Expressing a widely-held view, David Hitchcock claims that "an enthymematic argument ... assumes at least the truth of the argument's associated conditional ... whose antecedent is the conjunction of the argument's explicit premises and whose consequent is the argument's conclusion." But even definitionally, this view is problematic, since an argument's being "enthymematic" or incomplete with respect to its explicit premises means that the conclusion is not implied by these premises alone. The paper attempts to specify the ways in which the (...) view is incorrect, as well as seemingly correct (e.g., the case of a Modus Ponens wherein the major premise is implicit). -/- . (shrink)

The closing chapters of Aristotle’s Nicomachean Ethics x are regularly described as “puzzling,” “extremely abrupt,” “awkward,” or “surprising” to readers. Whereas the previous nine books described—sometimes in lavish detail—the multifold ethical virtues of an embodied person situated within communities of family, friends, and fellow-citizens, NE x 6-8 extol the rarified, god-like and solitary existence of a sophos or sage (1179a32). The ethical virtues that take up approximately the first half of the Ethics describe moral exempla who experience fear fighting for (...) their communities, are sensitive to the esteem and recognition of others, and feel love for a desire to live together with a wide variety of kinds of friends. Such good people take pleasure in prudently expending sums to improve their communities—communities in which they exchange goods and participate in ruling and being ruled in a cooperative fashion. The exemplum of x 7-8, by contrast, is a person whose activity consists almost entirely in exercising his or her mind (nous)—a part of one’s soul that Aristotle explicitly notes is disconnected from human emotions and that can be exercised, insofar as one as wise, in a wholly solitary fashion (1178a15-16, a19-20; 1177a33-34). Although Aristotle’s claim that a “life in accord with the mind” is best and most pleasant (1178a6-7) may jar the intuitions of many people—he himself endorses Anaxagoras’ claim that the happy person will appear as “someone who is absurd” (atopos, 1179a15) to most people—it is false to claim that his conclusions in NE x 6-8 are unexpected or unanticipated, or that the text is in any way discontinuous with what precedes it. The Nicomachean Ethics exhibits aspects of ring-composition both within the work as a whole and within book 10. In NE i 5 Aristotle introduces his rendition of a trope that he inherits (most immediately) from Plato, viz. that the problem of the good can be considered like a contest between three different kinds of life—the life of enjoyment (apolaustikos), the life of politics (politikos), and the life of contemplation (theôrêtikos). NE x 6-8 returns to that contest, rendering a verdict about which life takes first, second, and third place. As the opening lines of NE x 6 note, that verdict presupposes central claims articulated between the first and last books of the Ethics, specifically about the nature of the virtues, the nature of friendship, and the nature of pleasure. NE i 5 and x 6-8 thus serve as “bookends” which encase arguments and proposition located between them. Book 10 exhibits a similar ring-composition. NE x opens with methodological reflection on the gap between the theoretical positions that thinkers articulate and the way they live their lives (especially in the case of scolds who simultaneously criticize pleasure on a scientific level but seek it on a practical level [1172a33-b8]). Chapter 8 concludes with an explicit reiteration of the methodological point, a reiteration that underscores how Aristotle’s treatment of the contest of lives incorporates central aspects of the discussion of pleasure in NE x 1-5. Aristotle’s reiteration of the problem of a gap between theory and practice also draws attention to the centrality of his treatment of pleasure in his adjudication of the three lives. Although the life of pleasure takes a distant third in the contest of lives, the contemplative life wins the contest in part because it itself is the most pleasant form of life. The central philosophical problem looming behind Aristotle’s treatment of the contest of lives concerns the relationship between the notion of activity (energeia) and the notion of a way of life (bios). In the last four decades, much of the scholarship on NE x 6-8 has sought to address the question of what activities a certain way of life includes or excludes. “Monistic” or “dominant” end interpretations of the best life have viewed it as including only contemplative activities whereas “inclusivist” end interpretations of the best life have viewed it as including non-contemplative activities. Although this chapter largely side-steps this debate—partially because there are ample recent first-rate introductory treatments of the debate, partially because I have addressed the question elsewhere in my own writing —I argue that focusing solely on the contest between the two best ways of life overshadows the way that Aristotle incorporates insights from the third way of life into the best way of life. Although the notion of a contest among different kinds of lives presupposes that the lives are mutually exclusive, Aristotle has no problem saying that the contemplative life trumps the life of pleasure because the contemplative life is more pleasant. I proceed in two parts. In the first part I examine what I will call the “outer” ring of the Ethics, namely the relationship between the contest of lives proposed in NE i 5 and its overall resolution in x 6-8. I show how i 5 and x 6 establish the framework for the contest, how x 7 adjudicates that contest in large part by relying upon premises articulated in the interim between books 1 and 10, and how x 6 and x 8 determine the second and third place positions in the contest. In the second part I focus on what I will call the “inner” ring of NE x. More than half of NE x struggles with the nature of pleasure, its role in a happy life, and the methodological problems of examining pleasure within a practical science. I show how x 1 and x 8 are “bookends” that underscore the methodological problem of examining pleasure and how the contest of lives draws upon the proximate conclusions concerning the nature of pleasure in NE x 1-5. (shrink)

