminacy, would be shocking if true. (3) Argue that the case for radical parochialism turns on the explanatory purposes of “reference”-talk: on relatively “thin” conceptions, the argument goes through, and radical parochialism is (shockingly!) true; on richer conceptions, the argument can be blocked. We conclude that non-revisionists must endorse, and justify, a relatively rich conception of the explanatory purposes of “reference”-talk.     

Propositions,Numbers, And The Problem Of Arbitrary Identification

Those inclined to believe in the existence of propositions as traditionally conceived might seek to reduce them to some other type of entity. However, parsimonious propositionalists of this type are confronted with a choice of competing candidates – for example, sets of possible worlds, and various neo-Russellian and neo-Fregean constructions. It is argued that this choice is an arbitrary one, and that it closely resembles the type of problematic choice that, as Benacerraf pointed out, bedevils the attempt to reduce numbers to sets – should the number 2 be identified with the set Ø or with the set Ø, Ø? An “argument from arbitrary identification” is formulated with the conclusion that propositions (and perhaps numbers) cannot be reduced away. Various responses to this argument are considered, but ultimately rejected. The paper concludes that the argument is sound: propositions, at least, are sui generis entities.

     

Circular and question-begging responses to religious disagreement and debunking arguments

Disagreement and debunking arguments threaten religious belief. In this paper, I draw attention to two types of propositions and show how they reveal new ways to respond to debunking arguments and disagreement. The first type of proposition is the epistemically self-promoting proposition, which, when justifiedly believed, gives one a reason to think that one reliably believes it. Such a proposition plays a key role in my argument that some religious believers can permissibly wield an epistemically circular argument in response to certain debunking arguments. The second type of proposition is the epistemically others-demoting proposition, which, when justifiedly believed, gives one a reason to think that others are unreliable with respect to it. Such a proposition plays a key role in my argument that some religious believers can permissibly wield a question-begging argument to respond to certain types of disagreement.

     

Kant on materialism

ABSTRACT

In this paper I argue that Kant’s complex argument against materialism involves not only his generic commitment to the existence of non-spatio-temporal and thus non-material things in themselves (which follows directly from Transcendental Idealism), but also considerations pertaining to reason and the subject of our thoughts. Specifically, I argue that because Kant conceives of reason in such a way that it demands a commitment to the existence of the unconditioned so that we can account for whatever conditioned objects we encounter in experience, our thoughts, which are also conditioned, require something unconditioned that, because it is unconditioned, cannot be material. In this way, Kant’s attitude towards materialism is based not only on abstract features of his metaphysics and epistemology, but also on specific features that were under serious discussion in the early modern period.     

Outscoping and Discourse Threat

Abstract

For various philosophical purposes it is sometimes necessary to give truth-conditions for sentences of a discourse in other terms. According to Agustín Rayo, when doing so it is sometimes legitimate to use the terms of that very discourse, so long as the terms do not occur in the truth-conditions themselves. I argue that giving truth-conditions in this ‘outscoping’ way prevents one from answering ‘discourse threat’ (for example, the threat of indeterminacy).     

The necessary a posteriori: A response to Tichý

Conclusion Some of Tichý's conclusions rest on an assumption about substitutivity which Kripke would not accept. If we grant the assumption, then Tichý successfully shows that we can discover true identity statements involving names a priori, but not that we can discover a priori what properties things have essentially. Many of Tichý's arguments require an implausible rejection of the possibility of indirect belief as described in Section III. 25Are there necessary a posteriori propositions? I have argued that we certainly can discover necessary propositions a posteriori, but have left it an open question whether there are necessary propositions which we can only discover a posteriori.What effect do the considerations here presented have on the positivist doctrine that the a priori and the necessary coincide? My explanation of how we discover necessary propositions a posteriori involves our believing them indirectly, in virtue of believing contingent propositions. I would argue that Kripke's examples of the contingent a priori involve, similarly, our believing the contingent propositions in directly, in virtue of believing necessary propositions.This suggests that a reformulation of the positivist thesis along something like the following lines may well be correct. Let us say that someone directly believes a proposition just in case he could not fail to believe it without being in a different cognitive state. Then perhaps one can directly believe a proposition on the basis of a priori evidence only if it is necessary, and can directly believe a proposition on the basis of a posteriori evidence only if it is contingent.     

