Leslie Tharp proves three theorems concerning epistemic and metaphysical modality for conventional modal predicate logic: every truth is a priori equivalent to a necessary truth, every truth is necessarily equivalent to an a priori truth, and every truth is a priori equivalent to a contingent truth. Lloyd Humberstone has shown that these theorems also hold in the modal system Actuality Modal Logic, the logic that results from the addition of the actuality operator to conventional modal logic. We show (...) that Tharp’s theorems fail for the expressively equivalent Subjunctive Modal Logic, the logic that was developed by Kai Wehmeier as an alternative to AML. We then argue that the existence of Tharp’s theorems for AML is due to a faulty interpretation of the notion of necessary truth, a feature that is not shared by SML. The paper concludes with an argument for the thesis that the existence of the distinction between truth at all worlds w and truth at all worlds w from the point of view of w as the actual world is an artifact owing to the interaction of the necessity and actuality operator. (shrink)

From a purely formalist viewpoint on the philosophy of mathematics, experiments cannot (and should not) play a role in warranting mathematical statements but must be confined to heuristics. Yet, due to the incorporation of new mathematical methods such as computer-assisted experimentation in mathematical practice, experiments are now conducted and used in a much broader range of epistemic practices such as concept formation, validation, and communication. In this article, we combine corpus studies and qualitative analyses to assess and categorize the epistemic (...) roles experiments are seen—by mathematicians—to have in actual mathematical practice. We do so by text-mining a corpus of reviews from the _Mathematical Reviews_, which include the indicator word “experiment”. Our qualitative, grounded classification of samples from this corpus allows us to explore the various roles played by experiments. We thus identify instances where experiments function as references to established knowledge, as tools for heuristics or exploration, as epistemic warrants, as communication or pedagogy, and instances simply proposing experiments. Focusing on the role of experiments as epistemic warrants, we show through additional sampling that in some fields of mathematics, experiments can warrant theorems as well as methods. We also show that the expressed lack of experiments by reviewers suggests concordant views that experiments could have provided epistemic warrants. Thus, our combination of corpus studies and qualitative analyses has added a typology of roles of experiments in mathematical practice and shown that experiments can and do play roles as epistemic warrants depending on the mathematical field. (shrink)

The present study aims at giving factual support to the thesis that the Parmenides is serious in intention, rigorous in logical demonstration, and stylistically meticulous in its original composition. While this consideration may be tedious, still it is useful. Against a past history which has claimed to find the tone hilarious, the logic fallacious, the work inauthentic, the text in need of bracketing by divination, the whole incoherent— against these eccentricities a certain firm sobriety seems called for. I hope that (...) my conclusions find support and persist through fluctuations of philosophic and philological styles.The main difficulty with my thesis is that the text as we now have it (in Burnet's and Dies' editions) shows exceptions to every rule that might apply to style and even to logical structure. Thus it is almost but not quite uniformly true that each theorem opens with a theorem statement; that each is marked by a "questioning" response; that each deduction is valid when formalized in propositional calculus; and so on. Are the exceptions the result of careless composition; are they deliberate warnings not to take the proofs too seriously; or are they the result of errors in transmission? One way to test this is to reconstruct early versions of the text: if these show more logical rigor than the later versions the notion of a wholly valid original is supported; if they do not, the result may point toward the need for a less serious interpretation. A second thing to look for is the possibility that, here and there, parts of a coherent original text are uniquely conserved in sources other than the principal mss, B,T, and W. This assumes, of course, that the "original" text in question is the one with the best logical form, and that assumption seems justified. As a matter of fact, later copyings almost universally show deterioration, not improvement in style and logic.My textual findings are more compatible with some lines of interpretation than with others. Thus I offer some reasons for not accepting treatments of the work as a joke, mystical revelation, or abrupt metaphysical revision. The structure of the dialogue is best explained, I think, by reading it as an indirect proof that some non-Platonic interpretations of the theory of forms are unsatisfactory. In particular, these are the Megarian version (represented in the first part of the dialogue by Zeno, in the second by the First Hypothesis), and the Anaxagorean version put forward by Eudoxus (represented in the first part by Cephalus and his friends from Clazomenae, in the second by the Second Hypothesis). At the same time, the dialogue shows the need for a philosophic method other than the "hypothetical— deductive" way of dianoia; presumably this other method is the "dialectic" discussed in Republic VII. It also follows that any interpretation of the Phaedo which falls into either the Eudoxian or Megarian difficulties was not— at least at the date of the Parmenides—Plato's intended reading.Findings concerning the relations and reliability of the manuscripts of this dialogue also apply to the texts of the other Platonic dialogues which these mss contain.Further, the Parmenides is such an important work both historically and intrinsically that any insight which textual study can bring to its interpretation is a contribution to Western philosophy. (shrink)

