The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a (...) different status over the other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)

This paper (1) criticizes Patzig's explanation of Aristotle's reason for calling his first figure syllogisms perfect syllogisms, i.e. the transitivity relation: it can only be used for Barbara, not for the other three moods. The paper offers (2) an alternative interpretation: It is only in the case of the (perfect) first figure moods that we can move from the subject term of the minor premiss, taken to be a predicate of an individual, to the predicate term of the (...) major premiss. This contention is supported (i) by Aristotle's wording of the dictum de omni et nullo and (ii) by Aristotle's use of a formula which puts the minor term in the first position when he first states Barbara and Celarent. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is (...) a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates (...) the assertoric syllogistic. I argue that this mereological validation offers advantages over recent discussions in Morison, Malink, Ebert and Vlasits. (shrink)

Why does Aristotle not use the copulative wording for categorical propositions, but instead the clumsier terminological formulations (e. g. the B belongs to every A) in his syllogistic? The proposed explanations by Alexander, Lukasiewicz and Patzig: Aristotle wants to make clear the difference between subject and predicate, seems to be insufficient. In quantified categorical propositions, this difference is always sufficiently clear by the use of the pronouns going with the subject expressions. Aristotle opts for the terminological wording because in premiss (...) pairs of figures two and three he can thus suppress the middle term in one of the premisses and connect the major and minor term, using connecting particles. This renders the syllogisms more transparent. Had he used the copulative wording instead, he would have run into difficulties, in particular with o-propositions among the premisses (i. e. in Baroco and Bocardo) because in these cases the pronoun expressing the quantification would have to go with the subject term, the negation with the predicate. (shrink)

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not (...) discuss many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology. (shrink)

Redictio ad absurdum is an important part of Aristotle’s syllogistic. It is connected with direct proof and they are complementary methods. All moods of Aristotle are provable by direct methods and redictio ad absurdum. In this paper, I have studied on the bases and principles of redictio ad absurdum, I showed how to prove by redictio ad absurdum, and how to prove Aristotle by redictio ad absurdum. By redictio ad absurdum, all forms of Aristotle’s method proved in the first figure (...) can be reduced to the perfect forms. (shrink)

In these pages the author intends to examine the idea, quite widespread among Aristotle’s recent scholars, that the method of metaphysics were mainly dialectical. This problem is investigated in Aquinas, who decidedly denies that metaphysics uses dialectics because it just provides probability. Metaphysics, unlike dialectics, is not only based on the being of reason but also on the natural being. Therefore, it does not simply constitute a rational game about quiddities, but it studies things in their real actuality and must (...) therefore be supported by evidence. Although Aquinas agrees with Aristotle in affirming that not every science enjoys the same certainty, this fact is due to different reasons. First, all things do not possess the same stability and constancy. Secondly, there is not always a perfect match between the studied matter and the human faculty to ascertain. This match between the object and the subject is the most decisive factor for the certainty of sciences. (shrink)

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules which (...) establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises an (...) interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 864-886, December 2021.

In this article, I present a schema for generating counterexamples to the argument form known as Hypothetical Syllogism with indicative conditionals. If my schema for generating counterexamples to HS works as I think it does, then HS is invalid for indicative conditionals.

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

I sympathetically explore the thesis that God literally forgets sins. I articulate some altruistic God might have for forgetting certain sins. If so, then God may have altruistic reasons to relinquish a great-making trait (omniscience). But according to traditional Anselmian perfect being theology, God is necessarily perfect and so incapable of acting on these altruistic reasons. More broadly, a God who necessarily has all the perfections is a God who is incapable of making a certain kind of sacrifice: (...) God can never make tradeoffs that diminish God’s overall greatness, even when those diminishments are relatively small (like forgetting a particular proposition) and the (altruistic) rewards of making the tradeoff substantial. I argue that God’s inability to make such tradeoffs is not a trivial cost for traditional perfect-being theologians who also believe that God is in loving relationships with creatures. Along the way, I explore the prospects for a less traditional form of perfect being theology, perfect being kenoticism, and different models for divine forgetting. (shrink)

Ideas for integrating AI into politics are now emerging and advancing at accelerating pace. This chapter highlights a few different varieties and show how they reflect different assumptions about the value of democracy. We cannot make informed decisions about which, if any, proposals to pursue without further reflection on what makes democracy valuable and how current conditions fail to fully realize it. Recent advances in political philosophy provide some guidance but leave important questions open. If AI advances to a state (...) where it can secure superior political outcomes, leading perspectives in political philosophy suggest that democracy may become obsolete. If we find this suggestion troubling, we need to put the case for democracy on stronger foundations. (shrink)

