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A syllogism (Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
- 1 The Challenge of Translating “All” and “Some”
- 2 A New Syntax
- 3 Common Sentence Forms For Quantifiers
- 4 Problems
We are still not able to translate fully Aristotle’s argument. It began: All men are mortal. What does this “all” mean? Let’s start with a simpler example. Suppose for a moment we consider the sentence All is mortal. Or, equivalently, Everything is mortal. How should we understand this “all” or “everything”? This is a puzzle that stumped many gener...
For the propositional logic, our syntax was always trivial. For the first order logic our syntax will be more complex. We will need a new concept, the concept of a “well-formed formula”. And we will need to make more explicit use of the fact that our syntax is a recursive syntax, which means that our rules must be stated with a first case, and then...
Formulas using quantifiers can have very complex meanings. However, translating from English to first order logic expressions is usually surprisingly easy, because in English many of our phrases using “all” or “some” or similar phrases are of eight basic forms. Once we memorize those forms, we can translate these kinds of phrases from English into ...
Which of the following expressions has a free variable? Identify the free variable if there is one. Assume F is an arity one predicate, and Gis an arity two predicate.
- Craig DeLancey
- 2017
Singular propositions, such as "Socrates is mortal," are a genuinely distinct type, which we shall touch upoon at appropriate points; indefinites, such as "Men are mortal," seem merely to be universals or particulars in which the quantity is left unstateed.
1. The Organon. To those used to the silver tones of an accomplished writer like Plato, Aristotle’s prose will seem, at first glance, a difficult read. What we have are largely notes, written at various points in his career, for different purposes, edited and cobbled together by later followers.
Whoever pronounces the words, All men are mortal, has affirmed that Socrates is mortal, though he may never have heard of Socrates; for since Socrates, whether known to be so or not, really is a man, he is included in the words, All men, and in every assertion of which they are the subject.
May 24, 2016 · A first widening of the Aristotelian syllogistic consists in the admission of singular terms and premisses. William of Ockham (c.1287–1347) already knows of the substitution that was to become classic [Summa Logicae, III 1,3;36rb]: Every man is an animal; Socrates is a man; Therefore, Socrates is an animal.
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Apr 21, 2023 · As noted above, the statement, “all humans are mortal,” has a particular form: All H are M. This is one of the four categorical forms. The way we will represent these categorical forms generally are with an “S” (which stands for “subject term”) and a “P” (which stands for “predicate term”).
