본 논문의 목적은 아리스토텔레스로부터 시작하여 초기 페리파토스학파를 거쳐 고대후기에 이르기까지 ‘아리스토텔레스 논리학’의 특정 요소가 발전해 가는 과정을 추적하는 것이다. 고대 후기에는 가언삼단논법으로 분류된 4개의 논증형식이 있었다. 긍정적 긍정식(modus ponendo ponens), 부정적 부정식(modus tollendo tollens), 긍정적 부정식(modus ponendo tollens), 부정적 긍정식(modus tollendo ponens)이 그것들이다. 우리가 다루게 될 문제는 다음과 같은 것들이다. 앞에서 제시되었던 4개의 논증형식은 정확하게 어떤 상황에서 생겨났는가? 이 4개의 논증형식이 왜 ‘가언’ 삼단논법이라고 명명되었는가? 어떤 근거에서 이 4개의 논증형식이 타당하게 되는가? 논의를 진행하는 가운데 우리는 이 4개의 논증형식이 『분석론 전서』와 (...) 『토피카』에 보존되어 있는 아리스토텔레스 논리학의 특정 요소들이 오랜 기간에 걸쳐 점진적으로 발전한 결과임을 논증할 것이다.BR 우리의 논의결과는 이렇다. 첫째, 고대 후기에 오늘날의 조건명제와 선언명제가 가언명제로 분류된 이유는 단순히 조건명제와 선언명제에 조건적 요소가 포함되어 있기 때문이었다. 둘째, 고대 후기에 4가지 유형의 가언삼단논법이 ‘가언’ 삼단논법이라고 명명된 이유는 이 4가지 유형의 논증에 귀결관계와 비정합성관계의 조합으로부터 획득되는 가언명제가 적어도 한 개는 포함되어 있기 때문이었다. 셋째, 고대 후기에 4가지 유형의 가언삼단논법이 타당한 것으로 간주된 이유는 그것들 모두가 ‘모두스 포넨스’(modus ponens)유형의 형식을 갖고 있기 때문이었다. (shrink)

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by (...) example, varies in different authors. For instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

This paper proposes a classification of economic models into three types: historical, axiomatic and conditional. Historical or empirical models utilize the historical-deductive method, and are generalizations from the economic regularities and tendencies that we find in the real world. Axiomatic models utilize the hypothetical-deductive method; they are syllogisms whose major premise is an axiom – a self-evident truth; they are appropriate for methodological sciences such as mathematics and econometrics. Conditional economic models are likewise syllogisms, but they are (...) suitable for economics because they make for clearer and more precise economic reasoning. The criterion of truth of the substantive sciences is the conformity with reality, of the methodological science, its internal consistency. When a school of economic thought adopts mainly axiomatic models, as is the case with neoclassical economics, it implicitly falls into contradiction because their best representatives believe in the conformity with reality criterion. (shrink)

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.

McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.

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.

Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are (...) given for claiming that syllogistic validity is relevant validity. (shrink)

In this paper, I consider an argument of Harvey Siegel's according to which there can be no hypothetical normativity anywhere unless there is categorical normativity in epistemology. The argument fails because it falsely assumes people must be bound by epistemic norms in order to have justified beliefs.

This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of P|S from the premise set {.

Although written in Japanese, 実践的三段論法について（On Practical Syllogisms）pursues a logical form of the practical syllogism.

This paper critically analyzes the fiction-view of scientific modeling, which exploits presumed analogies between literary fiction and model building in science. The basic idea is that in both fiction and scientific modeling fictional worlds are created. The paper argues that the fiction-view comes closest to certain scientific thought experiments, especially those involving demons in science and to literary movements like naturalism. But the paper concludes that the dissimilarities prevail over the similarities. The fiction-view fails to do justice to the plurality (...) of model types used in science; it fails to realize that a function like idealization only makes sense in science because models, unlike works of fiction, can be de-idealized; it fails to distinguish sufficiently between the make-believe worlds created in fiction and the hypothetical worlds envisaged in models. Representation characterized in the fiction-view as a license to draw inferences does not sufficiently distinguish between inferences in fiction from inferences in scientific modeling. To highlight the contrast the paper proposes to explicate representation in terms of satisfaction of constraints. (shrink)

One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

This essay examines Jerrold Levinson’s hypothetical intentionalism with respect to the following two objections raised by actual intentionalists: (1) it is arbitrary to exclude certain kinds of evidence, such as the author’s pronouncements of intention, when hypothesizing about authorial intention; and (2) there exist counter-examples. I argue that these objections fail to establish that actual intentionalism is superior to hypothetical intentionalism and that hypothetical intentionalism is more plausible than actual intentionalism. I also suggest, however, that hypothetical (...) intentionalism has difficulties when applied to truth in fiction and thus may not be a complete theory of literary work meaning broadly construed. (shrink)

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a (...) corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic. (shrink)

