This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.

It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree (...) with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense.” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it. (shrink)

The rigid designation of proper names and natural kind terms is the most well-known doctrine of Kripke’s Naming and Necessity (1981). On the basis of rigidity, Kripke has shown that proper names and natural kind terms do not refer via a description as argued by descriptivists. In response to Kripke several people have argued that all general terms could be interpreted rigidly, which would make the notion of rigidity trivial. This leads to the ‘rigidity problem’: the notion of rigidity cannot (...) be used to argue against descriptivism anymore. I will show that the rigidity problem appears on a larger scale: firstly, because it appears independently of the trivialisation problem, secondly, because it appears for descriptions acting like singular terms as well. I will argue, however, that proper names and natural kind terms differ in an important manner from rigid descriptions. While the first are de jure rigid, the latter are de facto rigid. I will show that the rigidity problem indeed appears for de facto rigidity, but not for de jure rigidity, with the result that Kripke’s argument against descriptivism can withstand. (shrink)

Kripke has argued that definitions of units of measurements provide examples of statements that are both contingent and a priori. In this paper I argue that definitions of units of measurement are intended to be stipulations of what Kripke calls "theoretical identities": a stipulation that two terms will have the same rigid designation. Hence such a definition is both a priori and necessary. The necessity arises because such definitions appeal to natural kind properties only, which on Kripke's account are necessary.

Names are rigid designators, but what kind of rigidity do they exhibit? Both “obstinately” and “persistently” rigid designators pick out O at every world at which they pick out anything at all. They differ in that obstinately rigid designators also pick out O at worlds at which O fails to exist; persistently rigid designators have no extension whatsoever at worlds at which O fails to exist. The question whether names are obstinate or persistent arises in two contexts: in arguments against (...) rigidified descriptivism (on the grounds that names and rigidified descriptions exhibit different kinds of rigidity) and in considerations about what it means for an expression to be “directly referential.” This paper contends that names are persistent, not obstinate. The position thus clarifies the relationship between Millian theories of names and rigid designation, in addition to undermining attempts to rehabilitate the modal argument against rigidified descriptivism. (shrink)

By introducing a name ‘one meter’ and stipulating that it refers to the length of stick S, the stipulator appears to be in a position to gain immediate (and arguably a priori) knowledge of a mind‐ and language‐independent fact—the fact that the length of stick S is one meter. It appears that other users of the name can gain this knowledge only through empirical enquiry. I argue that this presents a paradox. After clarifying the nature of the paradox, I offer (...) a solution by arguing that, contrary to appearances, other users of ‘one meter’ implicitly knew that the length of stick S is one meter before learning the name, as did the stipulator prior to introducing the name. There is some distinct knowledge that other users of the name can only gain empirically, but the stipulator cannot gain this knowledge without empirical enquiry either. (shrink)

Famously, Saul Kripke proposes that there are contingent a priori truths, and has offered a number of examples to illustrate his claim. The most well-known example involves the standard meter bar in Paris. Purportedly, a certain agent knows a priori that the bar is one meter long. However, in response to a long-standing objection to such examples - the "existential complaint" - generally only modified examples having a conditional form are now considered candidates for the contingent a priori. Gareth Evans (...) argues that these conditionals must be understood free-logically, and on this basis argues against Keith Donnellan's analysis of the contingent a priori. I show Evans' argument mistaken. I also take issue with the existential complaint, and suggest a way of understanding Kripke's original examples that is not subject to it. My approach focuses the debate in its right place, and allows us to take Kripke's original examples seriously. (shrink)

The paper is an investigation into the concept of actuality from the standpoint of the philosophy of language. It is argued that expressions such as 'actually' and 'in fact' are not indexicals like 'here' and 'now'; when e.g. 'Snow is actually white' is uttered in a world, what proposition is conveyed does not depend on the world. Nor are such expressions ambiguous. The paper makes a suggestion about the role that 'actually' and its cognates do play. It is also argued (...) that the sentence ⌜Actually S ⌝ expresses a necessary truth only if S itself expresses one. In order to capture the necessitation of the proposition expressed in ⌜Actually S ⌝, it is not sufficient to prefix the word 'necessarily'. (shrink)

The paper is an investigation into the concept of actuality from the standpoint of the philosophy of language. It is argued that expressions such as ‘actually’ and ‘in fact’ are not indexicals like ‘here’ and ‘now’; when e.g. ‘Snow is actually white’ is uttered in a world, what proposition is conveyed does not depend on the world. Nor are such expressions ambiguous. The paper makes a suggestion about the role that ‘actually’ and its cognates do play. It is also argued (...) that the sentence ⌜Actually S⌝ expresses a necessary truth only if S itself expresses one. In order to capture the necessitation of the proposition expressed in ⌜Actually S⌝, it is not sufficient to prefix the word ‘necessarily’. (shrink)

In this paper I argue that Wittgenstein is correct when he says of the Standard Metre stick that we can neither say that it is or is not a metre in length – despite what our intuitions may tell us to the contrary. Specifically, the paper deals with Kripke's criticism of Wittgenstein's claim in Naming And Necessity and with Salmon's attempt to arbitrate between the two views. I conclude that, not only is Wittgenstein correct, but that both Kripke and Salmon (...) (and possibly the majority of philosophers) simply do not understand the concept of measurement. (shrink)

