Has the Later Wittgenstein Accounted for Necessity?

In this paper, I argue against the later Wittgenstein's conventionalist account of necessity. I first show that necessary propositions and grammatical rules differ in ways that make an explanation of the former in terms of the latter inadequate. I then argue that even if Wittgenstein's account were adequate, the explanation of necessity it offers would still fail to be genuinely reductive of the modal notion.     

The Tractatus on Logical Consequence

Abstract: I discuss the account of logical consequence advanced in Wittgenstein's Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein's claim that all propositions can be analysed as truth functions of elementary propositions.     

‘My Future Son is Possibly Alive’. Existential Presupposition and Empty Terms in Abelard's Modal Logic

The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions maintains its validity when some of the terms included in these propositions are empty. In the following, I first argue that, just as in the case of non-modal propositions, Abelard interprets modal propositions as having existential import, so that it is a necessary condition for the truth of propositions like ‘It is possible for my son to be alive’ or ‘it is necessary that all men are animals’ that their subjects’ referents exist. Then, I present the schemata of inferences that Abelard proposes to describe the logical behaviour of de rebus modal propositions. I argue that these systems of relations are valid only as long as all the terms contained in the formulas have an existing referent. I also claim that Abelard was aware of this difficulty (at least in the Logica Ingredientibus), and, accordingly, he explicitly decided to restrict the validity of his modal system to propositions that do not contain empty terms.     

Whistling in 1929: Ramsey and Wittgenstein on the Infinite

Cora Diamond has recently criticised as mere legend the interpretation of a quip of Ramsey's, contained in the epigraph below, which takes him to be objecting to or rejecting Wittgenstein's Tractarian distinction between saying and showing. Whilst I agree with Diamond's discussion of the legend, I argue that her interpretation of the quip has little evidential support, and runs foul of a criticism sometimes made against intuitionism. Rather than seeing Ramsey as making a claim about the nature of propositions, as Diamond does, we should understand him as making a claim about the grammar of the logical connectives. Such a view coheres with the extant evidence of the nature of Wittgenstein's and Ramsey's 1929 philosophical encounters. It is also compatible with attributing to Ramsey a recognition of Wittgenstein's distinction and with denying that criticising it is the lesson of the quip.     

Wittgenstein on Verification and Seeing-As, 1930–1932

This article examines the little-explored remarks on verification in Wittgenstein's notebooks during the period between 1930 and 1932. In these remarks, Wittgenstein connects a verificationist theory of meaning with the notion of logical multiplicity, understood as a space of possibilities: a proposition is verified by a fact if and only if the proposition and the fact have the same logical multiplicity. But while in his early philosophy logical multiplicities were analysed as an outcome of the formal properties of simple objects and simple signs, Wittgenstein in the early 1930s connects the notion of logical multiplicity with the notion of ways of seeing. I will argue that the relevant ways of seeing are closely similar to seeing-as or aspect seeing. According to Wittgenstein's view in the early 1930s, logical multiplicities are part of our perceptual experience of propositions and facts. In this sense, the verification relation depends on how we experience propositions and facts as being surrounded by a logical space of possibilities. Strikingly, Wittgenstein's way of thinking about the verification relation offers solutions to a set of seemingly intractable problems connected with the versions of verificationism developed by members of the Vienna Circle.     

The power and the limits of Wittgenstein's N operator

The power of Wittgenstein's N operator described in the Tractatus is that every proposition which can be expressed in the Russellian variant of the predicate calculus familiar to him has an equivalent proposition in an extended variant of his N operator notation. This remains true if the bound variables are understood in the usual inclusive sense or in Wittgenstein's restrictive exclusive sense. The problematic limit of Wittgenstein's N operator comes from his claim that symbols alone reveal the logical status of propositions. This would require knowledge of the size of the Tractarian domain of unchangeable, simple objects, and this, Wittgenstein maintained, cannot be known.     

What Is It to Make Clear the Working of Our Language?1

In The Logical Basis of Metaphysics, Dummett articulates and develops his “fundamental assumption” that the introduction rules for a logical constant determine its meaning. According to Dummett, logical laws in harmony with the introduction rules are justified, while logical laws not in harmony with the introduction rules are unjustified. This powerful picture enables Dummett to criticise certain aspects of our linguistic practice, such as the Law of Excluded Middle and the metaphysics of realism he believes it embodies, as not remaining responsible to the meanings of the logical constants. Against Dummett's fundamental assumption, I bring to bear what in the Tractatus Wittgenstein describes as his “fundamental thought” that the logical constants do not represent. Properly understood, Wittgenstein's point is that since the logical constants may be eliminated from the propositional signs of a fully precise logical notation, the constants do not express meanings to which our use of expressions containing the constants is responsible. I then apply Wittgenstein's fundamental thought to Dummett's proof‐theoretic notation to show that far from determining the meanings of the logical constants, the introduction rules merely allow the constants to be edited from certain inferences, leaving Dummett with no semantic kernel with which to criticise other sentences or inferences featuring the constants. Thus, his picture of what it is to make clear the working of our language collapses.     

