In this paper, using Mark Schroeder’s (2008a) expressivist semantic framework for normative language as a case study, I will identify difficulties that even an expressivist semantic theory capable of addressing the Frege-Geach problem will encounter in handling the logical possibility of moral dilemmas. To this end, I will draw on a classical puzzle formulated by McConnell (1978) that the logical possibility of moral dilemmas conflicts with some of the prima facie plausible axioms of the standard deontic (...) logic, which include obligation implies permission. On the tentative assumption that proponents of ethical expressivism should be generally committed to securing the logical possibility of moral dilemmas in their semantic theories, I will explore whether and how expressivists can successfully invalidate obligation implies permission within the framework developed by Schroeder. The case study eventually reveals that this can indeed be a hard task for expressivists. Generalizing from the case study, I will suggest that the source of the difficulty ultimately lies in the mentalist assumption of the expressivist semantic project that the logico-semantic relations exhibited by normative sentences should be modeled in terms of the psychological attitudes that speakers express by uttering them. My final goal will be to show that the difficulty expressivists face in dealing with the logical possibility of moral dilemmas is a reflection of the more general problem that their commitment to the mentalist assumption prevents them from flexibly adopting or dropping axioms in their semantic theories to get the right technical results. (shrink)

The thesis that entities exist in, at, or in relation to logically possible worlds is criticized. The suggestion that actually nonexistent fictional characters might nevertheless exist in nonactual merely logically possible worlds runs afoul of the most general transworld identity requirements. An influential philosophical argument for the concept of world-relativized existence is examined in Alvin Plantinga’s formal development and explanation of modal semantic relations. Despite proposing an attractive unified semantics of alethic modality, Plantinga’s argument is rejected on formal grounds as (...) supporting materially false actual existence assertions in the case of actually nonexistent objects in the framework of Plantinga’s own underlying classical predicate-quantificational logic. (shrink)

Palmer's “isomorphism constraint” presupposes the logical possibility of two qualitatively disparate sets of sensory experiences exhibiting the same relationships. Two arguments are presented to demonstrate that, because such a state of affairs cannot be coherently specified, its occurrence is not logically possible. The prospects for behavioral and biological science are better than Palmer suggests; those for functionalism are worse.

In the appendices to his Logic of Scientific Discovery, Karl Popper presents a number of arguments in favour of the thesis that the logical probability of any universal law in an infinite universe must be zero. According to Popper, from this it follows that any attempt to apply a Bayesian approach to the confirmation of scientific laws is a non-starter—if the prior probability of any hypothesis h is zero = 0), it follows from Bayes Theorem that p = 0 (...) for any possible e. In this essay, I will discuss what I deem to be Popper’s main argument in support of this thesis. I shall argue that the general validity of two of the three assumptions on which the argument is based can be challenged. (shrink)

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There (...) are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

Using yet untapped resources from moral and political philosophy, this book seeks to answer the question of whether an all good God who is presumed to be all powerful is logically compatible with the degree and amount of moral and natural evil that exists in our world. It is widely held by theists and atheists alike that it may be logically impossible for an all good, all powerful God to create a world with moral agents like ourselves that does not (...) also have at least some moral evil in it. James P. Sterba focuses on the further question of whether God is logically compatible with the degree and amount of moral and natural evil that exists in our world. The negative answer he provides marks a new stage in the age-old debate about God's existence. (shrink)

Throughout his whole work, Wittgenstein seizes on a distinction between logical and physical possibility, and impossibility. Despite this continuity and although, Wittgenstein brings in this distinction in various contexts and from different vantage points, he often solely brushes over it without elaborating in detail. In the so-called Big Typescript, however, he dedicates himself not only to the distinction between logical and physical possibility but also to the distinction between logical possibility and impossibility in particular (...) investigations. In the course of these investigations, another aspect arises and is tossed and turned repeatedly by Wittgenstein – namely, the place of “imaginability” in these considerations. On the basis of three focussed chapters in the Big Typescript, I argue that “imaginability” as an utterance of the form “being able to imagine ‘what it would be like’” can be allocated the place of a criterion for logical possibility. To this end, I will first outline the chapters 96., 27. and 26. in one section each. Although in these chapters, Wittgenstein only indicates rather than claiming explicitly “imaginability” to be a criterion for logical possibility, I will discuss in the last section how this conclusion can be drawn by combining the results of the previous sections. (shrink)

A philosophical zombie is a being physically indistinguishable from an actual or possible human being, inhabiting a possible world where the _physical_ laws are identical to the laws of the actual world, but which completely lacks consciousness. For zombies, all is dark within, and hence they are, at the most fundamental level, utterly different from us. But, given their definition, this singular fact has no direct implications about the kind of motion, or other physical processes, the zombie will undergo within (...) its own world. Under quite standard physicalist assumptions, such as certain assumptions about the 'initial conditions' of the zombie's world and that of the causal closure of the physical. (shrink)