This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises (...) of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic. (shrink)

The purpose of this paper is to outline an alternative approach to introductory logic courses. Traditional logic courses usually focus on the method of natural deduction or introduce predicate calculus as a system. These approaches complicate the process of learning different techniques for dealing with categorical and hypothetical syllogisms such as alternate notations or alternate forms of analyzing syllogisms. The author's approach takes up observations made by Dijkstrata and assimilates them into a reasoning process based on modified notations. The author's (...) model adopts a notation that addresses the essentials of a problem while remaining easily manipulated to serve other analytic frameworks. The author also discusses the pedagogical benefits of incorporating the model into introductory logic classes for topics ranging from syllogisms to predicate calculus. Since this method emphasizes the development of a clear and manipulable notation, students can worry less about issues of translation, can spend more energy solving problems in the terms in which they are expressed, and are better able to think in abstract terms. (shrink)

The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical Syllogism. The improved proof (...) relies upon the semantic claim that conditionals with antecedents irrelevant to the obtaining of an already true consequent are themselves true. Moreover, this semantic insight allows us to provide compelling counterexamples to Hypothetical Syllogism that are resistant to the usual contextualist response. (shrink)

The purpose of this paper is an attempt to delimitate what the dialectical syllogism looks like in Aristotle’s Topics. Aristotle never gave an example of a dialectical syllogism, but we have some clues spread over books I and VIII of the Topics which make it possible to understand at least what within a dialectical debate is a dialectical syllogism. The interpretation advanced here distinguishes the logical order of the dialectical argumentation from the order of the debate. This distinction enables us (...) to have a better understand of what is and how the dialectical syllogism is identified in the debate. In addition, we can solve some interpretative difficulties other interpretations could not solve, and have a more solid grasp of how endoxa are used in a dialectical debate. (shrink)

Anselmian theists claim (a) that there is a being than which none greater can be conceived; and (b) that it is knowable on purely—solely, entirely—a priori grounds that there is a being than which none greater can be conceived. In this paper, I argue that Anselmian Theism gains traction by conflating different interpretations of the key description ‘being than which no greater can be conceived’. In particular, I insist that it is very important to distinguish between ideal excellence and maximal (...) possible excellence. At the end of my paper, I illustrate the importance of this distinction by applying my discussion to the recent defence of Anselmian Theism in Nagasawa (Philos Q 58:577–591, 2008). (shrink)

The paper examines Posterior Analytics II 11, 94a20-36 and makes three points. (1) The confusing formula ‘given what things, is it necessary for this to be’ [τίνων ὄντων ἀνάγκη τοῦτ᾿ εἶναι] at a21-22 introduces material cause, not syllogistic necessity. (2) When biological material necessitation is the only causal factor, Aristotle is reluctant to formalize it in syllogistic terms, and this helps to explain why, in II 11, he turns to geometry in order to illustrate a kind of material cause that (...) can be expressed as the middle term of an explanatory syllogism. (3) If geometrical proof is viewed as a complex construction built on simpler constructions, it can in effect be described as a case of purely material constitution. (shrink)

Locke's claims about the "inadequacy" of substance-ideas can only be understood once it is recognized that the "sort" represented by such an idea is not wholly determined by the idea's descriptive content. The key to his compromise between classificatory conventionalism and essentialism is his injunction to "perfect" the abstract ideas that serve as "nominal essences." This injunction promotes the pursuit of collections of perceptible qualities that approach ever closer to singling out things that possess some shared explanatory-level constitution. It (...) is in view of this norm regulating natural-historical inquiry that a substance-idea represents a sort for which some such constitution serves as the "real essence," i.e. as that on which all the sort's characteristic "properties" depend. (shrink)

ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for a hypothetical syllogistic which predates Stoic propositional logic. It emerges that Galen is one of our main witnesses for such a theory, whose authors are most likely Theophrastus and Eudemus. A reconstruction of this theory is offered which - among other things - allows to solve some apparent textual difficulties in the Institutio Logica.