Polger on the Illusion of Contingent Identity

Abstract

Thomas Polger has argued in favour of the mind–brain type‐identity theory, the view that mental states or processes are type‐identical to states of the central nervous system. Acknowledging that the type‐materialist must respond to Kripke’s modal anti‐materialist argument, Polger insists that Kripke’s argument rests on dubious assumptions concerning the identity conditions of brain states. In brief, Polger claims that one knows that x and y are non‐identical when one knows the identity conditions for both x and y. Replace x and y with ‘brain states’ and ‘sensations’ and it follows that one can know that brain states and sensations are non‐identical only if one knows the identity conditions for brain states. But according to Polger, we do not know the identity conditions for brain states. Hence, we should not be so confident that brain states and sensations are non‐identical after all. But Polger’s account is terribly flawed. Ironically, if Polger’s scepticism is warranted, then Polger himself has no good reasons to be a type‐materialist. But more importantly, Polger’s scepticism regarding the identity conditions of brain states is deeply defective. We do, I submit, understand the identity conditions of brain states. In the end, I submit, Kripke is safe from Polger.     

Two Kinds of Definition in Spinoza's Ethics

Spinoza scholars have claimed that we are faced with a dilemma: either Spinoza's definitions in his Ethics are real, in spite of indications to the contrary, or the definitions are nominal and the propositions derived from them are false. I argue that Spinoza did not recognize the distinction between real and nominal definitions. Rather, Spinoza classified definitions according to whether they require a priori or a posteriori justification, which is a classification distinct from either the real/nominal or the intensional/extensional classification. I argue that Spinoza uses both a priori and a posteriori definitions in the Ethics and that recognizing both types of definitions allows us to understand Spinoza's geometric method in a new way. We can now understand the geometric method as two methods, one resulting in propositions that Spinoza considers to be absolutely certain and another resulting in propositions that Spinoza does not consider certain. The latter method makes use of a posteriori definitions and postulates, whereas the former method uses only a priori definitions and axioms.     

Is consciousness intrinsically valuable?

There are some things that we think are intrinsically valuable, or valuable for their own sake. Is consciousness—subjective, qualitative experience—one of those things? Some theorists favor the positive view, according to which consciousness is intrinsically valuable. According to a positive theorist, consciousness itself accrues intrinsic value, independent of the particular kind of experience instantiated. In contrast, I favor the neutral view, according to which consciousness is neither intrinsically valuable nor disvaluable. The primary purpose of this paper is to clarify what is at stake when we ask whether consciousness is intrinsically valuable, to carve out the theoretical space, and to evaluate the question rigorously. The secondary purpose is to show why the neutral view is attractive and why certain arguments for the positive view do not work.

     

There is no ‘Is’ of constitution

I defend the view that ordinary objects like statues are identical to the pieces of matter from which they are made. I argue that ordinary speakers assert sentences such as ‘this statue is a molded piece of clay’. This suggests that speakers believe propositions which entail that ordinary objects such as statues are the pieces matter from which they are made, and therefore pluralism contradicts ordinary beliefs. The dominant response to this argument purports to find an ambiguity in the word ‘is’, such that ‘is’ in these sentences means the same as ‘constitutes or is constituted by’. I will use standard tests for ambiguity to argue that this strategy fails. I then explore and reject other responses to the argument.     

Amie Thomasson's Easy Approach to Ontology

Philosophers have long debated whether abstract objects such as numbers and properties exist, but in recent years philosophical debate about what things exist has been ratcheted up more than a notch to question whether even ordinary objects such as pineapples and tables exist. One view has it that all existence questions are difficult questions whose answers hang on achieving an ontological theory that succeeds in carving nature at its joints. Some proponents of this view further claim to have succeeded in that carving, even without the benefit of any instrument sharper than the a priori arguments conjured in their armchairs, and to have discovered, alas, that no ordinary concrete objects exist. Naturally, many of us have been made to wonder what premise in the argument for that conclusion enjoys a plausibility greater than that of the negation of the argument's conclusion. In her remarkable new book, Ontology Made Easy, Amie Thomasson strives to do much more than that in defense of common‐sense ontology. But not only for common‐sense ontology. She propounds a unified approach to all existence questions—whether about the existence of dogs, shoes or tables, or about the existence of numbers, propositions or fictional characters—according to which existence questions “are not deep and difficult subjects for metaphysical dispute, but rather questions to be resolved straightforwardly by employing our conceptual competence, often combining this with empirical investigations” (20). Thomasson calls her way of resolving existence questions the easy approach to ontology, and to that I now turn.