A common reaction to Hegel’s suggestion that we collapse Kant’s distinction between form and content is that, since such a move would also deprive us of any way of distinguishing the merely logical from the real possibility of our concepts, it is incoherent and ought to be rejected. It is true that these two distinctions are intimately related in Kant, such that if one goes, the other does as well. But it is less obvious that giving them up as (...) Kant conceives them is as incoherent a proposal as many of Hegel’s critics think. It has been the point of a recent account of Hegel’s idealism to demonstrate that his critique of Kant’s dichotomy between form and content or concept and intuition does not commit him to the view that human cognition is materially creative of its content in the manner of a God-like or intuitive intellect—does not, in other words, signify a return to a pre-Critical metaphysics. This is the interpretative stance I adopt here as well, in hope of giving defenders of Kant reasons for taking Hegel more seriously. (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)

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)

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.

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)

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)

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)

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)

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 discusses critically what simulation models of the evolution of cooperation can possibly prove by examining Axelrod’s “Evolution of Cooperation” (1984) and the modeling tradition it has inspired. Hardly any of the many simulation models 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. 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. It would be better not to use this kind of simulations at all. (shrink)

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)

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 (“rigid designators”) and Hintikka’s (“world-lines”). ‘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)

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)

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)

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 physical1, a zombie's behaviour, as well as its underlying physical state, should be indistinguishable from the behaviour and physical state of a genuine human being. (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.

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].

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)

Abstract This paper discusses some recent work on the notion of possibility in Wittgenstein's Tractatus assessed by means of an interpretation of the notion put forward in Cerezo 2005. It argues that the proper way to understand the notion of possibility in the Tractatus must pay equal attention both to the picture theory and the truth-functions theory. From this perspective, through an examination of Peach's proposal (2007) it shows that the role played by the notion of logical space in (...) the determination of sense needs to be emphasized. In addition, the paper considers some consequences of the Tractarian notion of possibility, namely, the strong contingency of the world that it involves, which is revealed by the thinkability of logical space as empty envisaged by Wittgenstein in T 2.013, and also discusses the recent debate between Reinhardt (2005) and Geach (2006) on this issue. (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)

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)

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)

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

How "red", "green" were defined? Through analyzing how two children with congenitally inverted color sensations corresponding to red flags and green grass accept their grand mothers’ teaching about colors, the paper get opposite conclusions against logical empiricism. The “red” and “green” and other names of properties of objects were defined by objective physical properties (or together with behavior, such as in defining “beauty”), instead our sensations. So language directly points to things in themselves passing through sensations and presentative world. (...) It is not that things in themselves are unknowable, but that sensations and presentative world cannot be exactly described by daily language. (shrink)

object an item which does not have a position in space and time but which exists. (Philosophers have nominated such things as numbers, sets, and propositions to this category. The need to posit such entities has been discussed and disputed for at least 2400 years.).

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)