God is typically conceived as perfectly good and necessarily so, in two senses: in terms of always performing the best possible act and in terms of having maximal moral worth. Yet any being that freely performs the best act she can must be accorded greater moral worth for any such action than a being that does so necessarily. I conclude that any being that performs the best possible act of necessity cannot also have maximal moral worth, making the concept of (...) God’s perfect goodness incoherent. (shrink)

In this paper, I ask whether there is a defensible philosophical view according to which everybody is beautiful. I review two purely aesthetical versions of this claim. The No Standards View claims that everybody is maximally and equally beautiful. The Multiple Standards View encourages us to widen our standards of beauty. I argue that both approaches are problematic. The former fails to be aspirational and empowering, while the latter fails to be sufficiently inclusive. I conclude by presenting a hybrid ethical–aesthetical (...) view according to which everybody is beautiful in the sense that everybody can be perceived through a loving gaze. I show that this view is inclusive, aspirational and empowering, and authentically aesthetical. (shrink)

Classic perfect being theologians take ‘being perfect’ to be conceptually necessary and sufficient for being God. I argue that this claim is false because being perfect is not conceptually necessary for being God. I rest my case on a simple thought experiment inspired by an alternative I developed to perfect being theology that I call “functional theology.” My findings, if correct, are a boon for theists since if it should turn out that there is no (...) class='Hi'>perfect being, there could still be a God. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

My paper discusses the philosophical interrelationship between perfection, truth, and knowledge. The connection that exists between these three concepts underscores the argument of my paper that they are all one and the same thing. -/- The concepts of perfection, truth and knowledge are analysed in that order. I analyse perfection and demonstrate the practicalities of my arguments. Truth is then scrutinized and defined to illustrate its intimate relationship with perfection leading to the conclusion that knowledge being ‘truth that is (...) class='Hi'>perfect’. -/- In dealing with the theory of knowledge, I take into account the justification of knowledge and highlighted arguments that I found to be insufficient. I derive a premise to refute and replace both the traditional and contemporary views of knowledge. -/- In the paper presented, I consider views of some prominent philosophers including; Locke, Russell, Plato, Aristotle and Leibniz. (shrink)

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / PP (...) d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)

Perfect being theism is the view that the perfect being exists and the property being-perfect is the property being-God. According to the strong analysis of perfection, a being is perfect just in case it exemplifies all perfections. On the other hand, the weak analysis of perfection claims that a being is perfect just in case it exemplifies the best possible combination of compatible perfections. Strong perfect being theism accepts the former analysis while weak (...) class='Hi'>perfect being theism accepts the latter. In this paper, I argue that there are good reasons to reject both versions of perfect being theism. On the one hand, strong perfect being theism is false if there are incompatible perfections; I argue that there are. On the other hand, if either no comparison can be made between sets of perfections, or they are equally good, then there is no best possible set of perfections. I argue for the antecedent of this conditional statement, concluding that weak perfect being theism is false. In the absence of other analyses of perfection, I conclude that we have reason to reject perfect being theism. (shrink)

In the Principles of Philosophy, Descartes attempts to explicate the well-known phenomena of varying bodily size through an appeal to the concept of "solidity," a notion that roughly corresponds to our present-day concept of density. Descartes' interest in these issues can be partially traced to the need to define clearly the role of matter in his natural laws, a problem particularly acute for the application of his conservation principle. Specifically, since Descartes insists that a body's "quantity of motion," defined as (...) the product of its "size" and speed, is conserved in all material interactions, it is imperative that he explain how solidity influences the magnitude of this force. As a means of resolving this problem, Descartes postulated an idealized condition of "perfect solidity" which correlates a body's "agitation" force (a forerunner of Newton's concept of non-accelerating, or "inertial" motion) with the interplay of its volume, surface area, and composition of minute particles. This essay explores this often misunderstood aspect of Descartes' physics, as well as the special function of idealized conditions in his collision rules. Contrary to those commentators who regard "perfect solidity" as a stipulation on bodily impact, this notion, it will be argued, is primarily concerned with the internal composition of macroscopic bodies, and only indirectly with their collision characteristics. Along the way, many of Descartes' hypotheses will be shown to display a level of sophistication and intricacy that, despite their essential incompatibility, belie several of the common misconceptions of Cartesian science. (shrink)

This paper examines how Plato’s rejection of the friends of the forms at 248a–249b in the Sophist is continuous with the arguments that he develops shortly after this part of the dialogue for the interrelatedness of the forms. I claim that the interrelatedness of the forms implies that they are changed, and that this explains Plato’s rejection of the friends of the forms. Much here turns on the kind of change that Plato wants to attribute to the forms. I distinguish (...) my view of the sort of change that the forms experience from other kinds of change—such as ‘Cambridge change’—that scholars have believed Plato has in mind in rejecting the friends of the forms. On the view that I advance, a form experiences a change (which I call ‘perfect change’) in its association with another form that distinguishes it as the distinctive being that it is—that is, through its possession of its distinctive properties. (shrink)