Among philosophers, Don Campbell is best known for his naturalistic, evolutionary approach to epistemology. There can be no doubt, however, that he was a thoroughgoing naturalist in all matters, even though he seems to have had little interest in exploring naturalism as a general philosophical position. He was professionally more interested in the origins and workings of knowledge producing social systems. I am interested in these things too, but also naturalism in general. So my tribute to Don will be to (...) present some aspects of a generalized naturalism that I hope he would have liked. Campbell's naturalism, like his epistemology, would be evolutionary, but, like his realism, would be more. It would be hypothetical, a posit, and not a first principle. And it would be critical, subject to ongoing refinement in light of new experience. Thus my title. It is a title I fancy Don would have liked, perhaps one he himself would have used had he ever taken up naturalism as a general theme. It is much easier to give a negative characterization of naturalism than to provide a positive account of what it.. (shrink)

In the first half of this paper, we present a fragment of relational syllogisms named RELSYLL consisting of quantified statements with a special set of numerical quantifiers, and introduce a number of concepts that are useful for the later sections, including indirect reduction, quantifier transformations and equivalence of syllogisms. After determining the valid and invalid syllogisms in RELSYLL, we then introduce two Derivation Methods which can be used to derive valid relational syllogisms based on known valid (...) simple syllogisms. We also show that the two Methods are sound and complete for RELSYLL. In the second half of this paper, we discuss ways to extend the Derivation Methods, including the use of more valid syllogisms and the use of existential assumptions. In this way, we are able to derive more relational syllogisms that contain other types of non-classical quantifiers, including “only” and proportional quantifiers. Finally, we state and prove a proposition concerning the relationship between the two Methods. (shrink)

This study makes a case for the conversational phenomenon the authors have named the comical hypothetical. The CH becomes discursively co-created during ongoing conversation when one or more speakers depart from the normal turn-taking system and engage in the interactional creation of an imaginary world. Data stem from ethnographic observations as well as from spontaneous recordings of social situations in three different locations. Out of 20 hours of taped conversations, 10 recognizable CH segments were analyzed for the present study. (...) The authors present a macro-structure analysis of the comical hypothetical using Hymes's SPEAKING mnemonic, with an emphasis on the act sequence. A second-level micro-analysis uncovers the interactional properties of the CH using a conversation analytic approach. The examination reveals a distinct four-part act sequence of the CH made up of intricate and creative interactional turns. Lastly, the significance and functions of the CH are also discussed. (shrink)

We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundamental theorem to conditional probability, we investigate the coherent probability propagation rules (...) of argument forms of the syllogistic Figures I, II, and III, respectively. These results allow to show, for all three Figures, that each traditionally valid syllogism is also valid in our coherence-based probability semantics. Moreover, we interpret the basic syllogistic sentence types by suitable defaults and negated defaults. Thereby, we build a knowledge bridge from our probability semantics of Aristotelian syllogisms to nonmonotonic reasoning. Finally, we show how the proposed semantics can be used to analyze syllogisms involving generalized quantifiers. (shrink)

Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. (...) Lukasiewicz evidence is presented fully; it is irrefutable. But, instead of considering the possibility that Aristotle’s discourses were not intended to express indirect proofs of universalized conditions presupposing axiomatic premises, Lukasiewicz came to the amazing conclusion that Aristotle did not understand indirect proof. This paper builds on the admirable Lukasiewicz scholarship to establish a conclusion diametrically opposed to the one Lukasiewicz asserted. This paper points out that if Aristotle had not been establishing an underlying logic but he was instead axiomatizing a theory of terms, Aristotelians could not claim for Aristotle the title Founder of Logic. People who take Euclid, Peano, and Zermelo to have first axiomatized geometry, arithmetic, and set theory, respectively, do not think that this qualifies them for the titles Founder of Geometry, Founder of Arithmetic, and Founder of Set Theory, respectively. Such people do think that this would qualify the three for the titles Founder of Axiomatic Geometry, Founder of Axiomatic Arithmetic, and Founder of Axiomatic Set Theory, respectively: titles that carry no honors in logic. Being the Founder of Axiomatic Term Theory would likewise carry no honors in the field of logic. CORRECTION: The paper inadvertently implied that Euclid was the first to axiomatize geometry. In order to understand Aristotle’s Analytics as a treatise on demonstration it helps to realize that axiomatized geometry was studied in Plato’s Academy when Aristotle was a student. Euclid was the author of the only ancient axiomatized geometry now available. (shrink)

In his Mathesis rationis Leibniz discounted out of hand four categorical propositions that would have considerably broadened the resultant syllogistic logic. He did this despite the facts both that he had devised a suitable manner for expressing the latent quantification over terms, and that he had reasoned adequately to determine which of the syllogisms in the resulting broadened logic were valid. Leibniz's reasons for discounting these non-standard propositions are shown to be inadequate, and the resultant syllogistic logic is outlined.

In this paper I examine how Aristotle thinks syllogisms establish existence. I argue against the traditional "Instantiation" reading and in favor of an alternative "causal" or "structural" account of existential syllogisms. On my interpretation, syllogisms establish the existence of kinds by revealing that they are per se unities whose features are causally underwritten by a single cause/essence. They do so by tracing correlations between propria--peculiar, coextensive features--of the kind in question.