Necessity and Language: The Gap Is Still Very Real

In my previous paper “Has the later Wittgenstein accounted for necessity?” I argued against the conventionalist account of necessity proposed by Wittgenstein and his followers. Glock has addressed some of my objections in his paper “Necessity and Language: In Defence of Conventionalism”. This brief rejoinder considers Glock's replies to three of those objections. In the course of doing so, I revisit Wittgenstein's explanation of the special status of necessary propositions, the supposedly arbitrary nature of colour‐grammatical propositions, and the relation between rules and modality.     

Doing what one meant to do

When I engage in some routine activity, it will usually be the case that I mean or intend the present move to be followed by others. What does ‘meaning’ the later moves consist in? How do I know, when I come to perform them, that they were what I meant? Problems familiar from Wittgenstein's and Kripke's discussions of linguistic meaning arise here. Normally, I will not think of the later moves. But, even if I do, there are reasons to deny that thinking of them can constitute what it is to mean to perform them. I argue that the problem can be solved, in the case of routine action, by the notion that our behavioural routines are guided by what I callmodest agent memory. It will help explain both how wecan have future moves ‘in mind’ and how we can be in a position to avow the fact.     

Do the Concepts of Grammar and Use in Wittgenstein Articulate a Theory of Language or Meaning?

The paper elucidates Wittgenstein's later conception of philosophy as devoid of theories or theses, comprehending this as an articulation of a strategy for avoiding dogmatism in philosophy. More specifically, it clarifies Wittgenstein's conception by using what he says about the concepts of meaning and language as an example and by developing an interpretation that purports to make plain that what Wittgenstein says about these issues does not constitute a philosophical thesis. Adopting Wittgenstein's approach, we can, arguably, have a richer view of meaning and language than a commitment to philosophical theses allows for. I conclude with remarks on the method of analysis in terms of necessary conditions.     

Wittgenstein and logical necessity

An attempt is made to show that Wittgenstein's later philosophy of logic is not the kind of conventionalism which is often ascribed to him. On the contrary, Wittgenstein gives expression to a “mixed” theory which is not only interesting but tends to resolve the perplexities usually associated with the question of the a priori character of logical truth. I try to show that Wittgenstein is better understood not as denying that there are such things as “logical rules” nor as denying that the results of applying such rules are “logically necessary,” but as trying to understand what it is to appeal to a logical rule and what it means to say that the results of applying such a rule are “necessary.” He is not so much overthrowing standard accounts of logical necessity as discovering the limits of the concept.     

Wittgenstein,Theories of Meaning,and Linguistic Disjunctivism

This paper argues that Wittgenstein opposed theories of meaning, and did so for good reasons. Theories of meaning, in the sense discussed here, are attempts to explain what makes it the case that certain sounds, shapes, or movements are meaningful linguistic expressions. It is widely believed that Wittgenstein made fundamental contributions to this explanatory project. I argue, by contrast, that in both his early and later works, Wittgenstein endorsed a disjunctivist conception of language which rejects the assumption underlying the question that such theories seek to answer—namely, the assumption that the notion of a meaningful linguistic expression admits of non‐circular analysis. Moreover, I give two arguments in favor of the view I ascribe to Wittgenstein: one based on later Wittgenstein's discussion of meaning skepticism and one based on considerations concerning the identity of linguistic expressions.     

How Not to Read Philosophical Investigations: McDowell and Goldfarb on Wittgenstein on Understanding

In a recent article, John McDowell has criticised Warren Goldfarb for attributing an anti‐realist conception of linguistic understanding to Wittgenstein. 1 I argue that McDowell is right to reject Goldfarb's anti‐ realism, but does so for the wrong reasons. I show that both Goldfarb's and McDowell's interpretations are vitiated by the fact that they do not pay attention to Wittgenstein's positive claims about understanding, in particular his claim that understanding is a kind of ability. The cause of this oversight lies in their endorsement of an excessively anti‐systematic or “therapeutic” reading of Wittgenstein.     