The growing power of communication and information technologies and their reliance on systems, poses great challenges to cultural and religious diversity, and even education. Will these technological systems continue to homogenize cultures and religions? Will this process lead to increasing strife? Or is there a possibility of maintaining both identity and diversity in a peaceful manner? This paper explores an early attempt to consider this problem. It will focus on the Ikhwān al-Ṣafā and their attempt to construct an encyclopedic system (...) to coordinate knowledge during the flowering of Islamic Civilization in the tenth century. It will primarily deal with Epistle or Rasā'il twenty-two – a fable concerning a debate between the humans, the animals and the Jinn. It will discuss their debate and show how the major concern for the Ikhwān al-Ṣafā was not only to embrace the diversity of knowledge but also the need to navigate through this diversity. I would like to suggest through this analysis that a culture gains its richness and identity by recognizing perfections outside of their own identity. This is analogous to the way that the individual human being gains meaning and dignity by reaching beyond its individuality. It also shows the importance of cultural and religious diversity and how the world cannot be unified by a single all-encompassing system. This approach is important because it shows the possibility of maintaining cultural and religious identity while participating in a technological world involving the flow of information on one hand, and global cultural diversities on the other. (shrink)

Modal dispositionalism is the view that possibilities are a matter of the dispositions of individual objects: it is possible that p if and only if something has a disposition for p to be the case. We raise a problem for modal dispositionalism: nothing within the theory rules out that there could be necessary, perfect masks, which make the manifestation of a disposition impossible. Unless such necessary perfect masks are ruled out, modal dispositionalism runs the risk of failing to (...) provide a sufficient condition for possibility, and indeed of engendering contradictions. But to rule them out, modal dispositionalism would have to revise a crucial tenet of the view, its localism. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...) attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

I consider a new, non-disjunctive strategy for ‘relational’ or ‘naïve realist’ theories to respond to arguments from ‘perfect’ (causally matching) hallucinations. The strategy, in a nutshell, is to treat such hypothetical cases as instances of perception rather than hallucination. After clarifying the form and dialectic of such arguments, I consider three objections to the strategy. I provide answers to the first two objections but concede that the third — based on the possibility of ‘chaotic’ (uncaused) perfect hallucinations — (...) cannot obviously be dealt with by the proposed strategy. However, such ‘chaotic’ scenarios are also problematic for standard representational accounts of experience. Thus I conclude that perfect hallucinations pose no more of a threat to the relational theory than to its main representational rival. (shrink)

Conditional perfection is the phenomenon in which conditionals are strengthened to biconditionals. In some contexts, “If A, B” is understood as if it meant “A if and only if B.” We present and discuss a series of experiments designed to test one of the most promising pragmatic accounts of conditional perfection. This is the idea that conditional perfection is a form of exhaustification—that is a strengthening to an exhaustive reading, triggered by a question that the conditional answers. If a speaker (...) is asked how B comes about, then the answer “If A, B” is interpreted exhaustively to meaning that A is the only way to bring about B. Hence, “A if and only if B.” We uncover evidence that conditional perfection is a form of exhaustification, but not that it is triggered by a relationship to a salient question. (shrink)

My chapter deals with an important part of how Wolff pursued the normative ambitions of his ethics in giving practical guidance with regard to specific moral issues. I first consider how Wolff’s ethics tackles the duties to others, which traditionally represent a difficult issue for moral perfectionism. In this regard, I argue that Wolff’s strategy combines two aspects: (a) he includes in perfection non-active aspects and (b) operates with an agent-neutral notion of perfection, in spite of important passages that might (...) suggest differently. I then focus on Wolff’s treatment of the duties concerning veracity and lying, and show how it follows that general strategy. Combining its two aspects, Wolff examines specific moral issues by adopting a non-welfarist notion of benefit and harm as the standard that can give guidance about practical cases. (shrink)

In this essay I will show that the incoherence many commentators have found in Kant’s Religion is due to Augustinian assumptions about human evil that they are implicitly reading into the text. Eliminate the assumptions, and the inconsistencies evaporate: both theses, those of universality and moral responsibility, can be held together without contradiction. The Augustinian view must be replaced with what John Hick has dubbed an “Irenaean” account of human evil, which portrays the human being and his or her task (...) in developmental terms. This developmental model is put forward by Kant in both the Lectures in the Philosophy of Religion and in his Conjectural Beginnings of Human History. In this essay I discuss both the Augustinian and Iranaean accounts of human evil, and argue for the advantages of the developmental (Iranaean) account in making philosophical sense of Kant’s texts. I show that Kant indeed held such a view in both the Lectures and in the Conjectural Beginnings, and that he never abandoned the developmental model in Religion. Reading Kant’s Religion through an “Iranaean” lens reframes the locus of the debate, illumines multiple elements of the text that previously remained obscure, and demonstrates why Kant had good reason to claim that we all begin in a condition of radical evil but must nevertheless assume responsibility for this. (shrink)

This book presents a (new) attempt to apply the notion of an underlying logic to Aristotle’s Organon and certain passages of the Metaphysics. The author situates his approach as part of a ‘deductio...