Concerns the ‘problem of existence’ in mathematics: the problem of how to understand existence assertions in mathematics. The problem can best be understood by considering how Mathematical Platonists have understood such existence assertions. These philosophers have taken the existential theorems of mathematics as literally asserting the existence of mathematical objects. They have then attempted to account for the epistemological and metaphysical implications of such a position by putting forward arguments that supposedly show how humans can come to know of (...) the existence of mathematical objects. The reasoning of the most prominent philosophers in this Literalist tradition, Quine and Gödel, are critically discussed. By way of contrast, an alternative position, Heyting's Intuitionism, is examined. (shrink)

An anthology, in German translation with brief historical and mathematical notes, of selected theorems and proofs which the author has chosen as perfect specimens of the mode of mathematical thinking reflected in the development of pure mathematics in Greece. Both the scholarship and the selection are excellent.--R. S. B.

This volume gathers together for the first time are all the key texts in a crucial debate in modern philosophy, centered on Leibniz's famous 1695 essay, the "New System of the Nature of Substances and their Communication," in which he introduced his strikingly original theory of metaphysics. His "system" became increasingly famous and drew him into discussion and development of these ideas, both in public and in private, with a variety of thinkers, most notably the great French philosopher Pierre (...) Bayle. Woolhouse's and Francks's new English edition gives the only full representation of this debate, and will therefore be essential reading for anyone who wishes to gain a proper understanding of Leibniz's philosophy and its intelletual context. All the texts are newly translated and extensively annotated; many appear in English for the first time. (shrink)

This paper proposes a solution to the problem of non-locality associated with Bell’s theorem, within the counterfactual approach to the problem. Our proposal is that a counterfactual definition of locality can be maintained, if a subsidiary hypothesis be rejected, “locality involving two counterfactuals”. This amounts to the acceptance of locality in the actual world, and a denial that locality is always valid in counterfactual worlds. This also introduces a metaphysical asymmetry between the factual and counterfactual worlds. This distinction is analogous (...) to what occurs in the derivations of Bell’s theorem which assume hidden-variables, where macroscopic locality can be maintained at the price of rejecting outcome independence. This can be interpreted as non-locality at the level of potentialities, which might be identified with the non-locality of counterfactual worlds. Our solution, presented for the CHSH inequality, is falsifiable, and we test it with two other setups, Bell’s original inequality and the EPR thought-experiment. (shrink)

Gödel's Theorem is often used in arguments against machine intelligence, suggesting humans are not bound by the rules of any formal system. However, Gödelian arguments can be used to support AI, provided we extend our notion of computation to include devices incorporating random number generators. A complete description scheme can be given for integer functions, by which nonalgorithmic functions are shown to be partly random. Not being restricted to algorithms can be accounted for by the availability of an arbitrary random (...) function. Humans, then, might not be rule-bound, but Gödelian arguments also suggest how the relevant sort of nonalgorithmicity may be trivially made available to machines. (shrink)

This paper has two specific goals. The first is to demonstrate that the theorem in MetaphysicsΘ 9, 1051a24-27 is not equiva-lent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I ar-gue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosoph-ical reason for the Aristotelian theorem being shorter than the (...) Euclidean one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theo-rems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amend-ments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge. (shrink)

Kant famously insists that free will is a condition of morality. The difficulty of providing a demonstration of freedom has left him vulnerable to devastating criticism: critics charge that Kant's post-Groundwork justification of morality amounts to a dogmatic assertion of morality's authority. My paper rebuts this objection, showing that Kant offers a cogent demonstration of freedom. My central claim is that the demonstration must be understood in practical rather than theoretical terms. A practical demonstration of x works by bringing x (...) into existence, and what the demonstration of freedom brings into existence is a moral will, a will regulated by the moral law and capable of acting in accordance with it. Since to act morally is to act freely, bringing a moral will into existence actualizes our capacity for freedom and demonstrates that we possess it. To confirm the viability of such a demonstration, Kant must establish that agents can regulate their wills by practical principles, and that practical judgments are efficacious of themselves (i.e., that non-Humean motivational internalism is true). Kant, I argue, is successful on both counts. (shrink)