Anselm's argument for the existence of God in Proslogion Chap.II starts from the contention that `lq when a Fool hears `something-than-which-nothing-greater-can-be-thought', he understands what he hears, and what he understands is in his mind. This is a special feature of the Pros.II argument which distinguishes the argument from other ontological arguments set up by, for example, Descartes and Leibniz. This is also the context which makes semantics necessary for evaluation of the argument. It is quite natural to ask `lq What (...) is understood by the Fool, and what is in his mind? It is essential for a proper consideration of the argument to identify the object which is understood by the Fool, and so, is in his mind. A semantics gives answers to the questions of `lq What the Fool understands? and `lq What is in the Fool's mind? If we choose a semantics as a meta-theory to interpret the Pros.II argument, it makes an effective guide to identify the object. It is a necessary condition for a proper evaluation of the Pros.II argument to fix our universe of discourse, especially since, in the argument, we are involved in such talk about existing objects as Anselm's contention that `when a Fool hears `something-than-which-nothing-greater-can-be-thought', he understands what he hears, and what he understands is in his mind. The ontology to which a semantic theory commits us will be accepted as our scope of objects when we introduce our semantic theory to interpret the Pros.II argument, and this ontological boundary constrains us to identify the object in a certain way. Consistent application of an ontology, most of all, is needed for the evaluation of the logical validity of an argument. If we take Frege's three-level semantics, we are ontologically committed to intensional entities, like meaning, as well as extensional entities. Sluga contends that Frege's anti-psychologism for meanings should not be interpreted as vindicating reification of intensional entities in relation to Frege's contextualism, that Frege's anti-psychologism with his contextualism is nothing but a linguistic version of Kantian philosophy for the transcendental unity of a judgement. There is, however, another possible interpretation of Frege's contextualism. According to Dummett, the significance of Frege's contextualism must be understood as a way of explanation for a word's having meaning. If Dummett's view is cogent, we could say that Frege's contextualism does not prevent our interpreting his semantics as being committed to intensional entities. We need not worry that Frege's over all semantics, especially with his contextualism, would internally deny the ontological interpretation of his theory. We see Anselm's argument for the existence of God in Pros.II is an invalid argument if we introduce Frege's three-level semantics, i.e. if we acknowledge meanings of words as entities in our universe of discourse. We can also employ extensional semantics for the interpretation of the Pros.II argument. According to extensionalists, like Quine and Kripke, we need not assume intensional entities, like meaning, to be part of our ontological domain. They argue that we can employ our language well enough without assuming intensional entities. If we choose extensional semantics as a meta-theory to interpret the Pros.II argument, it commits us only to extensional entities as objects in the Universe of our interpretation. In Sections 1.4 and 1.5, I show that extensional semantics makes the Pros.II argument a valid argument for the existence of God. `lq Necessary existence is the central concept of Anselm's argument for the existence of God in Proslogion Chap.III. It has been said that, even if the argument is formally valid, it cannot stand as a valid argument for the existence of God, since `lq necessary existence is an absurd concept like `lq round square. And further that even if there is a meaningful combination of concepts for `lq necessary existence, it cannot quality as a subject of an a priori argument. As objections to the interpretations which make the Pros.III argument valid, it has been argued that even if there is a concept of `lq necessary existence which is meaningful and there is another concept of `lq necessary existence which is suitable as a subject of an a priori argument, there is no concept of `lq necessary existence which is meaningful and at the same time suitable as a subject of an a priori argument. In Chap.2 and Chap.3, I try to show that there can be concepts of `lq necessary existence which are proof against these objections. Anselm's arguments for the existence of God in Proslogian Chap.II and Chap.III are logically valid arguments on some logical principles. Some fideists, K. Barth, for example, argue that Anselm's arguments for the existence of God in Proslogion are not proofs for the existence of God even if they are logically valid arguments. I raise the question how this attitude could be possible, in Chap.4 and Chap.5. Barth's fideistic interpretation of Anselm's Proslogion arguments does not find any flaw in the validity of the arguments, and it accepts the meaningfulness and truth of the premises even to the fool in Proslogion. If this is the case, i.e. if Barth's interpretation accepts the validity of the arguments and the truth of the premises, I raise the question, how can the arguments not be interpreted as proofs for the existence of God? How is it possible that the function of the arguments is not that of proving the existence of God? According to Wittgensteinian fideism, premises in the arguments should not be intelligible to those who do not believe in God's existence already, and so the real function of the arguments is the elucidation, the understanding of believer's belief, rather than proving articles of belief to unbelievers. Barth's fideistic interpretation of the arguments, however, fully recognizes the meaningfulness and truth of the premises in the arguments as well as the validity of the arguments. I argue that there could be a justification for the Barthian fideism. As Malcolm notices, there are still atheists who understand Anselm's arguments as valid, but the only possibility for the people who recognize the validity of Anselm's arguments still to remain atheists has been thought to be to challenge the truth of premises employed in the arguments. Now, of the atheistic possibility, we can change the direction of our attention, that is, to the question about the function of a logically valid argument itself. What has not been thought of in relation to Anselm's arguments is the significance of logical truth or the logical validity of an argument. We have not asked such questions as `lq What does a logical truth say? and `lq What does a logically valid argument guarantee with true premises? Let us assume that even the premises are accepted by atheists. Do they all convert to theism? If that were so, the disagreement between atheist and believer over the ontological arguments should turn only on the truth of premises. If that is not so, there is some point in raising this other question. If there are people who, recognizing the premises and validity of an argument, are still reluctant to accept the conclusion, we have reason to question the function of a valid argument. I argue that there is a way of being consistently reasonable while accepting the premises and the validity of the ontological arguments and yet remaining an atheist or an agnostic. (shrink)