It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. (...) Because of the symmetry between the principles, they come as a package: either both will have to be rejected or both will have to be revised. (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

Many philosophers have been attracted to the view that reasons are premises of good reasoning – that reasons to φ are premises of good reasoning towards φ-ing. However, while this reasoning view is indeed attractive, it faces a problem accommodating outweighed reasons. In this article, I argue that the standard solution to this problem is unsuccessful and propose an alternative, which draws on the idea that good patterns of reasoning can be defeasible. I conclude by drawing out implications for the (...) debate over pragmatic reasons for belief and other attitudes and for one influential form of reductionism about the normative. (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, the (...) problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

In ‘Against vaccine nationalism’, Nicole Hassoun misrepresents our argument, distorts our position and ignores crucial distinctions we present in our article, ‘Love thy neighbor? Allocating vaccines in a world of competing obligations’. She has created a strawman that does not resemble our position. In this reply, we address two features of ‘Against vaccine nationalism’. First, we address a phantom premise. Hassoun misattributes to us a thesis, according to which citizen-directed duties are stronger than noncitizen-directed duties. This thesis is a (...) figment of her imagination, not a fragment of our argument. Second, we address a shape-shifting ism. Ambiguity attaches to ‘vaccine nationalism,’ ambiguity that Hassoun exploits despite our distinguishing various meanings of the phrase. As a result, the type of vaccine nationalism she argues against is not the type we defend. (shrink)

It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure. But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that (...) single-premise closure succumbs to risk aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of (...) deliberation and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

Body and Soul, the infinite dualism of existenz.

Many contemporary moral theories accept and rely upon a singular (often unstated) premise. Contractualisms, traditionally construed rights theories and Millian utilitarianisms all accept a uniquely indefensible claim about the nature of the moral value of rationality. As a result, these moral theories are, despite their differences, equally and seriously marked for reliance on what I will call "the rationality premise". In this work I explain how it is that said reliance guarantees that a theory is impervious to demonstration (...) of soundness. My conclusion deals a serious blow to any theory which relies on the aforementioned premise. (I elsewhere defend an "alternative rights theory" which does not turn on the unique value of rationality, or reason. The work at hand provides the groundwork necessary to a move away from longstanding insistence on human superiority in the carving out of moral theory. (shrink)

My contention is to adumbrate three general premises leading to religious tolerance. The first is that emphasis should be laid much more on ethics than on metaphysics. Religions greatly differ in supernatural beliefs but all advocate justice, love, truthfulness, self-control and other virtues. Second, the beliefs about God are not true in their exact meaning, but rather as remote analogies to scientific truth. Religion is more resemblant of poetry than science. Third, real tolerance consists in the readiness to assimilate some (...) of the values of other religions, since no one has expressed the transcendent in an exhausting and perfect way. Key Words: tolerance, ethics, objective knowledge, world religions, openness for the Other. (shrink)