Modal skepticism and counterfactual knowledge

Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic (Reducibility). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference (counterfactual development, or CD) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in a Reducibility-based reply to two kinds of modal skepticism. I argue that its use is entirely dispensable, and that Reducibility makes available replies to modal skeptics which show certain propositions to be metaphysically necessary by deductive arguments from premises the modal skeptic accepts can be known.     

The Disenchantment of Nonsense: Understanding Wittgenstein's Tractatus

This paper aims to argue against the resolute reading, and offer a correct way of reading Wittgenstein's Tractatus. According to the resolute reading, nonsense can neither say nor show anything. The Tractatus does not advance any theory of meaning, nor does it adopt the notion of using signs in contravention of logical syntax. Its sentences, except a few constituting the frame, are all nonsensical. Its aim is merely to liberate nonsense utterers from nonsense. I argue that these points are either not distinctive from standard interpretations or incorrect. Instead, the Tractarian elucidations help to shed light on the nature of language and logic, and introduce the correct method in philosophy. Philosophy deals with philosophical utterances and Tractarian elucidations by pointing out that they are nonsensical. By doing this, one is helped to see that what they appear to be saying is shown by significant propositions saying something else.     

奎因对模态逻辑的批评

奎因对模态逻辑的批评包括：(i)因为模态语境是指称不透明的,所以对其量化纳入没有意义;(ii)一些关于必然真理的经验知识与关于必然性的语言学理论不相容;(iii)模态语境中的量化纳入承诺了“亚里士多德式的本质主义”。丘奇,克里普克和福雷斯达尔对奎因提出了批评。他们提出,模态构造应该是外延上不透明但指称上透明的。奎因式诉诸于模态环境指称不透明的批评,在不采用单称词项的模态逻辑中不成立。他对本质主义的批评引入了一种必然性,但这种必然性没有办法用语言陈述词项进行解释。通过对语言中名称使用的讨论,我们可以看出,有关包含名称的同一性陈述的真值的经验知识,和卡苏洛称之为“一般模态地位”的先验知识是相容的。既然奎因论证了真同一性陈述的必然真是逻辑真,而且所有逻辑真都遵循戴维森式的意义理论（另文讨论）,那么我们可以给出一个关于包含名称的同一性的真陈述的模态地位的先验知识的语言学理论。     

IS THERE A TENSION IN WITTGENSTEIN'S PHILOSOPHY OF RELIGION?

This paper responds to Severin Schroeder's recent charge that Wittgenstein's philosophy of religion contains an ‘unresolved tension’ between three propositions, namely: (1) ‘As a hypothesis, God's existence (&c) is extremely implausible’; (2) ‘Christian faith is not unreasonable’; and (3) ‘Christian faith does involve belief in God's existence (&c)’. I argue as follows: that the first of these propositions has no place in Wittgenstein's thinking on religion; that the second is ill‐phrased and should be re‐worded as the proposition that ‘Christian faith is neither unreasonable nor reasonable’; and that the third proposition (contrary to what Schroeder seems to assume) tells us nothing about the nature of the objects of religious belief. It follows from my argument that Schroeder has not exposed a tension in Wittgenstein's thoughts on religion. I end with some positive remarks about Wittgenstein's method.     

Term Kinds and the Formality of Aristotelian Modal Logic

Recent formalizations of Aristotle's modal syllogistic have made use of an interpretative assumption with precedent in traditional commentary: That Aristotle implicitly relies on a distinction between two classes of terms. I argue that the way Rini (2011. Aristotle's Modal Proofs: Prior Analytics A8–22 in Predicate Logic, Dordrecht: Springer) employs this distinction undermines her attempt to show that Aristotle gives valid proofs of his modal syllogisms. Rini does not establish that Aristotle gives valid proofs of the arguments which she takes to best represent Aristotle's modal syllogisms, nor that Aristotle's modal syllogisms are instances of any other system of schemata that could be used to define an alternative notion of validity. On the other hand, I argue, Robert Kilwardby's ca. 1240 commentary on the Prior Analytics makes use of a term-kind distinction so as to provide truth conditions for Aristotle's necessity propositions which render Aristotle's conversion rules and first figure modal syllogisms formally valid. I reconstruct a suppositio semantics for syllogistic necessity propositions based on Kilwardby's text, and yield a consequence relation which validates key results in the assertoric, pure necessity and mixed necessity-assertoric syllogistics.