The third Meditation is typically understood to contain two a posteriori arguments for the existence of God. The author focuses on the second argument, where Descartes proves the existence of God partly in virtue of proving that Descartes cannot be the cause of himself. To establish this, Descartes argues that if he were the cause of himself, then he would endow himself with any conceivable perfection. The justification for this claim is that bringing about a substance is more difficult than (...) creating an attribute, so anything that can do the former can do the latter. While current explanations of this justification are either implausible or inadequate, the author argues that this principle derives support from a scholastic distinction between being-as-such and determinate being. With this distinction in view, we can make sense of Descartes's argument without appealing to ambiguous or inadequate notions. (shrink)

Shows how, as a consequence of the Arrow Impossibility Theorem, objectivity in grading is chimerical, given a sufficiently knowledgeable teacher (of his students, not his subject) in a sufficiently small class. -/- PDF available from JStor only; permission to post full version previously granted by journal editors and publisher expired. -/- Unpublished reply posted gratis.

It is often thought that traditional recidivism prediction tools used in criminal sentencing, though biased in many ways, can straightforwardly avoid one particularly pernicious type of bias: direct racial discrimination. They can avoid this by excluding race from the list of variables employed to predict recidivism. A similar approach could be taken to the design of newer, machine learning-based (ML) tools for predicting recidivism: information about race could be withheld from the ML tool during its training phase, ensuring that the (...) resulting predictive model does not use race as an explicit predictor. However, if race is correlated with measured recidivism in the training data, the ML tool may ‘learn’ a perfect proxy for race. If such a proxy is found, the exclusion of race would do nothing to weaken the correlation between risk (mis)classifications and race. Is this a problem? We argue that, on some explanations of the wrongness of discrimination, it is. On these explanations, the use of an ML tool that perfectly proxies race would (likely) be more wrong than the use of a traditional tool that imperfectly proxies race. Indeed, on some views, use of a perfect proxy for race is plausibly as wrong as explicit racial profiling. We end by drawing out four implications of our arguments. (shrink)

The claim that perfect hallucination is introspectively indistinguishable from perception has been a centrepiece of philosophical theorizing about sense experience. The most common interpretation of the indistinguishability claim is modal: that it is impossible to distinguish perfect hallucination from perception through introspection alone. I run through various models of introspection and show that none of them can accommodate the modal interpretation. Rejecting the modal interpretation opens up two alternative interpretations of the indistinguishability claim. According to the generic interpretation, (...) hallucination is indistinguishable from perception despite the existence of possible exceptions, while according to the actuality interpretation, the indistinguishability of hallucination from perception consists in the actual failure to distinguish hallucination from perception. These alternative understandings of the indistinguishability claim have a number of significant implications for the problem of perception, including the rejection of perfect hallucination and illusion in favour of our ordinary, non-philosophical concepts of these states. (shrink)

In “On Oppy’s Objections to the Modal Perfection Argument,” Philo 8, 2, 2005, 123–30, Robert Maydole argues that his modal perfection argument—set out in his “The Modal Perfection Argument for a Supreme Being,” Philo 6, 2, 2003, 299–313—“remains arguably sound” in the face of the criticisms that I made of this argument in my “Maydole’s 2QS5 Argument,” Philo 7, 2, 2004, 203–11. I reply that Maydole is wrong: his argument is fatally flawed, and his attempts to avoid the criticisms that (...) I have made of his argument are to no avail. (shrink)

This paper attacks an account of Kant's controversial distinction between "free" and "dependent" beauty. I present three problems—The Lorland problem, The Crawford Problem, and the problem of intrinsic relation—that are shown to be a consequence of various interpretations of Kant's distinction. Next, I reconstruct Robert Wicks' well-known account of dependent beauty as "the appreciation of teleological style" and point out a key equivocation in the statement of Wicks' account: the judgment of dependent beauty can be thought to consist in comparing (...) any two objects' teleological styles either in respect of how or in respect of how well each realizes a common purpose. I argue that this equivocation forces Wicks into a dilemma: either he must assert the impossibility of ugliness or he must assert that the judgment of dependent beauty is reducible to the judgment of perfection. Either way, he denies important theoretic desiderata. (shrink)

Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...) a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle's text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. (shrink)