The hypergrowth and hyperconnectivity of networks of artificial intelligence (AI) systems and algorithms increasingly cause our interactions with the world, socially and environmentally, more technologically mediated. AI systems start interfering with our choices or making decisions on our behalf: what we see, what we buy, which contents or foods we consume, where we travel to, who we hire, etc. It is imperative to understand the dynamics of human-computer interaction in the age of progressively more competent AI. This essay presents five (...) premises to serve as starting points for building our understanding of the “interactions’ in human-computer interactions. (shrink)

The implicit dimension of enthymemes is investigated from a pragmatic perspective to show why a premise can be left unexpressed, and how it can be used strategically. The relationship between the implicit act of taking for granted and the pattern of presumptive reasoning is shown to be the cornerstone of kairos and the fallacy of straw man. By taking a proposition for granted, the speaker shifts the burden of proving its un-acceptability onto the hearer. The resemblance of the tacit (...) premise with what is commonly acceptable or has been actually stated can be used as a rhetorical strategy. (shrink)

Descartes insists, “[...] there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me [...]” (AT-VII, 25; CSM-II, 17). In what way can we draw evidence that our existence can be drawn from our being deceived? The interpretations that the earlier studies have shown is not a monolith. Then I will search for some inherent characteristics of deception, and analyse the construction of the (...) reasoning, “if a deceiver deceives me, I exist.” To be concrete, I show: 1) that it is not “I exist” but “I think” that is concluded from the supposition “a deceiver deceives me/I am deceived by a deceiver”; 2) that the attributions of the self as a thinking thing, i.e. understanding, affirming, and denying (AT-VII, 28; CSM-II, 19), are discovered in the very supposition of a deceiver. (shrink)

The causal premise of the evolutionary debunking argument contends that human moral beliefs are explained by the process of natural selection. While it is universally acknowledged that such a premise is fundamental to the debunker’s case, the vast majority of philosophers focus instead on the epistemic premise that natural selection does not track moral truth and the resulting skeptical conclusion. Recently, however, some have begun to concentrate on the causal premise. So far, the upshot of this (...) small but growing literature has been that the causal premise is likely false due to the seemingly persuasive evidence that our moral beliefs are in fact not the result of natural selection. In this paper, I argue that this view is mistaken. Specifically, I advocate the Innate Biases Model, which contends that there is not only compelling evidence for an evolved cognitive capacity for acquiring norms but also for the existence of an evolutionarily instilled set of cognitive biases that make it either more or less likely that we adopt certain moral beliefs. (shrink)

The aim of this paper is to propose a new approach in the form of multimodality as a semiotic method that can be used by marketers and semioticians to induce online flow, a psychological state, on a brand website. First, we refer to multimodality as a semiotic analysis that can be used for a better optimization of semiotic resource sets in meaning-making, and we distinguish it from another similar concept: multimedia. Second, after a critical literature review, we address the flow (...) construct - a state of mind sometimes experienced by people who are deeply involved and immersed in some event, object or activity. Previous quantitative studies show a correlation between online flow experience and other variables such as design, content, sound and layout that are suggested to be its antecedents. In our study, these flow antecedents are viewed as sets of signs or modes that can be orchestrated in order to create different levels of perceived challenge for brand website users. We consider that multimodality can be used for a better optimization of these various meanings as expressed by modes that are "essentially different in nature" (Bateman, 2008, p.54). Also, we refer to the online marketing outcomes of the online flow experience, in order to outline its importance and its implications in the online environment. The main conclusion of our paper is that multimodality can be used by scholars and practitioners as a premise to induce online flow on a brand website, by optimizing the sets of signs or modes. Originality – our contribution consists of an interdisciplinary approach. We use concepts from semiotics, positive psychology, and online marketing for a better understanding of how marketers and semioticians can positively influence online customer behaviour. (shrink)

The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent—all having positional, relational connotations now totally absent in contemporary use of proposition. Taking protasis for premise, Aristotle’s statement (24a16) -/- A protasis is a sentence affirming or denying something of something…. -/- is not a definition of premise—intensionally: the relational feature is absent. Likewise, it is not a general definition of proposition—extensionally: it is too narrow. This paper explores recent literature on these issues.

This paper is a critique of a paper by Alex Pruss. I argue that Pruss's attempt to motivate acceptance of the key possiblity premise in modal ontological arguments fails.

