Different Forms of Generalized Hypothetical Syllogism with Regard to R-Implications

2019 ◽  
pp. 304-313 ◽  
Author(s):  
Katarzyna Miś ◽  
Michał Baczyński
Keyword(s):  
Hypothetical Syllogism

Keeping a Firm and Certain Faith in the Inspired Word

2018 ◽  
Author(s):  
Theodore G. Van Raalte
Keyword(s):  
Medieval History ◽  
Word Of God ◽  
History Of ◽  
Written Word ◽  
Hypothetical Syllogism

This chapter surveys all of De Verbo Dei Scripto (i.e., Concerning the Written Word of God) in some detail. Significant translated sections are provided. The careful structure followed by Chandieu in this treatise of 1580 will be utilized by him in five further “theological and scholastic” treatises of that decade, and thus this structure is uniquely important. Besides Chandieu’s close adherence throughout to this intricate disputational structure, one also notices his predominant use of the hypothetical syllogism. While the disputational structure is a finely honed arrangement that very likely grows out of classroom disputations with their long medieval history (to be examined in chapter 8), the use of hypothetical syllogisms is a highly unusual element in Chandieu’s works that will be set within the history of the hypothetical syllogistic to determine how “Aristotelian” was its use (in chapter 9).

scholarly journals On Basic Probability Logic Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Marija Boričić Joksimović
Keyword(s):  
Probability Theory ◽  
Inference Rule ◽  
Modus Ponens ◽  
Probability Logic ◽  
Modus Tollens ◽  
Short Overview ◽  
Basic Probability ◽  
Probabilistic Version ◽  
Hypothetical Syllogism

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

scholarly journals Against Hypothetical Syllogism

2013 ◽  
Vol 43 (5) ◽  
pp. 979-997 ◽  
Author(s):  
Lee Walters
Keyword(s):  
Hypothetical Syllogism

scholarly journals Cicero, On Invention 1.51–77 Hypothetical Syllogistic and the Early Peripatetics

1998 ◽  
Vol 16 (1) ◽  
pp. 25-42 ◽  
Author(s):  
William W. Fortenbaugh
Keyword(s):  
Deductive Reasoning ◽  
Hypothetical Syllogism ◽  
As If

Abstract: In On Invention, Cicero discusses both induction and deduction. In regard to the latter, Cicero presents a controversy between those who advocate a five-part analysis of deductive reasoning and those who prefer three parts. The issue is not practical or pedagogical, but conceptual in nature. Cicero himself prefers analysis into five parts, and rather confusingly he presents the argument of the advocates of five parts as if it were his own. The argument is striking in that it makes elaborate use of mixed hypothetical syllogisms in order to argue for five parts. Cicero claims that the five-part analysis has been preferred by all who take their start from Aristotle and Theophrastus. A survey of what Theophrastus is reported to have said concerning the hypothetical syllogism renders Cicero's claim intelligible. That is not to say that Theophrastus himself advocated a five-part analysis. Most likely the association with him derives from his known interest in hypothetical syllogistic. Later rhetoricians who identified themselves with the Peripatos made the cormection with the founders of the school, thereby gaining authority for a controversial analysis.

Burleigh's Paradox

Philosophy ◽  
2007 ◽  
Vol 82 (3) ◽  
pp. 437-448 ◽  
Author(s):  
Dale Jacquette
Keyword(s):  
Critical Analysis ◽  
Fallacy Of Equivocation ◽  
Hypothetical Syllogism

AbstractWalter Burleigh in his c. 1323 De Puritate Artis Logicae Tractatus Longior considers a counterexample to hypothetical syllogism. The paradox implied by Burleigh's inference has come to be known as the problem of the ass (asinum), or, more prosaically, ‘You are an ass’. The argument states: ‘If I call you an ass, then I call you an animal; if I call you an animal, then I speak truthfully; therefore, if I call you an ass, then I speak truthfully’. Burleigh's paradox is reconstructed and formalized for purposes of critical analysis, in which the putative counterexample is ultimately shown to involve a fallacy of equivocation.

scholarly journals Dynamic Probabilistic Entailment. Improving on Adams' Dynamic Entailment Relation

2021 ◽  
pp. 1-26
Author(s):  
Robert Van Rooij ◽  
Patricia Mirabile
Keyword(s):  
Original System ◽  
Modus Ponens ◽  
Behavioral Experiment ◽  
Truth Conditions ◽  
Indicative Conditionals ◽  
Indicative Conditional ◽  
Entailment Relation ◽  
New Information ◽  
General Relevance ◽  
Hypothetical Syllogism

The inferences of contraposition (A ⇒ C ∴ ¬C ⇒ ¬A), the hypothetical syllogism (A ⇒ B, B ⇒ C ∴ A ⇒ C), and others are widely seen as unacceptable for counterfactual conditionals. Adams convincingly argued, however, that these inferences are unacceptable for indicative conditionals as well. He argued that an indicative conditional of form A ⇒ C has assertability conditions instead of truth conditions, and that their assertability ‘goes with’ the conditional probability p(C|A). To account for inferences, Adams developed the notion of probabilistic entailment as an extension of classical entailment. This combined approach (correctly) predicts that contraposition and the hypothetical syllogism are invalid inferences. Perhaps less well-known, however, is that the approach also predicts that the unconditional counterparts of these inferences, e.g., modus tollens (A ⇒ C, ¬C ∴ ¬A), and iterated modus ponens (A ⇒ B, B ⇒ C, A ∴ C) are predicted to be valid. We will argue both by example and by calling to the results from a behavioral experiment (N = 159) that these latter predictions are incorrect if the unconditional premises in these inferences are seen as new information. Then we will discuss Adams’ (1998) dynamic probabilistic entailment relation, and argue that it is problematic. Finally, it will be shown how his dynamic entailment relation can be improved such that the incongruence predicted by Adams’ original system concerning conditionals and their unconditional counterparts are overcome. Finally, it will be argued that the idea behind this new notion of entailment is of more general relevance.

Basic Logical Knowledge

2002 ◽  
Vol 51 ◽  
pp. 279-304 ◽  
Author(s):  
Bob Hale
Keyword(s):  
The Other ◽  
Sort It ◽  
Hypothetical Syllogism

At least some of us, at least some of the time—when not in the grip of radical sceptical doubt—are inclined to believe that we know, for example, that if we infer a conclusion from two true premises, one a conditional whose consequent is that conclusion and the other the antecedent of that conditional, then our conclusion must be true, or that we know similar things about other simple patterns of inference. If we do indeed have knowledge of this sort, it is what I mean by logical knowledge. Logical knowledge is, roughly speaking, knowledge about logic—such as knowledge that a certain principle of inference necessarily preserves truth, or that every proposition of a certain form must be true—and so is not the same thing as knowledge that is gained by using logic, i.e. inferential knowledge. That is not to say, of course, that logical knowledge can't be inferential. On the contrary, it is barely open to question that—if there is any logical knowledge at all—there is a lot of inferential logical knowledge. For example, if we know that the introduction and elimination principles for the conditional are truth-preserving, we can surely get to know, by inference, that the principle of hypothetical syllogism (i.e. transitivity of the conditional) is so too, not to mention other, less obvious and more recondite, examples of putative logical knowledge.

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