Are skeptical arguments invalid because they trade on an ambiguity of the word "possible," asserting that it is possible that our experiences are not of anything outside our own minds and concluding that it is not certain that there is an external world outside our own minds? It is sometimes asserted that such arguments invalidly trade on an ambiguity of "possible" where the premise is true only in the sense "logically possible" while the inference is valid only in the sense (...) "empirically possible." However, once we distinguish different grammatical complements of the phrase "it is possible" we recognize that, when used with the same complement, "possible" is not ambiguous. So the claim that skeptical arguments trade on an ambiguity of "possible" fails. (shrink)

This paper consists of a combination of material from sections 3.2, 4.5, and 4.6 from the 1997 edition of Time, Tense, and Causation, together with material added to correct an error in that earlier discussion. The added material was then used in the revised, paperback edition of Time, Tense, and Causation (2000), partly in section 4.6.2, but mainly in the Appendix.

In this paper I want to argue for the optimal way to characterise the logical and semantical behaviour of the singular term 'God' used in religious language. The relevance of this enterprise to logical theory is the main focus as well. Doing this presupposes to outline the two rivaling approaches of well-definition of singular terms: Kripke's and Hintikka's. 'God' as a "rigid designator" is purified from all real-life-language-games of identification and only spells out a metaphysical tag, which favours (...) the view of "anything goes". Instead, 'God' as a "world-line," plus two ways of quantification, is much more flexible to theological traditions, teachings of the church, religious practices and personal feelings. Thus, it provides a sufficiently well-defined singular term for the purposes of logical theory. (shrink)

This paper discusses critically what simulation models of the evolution ofcooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” and the modeling tradition it has inspired. Hardly any of the many simulation models of the evolution of cooperation in this tradition have been applicable empirically. Axelrod’s role model suggested a research design that seemingly allowed to draw general conclusions from simulation models even if the mechanisms that drive the simulation could not be identified empirically. But this research design was (...) fundamentally flawed, because it is not possible to draw general empirical conclusions from theoretical simulations. At best such simulations can claim to prove logical possibilities, i.e. they prove that certain phenomena are possible as the consequence of the modeling assumptions built into the simulation, but not that they are possible or can be expected to occur in reality I suggest several requirements under which proofs of logical possibilities can nevertheless be considered useful. Sadly, most Axelrod-style simulations do not meet these requirements. I contrast this with Schelling’s neighborhood segregation model, thecore mechanism of which can be retraced empirically. (shrink)

The possibility of spectrum inversion has been debated since it was raised by Locke and is still discussed because of its implications for functionalist theories of conscious experience . This paper provides a mathematical formulation of the question of spectrum inversion and proves that such inversions, and indeed bijective scramblings of color in general, are logically possible. Symmetries in the structure of color space are, for purposes of the proof, irrelevant. The proof entails that conscious experiences are not identical (...) with functional relations. It leaves open the empirical possibility that functional relations might, at least in part, be causally responsible for generating conscious experiences. Functionalists can propose causal accounts that meet the normal standards for scientific theories, including numerical precision and novel prediction; they cannot, however, claim that, because functional relationships and conscious experiences are identical, any attempt to construct such causal theories entails a category error. (shrink)

Then some Pharisees and scribes came to Jesus from Jerusalem, saying, "Why do your disciples transgress the tradition of the elders?" .... And he answered and said to them, "And why do you yourselves transgress the commandment of God for the sake of your tradition?" [Matthew 15:1 3].

A. Collins once argued that time travel is only imaginable if we relate the "event" out of context. John Hospers argues that it is logically possible for an iron bar to float in water even if it is actually (empirically) impossible. My point in this piece is that Hospers relies on viewing the floating out of context, in Walt Disney fashion; but that is no way to establish any kind of possibility. I also discuss "conceivability", a term frequently used (...) either to clarify logical possibility or to interchange for the same. I argue that it cannot do either. (shrink)

This article reassesses Suárez’s claim that real essences are intrinsically logically possible. (Henceforth, this claim is referred to as ‘ILP.’) Most scholars have understood ILP as asserting the independence of logical possibility from God’s power; on their view, it in fact asserts that real essences in themselves explain logical possibility. As a result, the claim is in tension with Suárez’s other thesis that real essences are nothing in themselves. Scholars have taken two main approaches to assessing (...) this tension. Some, like John Doyle and Norman Wells, argue that Suárez contradicts himself. There is no way for real essences both to be intrinsically logically possible and also to be nothing. More recently, however, scholars have jumped to Suárez’s defense. They argue that he avoids contradiction because they claim that he accepts some further radical thesis which allows him to remove the tension. But these scholars still accept the claim that ILP asserts that real essences explain logical possibility. This article contests this basic interpretation. I will argue that ILP is not a thesis about the explanation or ground of logical possibility. First, it abstracts from notions of actual existence; as a result, it cannot be a claim about ontological explanation. Second, in order to conceive of logical possibility, intellectual operation is necessary; thus, it is not the sort of property which can have an ontological explanation in the usual sense. Third and finally, insofar as logical possibility can be explained, Suárez turns out to explain it through God’s power. (shrink)