The aim of this paper is to show that for Kant, a combination of epigenesis and monogenesis is the condition of possibility of anthropology as he conceives of it and that moreover, this has crucial implications for the biological dimension of his account of human nature. More precisely, I begin by arguing that Kant’s conception of mankind as a natural species is based on two premises: firstly the biological unity of the human species (monogenesis of the human races); and secondly (...) the existence of ‘seeds’ which may or may not develop depending on the environment (epigenesis of human natural predispositions). I then turn to Kant’s account of man’s natural predispositions and show that far from being limited to the issue of races, it encompasses unexpected human features such as gender, temperaments and nations. These predispositions, I argue, are means to the realisation of Nature’s overall purpose for the human species. This allows me to conclude that man’s biological determinism leads to the species’ preservation, cultivation and civilisation. (shrink)

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

ABSTRACT Wilfrid Sellars argued that Kant’s account of the conceptual structures involved in experience can be given a linguistic turn so as to provide an analytic account of the resources a language must have in order to be the bearer of empirical knowledge. In this paper I examine the methodological aspects of Kant’s transcendental philosophy that Sellars took to be fundamental to influential themes in his own philosophy. My first aim here is to clarify and argue for the plausibility of (...) what I claim is Sellars’ interpretation of Kant’s ‘analytic’ transcendental method in the first Critique, based ultimately on non-trivial analytic truths concerning the concept of an object of our possible experience. Kant’s ‘transcendental proofs’ thereby avoid a certain methodological trilemma confronting the candidate premises of any such proof, taken from Sellars’ 1970s undergraduate exam question on Kant. In part II of the essay I conclude by highlighting in general terms how Kant’s method, as interpreted in the analytic manner explained in part I, was adapted by Sellars to produce some of the more influential aspects of his own philosophy, expressed in terms of what he contends is their sustainable reformulation in light of the so-called linguistic turn in twentieth-century philosophy. (shrink)

This book-chapter briefs Eliezer Schweid's thought, and demonstrates the role of some core-concepts of classical American pragmatism within it.

The aim of this paper is to show that for Kant, a combination of epigenesis and monogenesis is the condition of possibility of anthropology as he conceives of it and that moreover, this has crucial implications for the biological dimension of his account of human nature. More precisely, I begin by arguing that Kant’s conception of mankind as a natural species is based on two premises: firstly the biological unity of the human species (monogenesis of the human races); and secondly (...) the existence of ‘seeds’ which may or may not develop depending on the environment (epigenesis of human natural predispositions). I then turn to Kant’s account of man’s natural predispositions and show that far from being limited to the issue of races, it encompasses unexpected human features such as gender, temperaments and nations. These predispositions, I argue, are means to the realisation of Nature’s overall purpose for the human species. This allows me to conclude that man’s biological determinism leads to the species’ preservation, cultivation and civilisation. (shrink)

In his article “Nudging and Informed Consent,” Shlomo Cohen (2013) argues, among other things, that 1) “to the extent that the nudge-influenced decision making is rational—in whatever sense,” there...

Most interpretations of Aristotle’s Posterior Analytics believe that the term ‘ameson’ is used to describe the principles or foundations of a given system of justification or explanation as epistemically prior to or more fundamental than the other propositions in the system. Epistemic readings (as I shall call them) arguably constitute a majority in the secondary literature. This predominant view has been challenged by Robin Smith (1986) and Michael Ferejohn (1994; 2013), who propose interpretations that should be classified as non-epistemic according (...) to the definition above. My aim in this article is purely negative. I intend to show that these non-epistemic interpretations are liable to serious objections and are in conflict with some important features of Aristotle’s theory of demonstration. (shrink)

According to various “harm-based” approaches to the non-identity problem, an action that brings a particular child into existence can also harm that child, even if his or her life is worth living. In the third chapter of The Non-Identity Problem and the Ethics of Future People, David Boonin surveys a variety of harm-based approaches and argues that none of them are successful. In this paper I argue that his objections to these various approaches do not impugn a harm-based approach that (...) Boonin does not consider, an approach I call the “existence solution to the non-identity problem.” I also argue that the existence solution is more plausible than Boonin’s own proposed solution. (shrink)