Bellʼs 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbachʼs principle of common cause. Despite being a hallmark of scientific thought, dropping the principle has been widely regarded as much less bitter medicine than the perceived alternative—dropping relativistic causality. Recently, however, some authors have proposed that modified forms of Reichenbachʼs principle could be maintained even with relativistic causality. Here we break down Reichenbachʼs principle into two independent assumptions—the principle of common cause proper and (...) factorization of probabilities. We show how Bellʼs theorem can be derived from these two assumptions plus relativistic causality and the law of total probability for actual events, and we review proposals to drop each of these assumptions in light of the theorem. In particular, we show that the non-commutative common causes of Hofer-Szabó and Vecsernyés fail to have an analogue of the notion that the common causes can explain the observed correlations. Moreover, we show that their definition can be satisfied trivially by any quantum product state for any quantum correlations. We also discuss how the conditional states approach of Leifer and Spekkens fares in this regard. (shrink)

We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.

Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due (...) to A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/Aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact. (shrink)

Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due (...) to A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact. (shrink)

I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations (...) underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. (shrink)

So much for the Aesthetic. We can now proceed to the Analytic, the philosophical importance of which is much greater. Kant's main contentions in this part of his work can be summed up in; two propositions: human understanding contains certain a priori concepts, and on these are based certain non-empirical principles; these concepts are only general concepts of a phenomenal object, and therefore the principles in question are only prescriptive to sense-experience. As has already been said, interest in the first (...) proposition has distracted attention from the fact that the important thing Kant has to say is contained in the second. (shrink)

The logical positivists’ critical attitude towards metaphysics is sketched. Strawson’s conception of descriptive and revisionary metaphysics is described. Revisionary metaphysics is argued to be chimerical, and descriptive metaphysics is argued not to be a form of metaphysics at all. Strawson’s failure to account for the status of propositions of descriptive metaphysics is held to be remediable by reference to Wittgenstein’s conception of grammatical propositions that express norms of representation.

Set theoretic formulation of Arrow's theorem, viewedin light of a taxonomy of transitive relations,serves to unmask the theorem's understatedgenerality. Under the impress of the independenceof irrelevant alternatives, the antipode of ceteris paribus reasoning, a purported compilerfunction either breaches some other rationalitypremise or produces the effet Condorcet. Types of cycles, each the seeming handiwork of avirtual voter disdaining transitivity, arerigorously defined. Arrow's theorem erects adilemma between cyclic indecision anddictatorship. Maneuvers responsive theretoare explicable in set theoretic terms. None ofthese gambits rival in (...) simplicity the unassistedescape of strict linear orderings, which, by virtueof the Arrow–Sen reflexivity premise, are notcaptured by the theorem. Yet these are therelations among whose n-tuples the effetCondorcet is most frequent. A generalization andstronger theorem encompasses these and all otherlinear orderings and total tierings. Revisions tothe Arrow–Sen definitions of `choice set' and`rationalization' similarly enable one to generalizeSen's demonstration that some rational choicefunction always exists. Similarly may onegeneralize Debreu's theorems establishing conditionsunder which a binary relation may be represented bya continuous real-valued order homomorphism. (shrink)

A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.

Contemporary philosophical discourse has deeply problematized the possibility of absolute existence. Hegel’s Foundation Free Metaphysics demonstrates that by reading Hegel’s Doctrine of the Concept in his Science of Logic as a form of Absolute Dialetheism, Hegel’s logic of the concept can account for the possibility of absolute existence. Through a close examination of Hegel’s concept of self-referential universality in his Science of Logic, Moss demonstrates how Hegel’s concept of singularity is designed to solve a host of metaphysical and epistemic (...) paradoxes central to this problematic. He illustrates how Hegel’s revolutionary account of universality, particularity, and singularity offers solutions to six problems that have plagued the history of Western philosophy: the problem of nihilism, the problem of instantiation, the problem of the missing difference, the problem of absolute empiricism, the problem of onto-theology, and the third man regress. Moss shows that Hegel’s affirmation and development of a revised ontological argument for God’s existence is designed to establish the necessity of absolute existence. By adopting a metaphysical reading of Richard Dien Winfield’s foundation free epistemology, Moss critically engages dominant readings and contemporary debates in Hegel scholarship. Hegel’s Foundation Free Metaphysics will appeal to scholars interested in Hegel, German Idealism, 19th- and 20th-century European philosophy, metaphysics, epistemology, and contemporary European thought. (shrink)

Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. We re-explore this idea and discover that in the setting of the (...) potential infinite one can interpret first-order Peano arithmetic, but not second-order Peano arithmetic. We conclude that in order for the logicist to weaken the metaphysically loaded claim of necessary actual infinities, they must also weaken the mathematics they recover. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:From the Sacrifice of the Letter to the Voice of TestimonyGiorgio Agamben’s Fulfillment of MetaphysicsJeffrey S. Librett (bio)By denying us the limit of the Limitless, the death of God leads to an experience in which nothing may again announce the exteriority of being, and consequently to an experience which is interior and sovereign. But such an experience, for which the death of God is an explosive reality, discloses as (...) its own secret and clarification, its intrinsic finitude, the limitless reign of the Limit, and the emptiness of those excesses in which it spends itself and where it is found wanting.—Michel Foucault, “Preface to Transgression”Can there be a discourse that, without being a metalanguage or sinking into the unsayable, says language itself and exposes its limits?—Giorgio Agamben, “The Idea of Language”I shall not rest until every German sees that it is a shameful thing to be a lawyer.—Adolf Hitler, speech before theReichstag, April 26, 1942From his early works on, Giorgio Agamben has opposed the thought of no contemporary philosopher more consistently and programmatically than that of Jacques Derrida, whose questioning of phonocentric metaphysics Agamben has tried to replace by a characterization of metaphysics as (what I am calling here) graphocentric. To go back behind the replacement of the voice by the letter is for Agamben to recover the event of language itself, the taking-place of language as Being.1 In his conceptualization of the project for such a recovery, as we shall see, Agamben’s commitment to Heidegger’s fundamental ontology is overdetermined by his investment in the Christian God as logos.This philosophical program in Agamben’s early essays guides his later work on the homo sacer-sovereign relation but also distorts and disturbs the later work in three principal ways. First, it prompts him to propose an exclusively juridicopolitical understanding of the sacredness of the homo sacer, effectively scapegoating the juridical sphere for a more broadly theopolitical problem, while placing the specifically Christian background [End Page 11] of his antinomianism in a misleadingly secular, rational, and universalist light. Symptomatically, in order to accomplish this juridicopolitical reduction Agamben must reject Bataille’s analysis of sacrifice—along with the entire modern anthropological reading of the sacred—out of hand. For this rejection protects his discourse against any sustained confrontation with the importance of the sacrificial dimension for both what he calls the homo sacer and his own approach to law in his theorization of the homo sacer..Second, Agamben’s philosophical program impoverishes the account he provides of the Nazi death camps as an extreme example of the sovereign-homo sacer relation by making it impossible for him to appreciate the importance of Christian antinomianism in the formation of National Socialist ideology. For Agamben’s philosophical orientation requires or presupposes that he ignore or underestimate, first of all, the sacrificially anti-Semitic dimension of Christian antinomianism—the tendency of such antinomianism to make Judaism responsible for the ontological desert into which representation exiles us all. Further, as a consequence of his continuing commitment to this tradition, Agamben cannot see how important the tradition remains, even if in a displaced form, for Nazi anti-Semitism. I argue that Agamben’s animus against the letter blinds him to the Christian and sacrificial dimensions of the Holocaust—he ignores the former and explicitly, emphatically denies the latter dimension—because this animus represents his own commitment to the Christian antinomianism that, in its racialized National Socialist form, attempts to rid itself of the letter by sacrificing not only Judaism but the (biologically, racially construed) Jews. Because his radically antinomian program would become unsettled by his recognition of its important overlap with the ideological bases of National Socialism, Agamben cannot ultimately acknowledge the Christian and sacrificial aspects of the Holocaust.Finally, in Remnants of Auschwitz—his main reading (outside of Homo Sacer) of the significance of the Nazi death camps—Agamben positions “testimony” as the exemplary instance of the speaking of speech, the taking-place of language. The result of the destruction of European Jewry becomes here the revelation of poetic speech as a manifestation of the absolute. Unwittingly, Agamben ends up participating in... (shrink)

Can philosophy offer reasonable grounds for the existence of a God possessing genuine religious significance and not proposed simply as the solution to a purely intellectual philosophical problem? Certainly many contemporary thinkers have insisted that no genuine religion could be based upon metaphysics. In this book, however, T. L. S. Sprigge examines sympathetically the most notable metaphysical systems of the last four centuries which purport to put religion on a rational footing and, after a thorough examination of their claims, (...) considers what kind of religious outlook they might support and how they actually affected the lives of their proponents. The thinkers studied include Spinoza, Hegel, T. H. Green, Bernard Bosanquet, Josiah Royce, A. N. Whitehead, and Charles Hartshorne, concluding with an exposition of the author's own viewpoint and a general discussion on the relation between metaphysics and religion. There is also a chapter on Kierkegaard as the most important critic of metaphysical religion. (shrink)