I conceive the Trinity doctrine as the proposition that there are three persons each of whom is God but just one being which is God. In two papers by Peter van Inwagen I distinguish three potential candidates for a reason that the Trinity doctrine is logically possible. First, a particular conjunction entailing the Trinity doctrine is formally consistent in relative identity logic. Second, the conjunction is formally consistent in the standard logic. Third, the conjunction shares a form in relative identity (...) logic with another logically possible conjunction. I explain how all these three reasons fail because of the distinction between logical possibility and formal consistency. In contrast to previous critiques, I dispense with epistemological and metaphysical assumptions about absolute and relative identity. Instead, I employ modal distinctions endorsed even by the inspirer of van Inwagen’s relative identity of the Trinity — the pioneering analytic scholastic Peter Geach. (shrink)

The general issue addressed in this dissertation is: what do the models of formal model-theoretic semantics represent? In chapter 2, I argue that those of first-order classical logic represent meaning assignments in possible worlds. This motivates an inquiry into what the interpretations of first-order quantified model logic represent, and in Chapter 3 I argue that they represent meaning assignments in possible universes of possible worlds. A possible universe is unpacked as one way model reality might be. The problem arises here (...) as to how we are to understand the distinction between the actual and the possible as it relates to modal reality. ;Along with the development of the main arguments in Chapters 2 and 3, the dissertation assesses the status of semantic accounts or logical properties and relations. Specifically, what does the model-theoretic account of a logically possible situation add to the syntactic account ? ;Proofs of invalidity in terms of the models of formal semantics do not establish that it is possible for the premises to be true and the conclusion false, since a formal model is merely given by a consistent set of sentences. Unless there is some way to generate a non-formal model from a formal one, such proofs do not really go beyond syntactic notions. The dissertation ends by concluding that there is no way to generate a non-formal model from a formal one without relying on logical intuitions that are syntactical. ;Hence efforts to construct a semantic basis for model logic independent of syntactic commitments are misguided. However, in classical logic the independence of the semantic account from the syntactic one is grounded on the intuition that it is metaphysically possible for there to be a denumerably infinite totality of objects. (shrink)

In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...) semantics can meet that challenge by allowing for each interpretation to be composed of multiple scenarios. Using that idea, a logic with a complex semantic behavior can be understood as an appropriate combination of ingredient logics with simpler semantic behaviors into which the original logic is given a collection of translations preserving its soundness. Completeness is then achieved through the judicious choice of the admissible translating mappings. The present note provides interpretation by way of possible-translations semantics for a group of fundamental paraconsistent logics extending the positive fragment of classical propositional logic. The logics PI, Cmin, mbC, bC, mCi and Ci, among others, are all initially presented through their non-truth-functional bivaluation semantics and sequent versions and then split by way of possible-translations semantics based on 3-valued ingredients. (shrink)

Our conception of logical space is the set of distinctions we use to navigate the world. Agustn Rayo argues that this is shaped by acceptance or rejection of 'just is'-statements: e.g. 'to be composed of water just is to be composed of H2O'. He offers a novel conception of metaphysical possibility, and a new trivialist philosophy of mathematics.

The paradox of knowability threatens to draw a logical equivalence between the believable claim that all truths are knowable and the obviously false claim that all truths are known. In this paper we evaluate prominent proposals for resolving the paradox of knowability. For instance, we argue that Neil Tennant’s restriction strategy, which aims principally to restrict the main quantifier in ‘all truths are knowable’, does not get to the heart of the problem since there are knowability paradoxes that the (...) restriction does nothing to thwart. We argue that Jon Kvanvig’s strategy, which aims to block the paradox by appealing to the special role of quantified epistemic expressions in modal contexts, has grave errors. We offer here a new proposal founded on Kvanvig’s insight that quantified expressions play a special role in modal contexts. On an articulation of this special role provided by Stanley and Szabo, we propose a solution to the knowability paradoxes. Introduction.. (shrink)