Although many libertarians share similar moral foundations, they disagree about whether the state can be justified. The most famous libertarian attempt to justify the state is that of Robert Nozick. This attempt has been criticized by, among others, the libertarian anarchist Murray Rothbard. In this article, Nozick’s theory and Rothbard’s critique are discussed, as well as some other attempts to justify the state from libertarian premises. Keeping the criticisms of those theories in mind, an alternative theory, which attempts to bypass (...) the criticisms, is put forward. This alternative theory explains how a state—most probably a nonminimal democratic state—can legitimately be formed in a condition of anarchy without violating anyone’s libertarian rights. One result of this is that the rights-based case for minarchism is severely weakened. (shrink)

Aquinas' Third Way is often dismissed as a howler, because he infers from the fact that, since the universe is metaphysically contingent that there was some time in the past when it didn't exist. I offer an argument to justify this inference.

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully (...) confident in one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

Many philosophers claim to employ intuitions in their philosophical arguments. Others contest that no such intuitions are used frequently or at all in philosophy. This article suggests and defends a conception of intuitions as part of the philosophical method: intuitions are special types of philosophical assumptions to which we are invited to assent, often as premises in argument, that may serve an independent function in philosophical argument and that are not formed through a purely inferential process. A series of philosophical (...) case studies shows that intuitions in these arguments contain the relevant features. The view has implications for philosophical method, offering a compromise between opponents on the divisive debate of the merits of experimental philosophy: experimental philosophy provides an especially useful role in philosophical assumption analysis. (shrink)

The multi premise closure principle states that the logical conjunction of known facts yields again a known fact. For absolute knowledge this principle holds. We show that for fallible knowledge, assuming knowing requires a minimum level of statistical certainty (whatever else it requires), and that there is a sufficient number of known facts above a given level of uncertainty, it does not hold, for simple statistical reasons. We present a modified version, the dependent conjunctive closure principle, that does hold.

Probabilistic theories of “should” and “ought” face a predicament. At first blush, it seems that such theories must provide different lexical entries for the epistemic and the deontic interpretations of these modals. I show that there is a new style of premise semantics that can avoid this consequence in an attractively conservative way.

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based (...) voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

Although in some contexts the notions of an ordinary argument’s presumption, assumption, and presupposition appear to merge into the one concept of an implicit premise, there are important differences between these three notions. It is argued that assumption and presupposition, but not presumption, are basic logical notions. A presupposition of an argument is best understood as pertaining to a propositional element (a premise or the conclusion) e of the argument, such that the presupposition is a necessary condition for (...) the truth of e or for a term in e to have a referent. In contrast, an assumption of an argument pertains to the argument as a whole in that it is integral to the reasoning or inferential structure of the argument. A logical assumption of an argument is essentially a proposition that must be true in order for the argument aside from that proposition to be fully cogent. Nothing that is both comparable and distinguishing can be said about presumptions of arguments. Rather, presumptions of arguments are distinctively conventional; they are introduced through conventional rules (e.g., those that concern how to treat promises). So not all assumptions and not all presuppositions of arguments are presumptions of those arguments, although all presumptions of arguments are either assumptions or presuppositions of those arguments. This account avoids making the (monological) notion of presumption vacuous and dissolving the distinction between assumption and presumption, which is a vulnerability of alternative views such as Hansen’s and Bermejo-Luque’s, as is shown. (shrink)

Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...) by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle's general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. (shrink)

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on (...) the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle's contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle's description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle's presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle's logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a semantically complete system of natural deductions including both direct and indirect deductions. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, or extended deductive discourses, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle's place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle's place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle's accomplishments in logic is a clarification of a distinction implicit in discourses among logicians--that between logic as formal ontology and logic as formal epistemology. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in (...) known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

I show that in our theoretical representations of argument, vicious infinite regresses of self-reference may arise with respect to each of the three usual, informal criteria of argument cogency: the premises are to be relevant, sufficient, and acceptable. They arise needlessly, by confusing a cogency criterion with argument content. The three types of regress all are structurally similar to Lewis Carroll’s famous regress, which involves quantitative extravagance with no explanatory power. Most attention is devoted to the sufficiency criterion, including its (...) relation to the view au courant that inferring necessarily involves the thinker taking her premises to support her conclusion. I contend that this view is mistaken and likewise that arguments make no such assumption or inference claim as that the premises support the conclusion. The core of the positive alternative model I propose is that there is commitment to, but not claiming, the proposition that the premises support the conclusion. (shrink)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