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

The first major work in the history of philosophy to bear the title "Metaphysics" was the treatise by Aristotle that we have come to know by that name. But Aristotle himself did not use that title or even describe his field of study as 'metaphysics'; the name was evidently coined by the first century C.E. editor who assembled the treatise we know as Aristotle's Metaphysics out of various smaller selections of Aristotle's works. The title 'metaphysics' -- (...) literally, 'after the Physics' -- very likely indicated the place the topics discussed therein were intended to occupy in the philosophical curriculum. They were to be studied after the treatises dealing with nature (ta phusika). In this entry, we discuss the ideas that are developed in Aristotle's treatise. (shrink)

Theorems of hyperarithmetic analysis occupy an unusual neighborhood in the realms of reverse mathematics and recursion-theoretic complexity. They lie above all the fixed iterations of the Turing jump but below ATR $_{0}$. There is a long history of proof-theoretic principles which are THAs. Until the papers reported on in this communication, there was only one mathematical example. Barnes, Goh, and Shore [1] analyze an array of ubiquity theorems in graph theory descended from Halin’s [9] work on rays in (...) graphs. They seem to be typical applications of ACA $_{0}$ but are actually THAs. These results answer Question 30 of Montalbán’s Open Questions in Reverse Mathematics [19] and supply several other natural principles of different and unusual levels of complexity.This work led in [25] to a new neighborhood of the reverse mathematical zoo: almost theorems of hyperarithmetic analysis. When combined with ACA $_{0}$ they are THAs but on their own are very weak. Denizens both mathematical and logical are provided. Generalizations of several conservativity classes are defined and these ATHAs as well as many other principles are shown to be conservative over RCA $_{0}$ in all these senses and weak in other recursion-theoretic ways as well. These results answer a question raised by Hirschfeldt and reported in [19] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong or very strong going up a standard hierarchy and at the end being stronger than full second-order arithmetic. (shrink)

Review of Substance and Essence in Aristotle: an Interpretation of Metaphysics VII-IX, by Charlotte Witt (Cornell University Press: 1989).

Aristotle asserts in Met. Theta 4 that „if A, then B“ is a consequence of „if A is possible, then B is possible,“ for any sentences A and B. His assertion has often been questioned, or even been suspected to be a crude mistake. After a discussion of a typical objection, it is shown that a plausible reading of Aristotle’s claim is true: The twice occurring „if – then“ has to be understood in the sense of logical entailment, and sentences (...) suitable as substitutes for the variables „A“ and „B“ are required to contain no modal expressions. The claim in question is the converse of the assertion also advanced in Theta 4 that „if A is possible, then B is also possible“ is a consequence of „if A, then B.“ An application of this cognate of pertaining to the incommensurability of a square’s diagonal is expounded. In the final section, the argument advanced by Aristotle himself in defence of is evaluated. (shrink)

Many thinkers have said that a God whose existence is argued for metaphysically would have no religious significance even if he existed. This book examines the God or Absolute which emerges in various metaphysical systems and asks whether he, she, or it could figure in any genuinely religious outlook. The systems studied are those of Spinoza, Hegel, T. H. Green, F. H. Bradley (very briefly), Bernard Bosanquet, Josiah Royce, A. N. Whitehead, Charles Hartshorne. There is also a chapter on Kierkegaard (...) as the most important critic of metaphysical religion (especially Hegelian Christianity). The book ends with a statement of a form of absolute or pantheistic idealism espoused by the author and an indication of what religious significance it may have. (shrink)

This is a comprehensive and appreciative account of Dewey’s philosophy of value. It succeeds in rectifying certain current misconceptions of Dewey’s aims and contributions to moral philosophy, and in clearly presenting a coherent theory of value. Gouinlock begins his account by laying stress upon Dewey’s Experience and Nature as a key to Dewey’s thought. Chapter 1 is devoted to this task. It is held that "Dewey develops and articulates an inclusive philosophy by characterizing such things as art, science, and value (...) with a common set of concepts denoting the generic traits of experience." There is also a discussion of Dewey’s philosophic method and the uses and abuses of experience. Chapter 2 deals with man and nature and Dewey’s critical response to bifurcation between mind and body, and the relation between individual and society. Chapter 3 begins with Nature and Value. Here one finds a good discussion of ends-in-view and values. A great stress is laid on Dewey’s use of metaphysical concepts in value analysis, in particular the needed stress on the inclusive unity of means and end. (shrink)