May the theory of radical interpretation developed by Donald Davidson on the basis of Quine's arguments for the indeterminacy of translation help fix the meaning of the logical constants? In particular, may the theory exclude ways of conferring meaning on the constants which, although developed within the Davidsonian framework, would lead to unexpected results? Could an interpreter fix the meaning of the constants in a non classical way, although still in accordance with the guiding principles of the interpretative strategy? (...) Or, on the contrary, does the theory incorporate constraints on interpretation which are stronger than those imposed by the possibility of non classical, or deviant logics? I examine the particular case of negation within the framework of the natural deduction system developed by Gentzen and Prawitz, and conclude that Davidson's theory, understood as an empirical theory of truth, leaves the problem of knowing which meaning should be assigned to the constant for negation without a satisfactory solution. Although interpetation has to be carried out according to the principle of charity, disagreements may come up regarding which meaning should be assigned to "not" in a properly regimented natural language. (shrink)

In this essay, I argue for a view that inclusive positivists share with Ronald Dworkin. According to the Moral Incorporation Thesis (MIT), it is logically possible for a legal system to incorporate moral criteria of legality (or “grounds of law,” as Dworkin puts it). Up to this point, the debate has taken the shape of attacks on the coherence of MIT with the defender of MIT merely attempting to refute the attacking argument. I give a positive argument for MIT. I (...) begin with an explanation of the logic of establishing possibility claims, such as MIT. At the outset, it is worth noting that the logic of establishing possibility claims is very different from the logic of establishing contingent descriptive claims or necessary claims. For this reason, some explication of the relevant features of the semantics of modal logic will be necessary here. Once the structural framework is adequately developed, the argument for MIT will be grounded on the strength of a thought experiment of a surprisingly simple kind. Indeed, the argument is inspired by a Razian argument for the possibility of a legal system without coercive enforcement machinery; on his view, a society of angels could still have a system of law without any coercive machinery. My argument will possess two theoretically important qualities that are also possessed by Raz’s powerfully simple, but ultimately unsuccessful, argument. (shrink)

This paper is a critique of Contessa’s . First, I show that Popper in The Logic of Scientific Discovery argues against the view that the logical probability of a hypothesis is identical to its degree of confirmation , rather than against Bayesianism. Second, I explain that his argument to this effect does not depend on the assumption that ‘the universe is infinite’. Third, and finally, I refine Popper’s case by developing an argument which requires only that some universal laws (...) have a logical probability of zero relative to any finite evidence, and providing an example concerning Newtonian mechanics. (shrink)

This paper is about the pragmatic inferences in play as conversational implicatures (Grice, P. 1989. Studies in the way of words. Cambridge, MA: Harvard University Press) occur. First, it constructs the deductivism versus abductivism debate that transpires from the extant literature but is rarely elaborated. Against deductivism, the paper argues that implicating inferences in conversational implicatures can instantiate an abductive logical form, as abductivism suggests. Against abductivism, however, it grants to deductivism that implicating inferences can have a deductive form (...) provided the latter is of a defeasible type. In sum, it thus argues for pluralist defeasibilism. Second, it turns to the issue of the ontological nature of implicating inferences and advocates normative inferentialism, on which these inferences are not primarily real psychological processes but rules of the practice of implicating. While this allows for the possibility of their psychological instantiation, to be sure, the paper also insists that psychological inferring processes in implicatures are neither necessarily isomorphic to the aforementioned rules nor even necessarily occur as an implicature occurs. (shrink)

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.

After some generalities about connections between functions and relations in Sections 1 and 2 recalls the possibility of taking the semantic values of ‐ary Boolean connectives as ‐ary relations among truth‐values rather than as ‐ary truth functions. Section 3, the bulk of the paper, looks at correlates of these truth‐value relations as applied to formulas, and explores in a preliminary way how their properties are related to the properties of “logical relations” among formulas such as equivalence, implication (entailment) (...) and contrariety (logical incompatibility), concentrating for illustrative purposes on binary logical relations such as those just listed. To avoid an excess of footnotes, some points have been deferred to an Appendix as “Longer Notes”. (shrink)

At the heart of the Stoic theory of modality is a strict commitment to bivalence, even for future contingents. A commitment to both future truth and contingency has often been thought paradoxical. This paper argues that the Stoic retreat from necessity is successful. it maintains that the Stoics recognized three distinct senses of necessity and possibility: logical, metaphysical and providential. Logical necessity consists of truths that are knowable a priori. Metaphysical necessity consists of truths that are knowable (...) a posteriori, a world order according to certain metaphysical principles and natures that god crafts within the constraints of matter. Finally, what is providentially necessary is what occurs according to the chain of fate, but only once it is in process or past. -/- The method of the paper is a close reading of Diogenes Laertius 7.75, adducing broad textual evidence along the way, to show that the Stoic theory of modality embraces Philonian possibility, both that which is capable of being true as a matter of logical consistency, and that which is possible according to the bare fitness of the entity. What differentiates the Stoics from Philo is their additional commitment to possibility as opportunity, resisting the collapse of determinism into necessity. (shrink)