Suppositional reasoning can seem spooky. Suppositional reasoners allegedly (e.g.) “extract knowledge from the sheer workings of their own minds” (Rosa), even where the knowledge is synthetic a posteriori. Can literary fiction pull such a rabbit out of its hat? Where P is a work’s fictional ‘premise’, some hold that some works reason declaratively (supposing P, Q), imperatively (supposing P, do Q), or interrogatively (supposing P, Q?), and that this can be a source of knowledge if the reasoning is good. (...) True, I will argue, although only within the context of judicious critical interpretation. Further evident constraints include that the form of the suppositional reasoning needs to be declarative or imperative, and that the fictional ‘premise’ of the work needs to be a metaphysical counterfactual possibility, not merely a temporal counterfactual and not merely an epistemic possibility or probabilistic supposition. (shrink)

I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument content, usually premise material.

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...) problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. -/- KEY WORDS: hypothesis, theorem, argumentation, proof, deduction, premise-conclusion argument, valid, inference, implication, epistemic, ontic, cogent, fallacious, paradox, formal, validation. (shrink)

As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...) proof of the completeness of Aristotle’s syllogistic. (shrink)

In 1995, the publication of Marleen Rozemond’s paper, Descartes’s Case for Dualism, triggered the revival of the discussion on his argument in favor of the real distinction between body and soul among the Anglo-Saxon scholars. In particular, the discussion then resumed on the necessity of introducing a hidden premise (the so-called attribute premise) in order to regain its probatory character. This debate has reflected on the Cartesian studies in Brazil, and my objective in this text is to bring (...) to the debate two texts still unexplored in relation to this interpretative problem. My hypothesis is that the attempts to justify the thesis that the substance has exactly one principal attribute have not yet succeeded because they underestimated the contribution brought about by the transformation of the notion of nature entailed by the introduction of the concept of principal attribute. Understanding the Cartesian proof of substantial dualism, and more particularly the "attribute premise", would involve, I suggest, the thesis according to which the concept of principal attribute, insofar as it expresses the essence of the substance, is not, and cannot be, according to Descartes, an abstract universal, but rather one of a particular nature. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an (...) argument's conclusion does not follow from its premises? This result does nothing to vitiate the theories of distribution developed over the period beginning in medieval times. What it does vitiate is many if not all attempts to use distribution in tests of invalidity outside of the standard two-premise categorical arguments—where they were verified on a case-by-case basis without further theoretical grounding. In addition it shows that there was no theoretical basis for many if not all claims of fundamental status of rules of distribution. These results are further support for approaching historical texts using mathematical archeology. (shrink)

This chapter argues that Fanon works to interrupt specular and spectacular renderings of suffering and colonial violence. The touch that Fanon advocates is neither optimal grip, violent grasp, nor uniform pressure, nor can it be predicted in advance. His writing touches colonial wounds; by palpating these wounds and dwelling in them, it resuscitates colonial wounds as feelings that are flesh, and does not leave them behind as if their scar tissue was merely a numb object of the past. Fanon seems (...) to reiterate Edmund Husserl’s phenomenological discovery in Ideas II that the hand that touches the surface of a table, as it moves across it, also feels itself touched. Fanon’s aim is not simply to calculate the destructive effects of colonization, against arguments for its partial “civilizing” benefits. (shrink)

The premise that every work belongs to an art-kind has recently inspired a kind-centred approach to theories of art. Kind-centred analyses posit that we should abandon the project of giving a general theory of art and focus instead on giving theories of the arts. The main difficulty, however, is to explain what makes a given kind an art-kind in the first place. Kind-centred theorists have passed this buck on to appreciative practices, but this move proves unsatisfactory. I argue that (...) the root of this dissatisfaction stems not from the act of kicking the can down the road, but from not kicking it far enough. The missing ingredient, I argue, is a notion of convention which does the work of marking the difference between art and non-art for a given physical medium. (shrink)