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22 votes
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Why bother with anything else besides Aristotle's syllogistic logic?

Aristotle's syllogistic logic is too weak for serious work. It does not readily express multi-place predicates. You cannot express two-place relations like, "John loves Mary", or three-...
Bumble's user avatar
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16 votes

Why does the Principle of Explosion not make Mathematical Logic inconsistent?

Explosion is a property of logical consequence relations, and thus of logics, that is not trivial: Some logics have it, some don't. So there is simply no sense asking Why can't we simply get rid ...
sequitur's user avatar
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8 votes
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How do I use the "Barbara, Celarent, … etc." mnemonic?

Explanation of the Mnemonic Brody, Boruch A. "Logical Terms, Glossary of." Encyclopedia of Philosophy. Ed. Donald M. Borchert. 2nd ed. Vol. 5. Detroit: Macmillan Reference USA, 2006. 533-560. Gale ...
Geremia's user avatar
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8 votes
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Real World Example to break the logic of this Syllogism

This is one of the classic 24 valid syllogisms, which means: It's a correct logical argument. In first-order logic, the premises can be written as ∀x(P(x)→Q(x)) and ∀x(R(x)→P(x)), and this implies ∀x(...
Uwe's user avatar
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8 votes

Why does the Principle of Explosion not make Mathematical Logic inconsistent?

Rather than give you the correct technical answer (edit: okay I ended up going into some technical details, oops), which has been provided, I think I'll try and diagnose where you're intuitions have ...
Daniel Prendergast's user avatar
7 votes

Does this syllogism by Russell show that Aristotelian logic doesn't work?

The syllogism is correct, according to Aristotle's doctrine, exactly because of Existential import: Aristotle's logic system does not cover cases where there are no instances. See The Traditional ...
Mauro ALLEGRANZA's user avatar
7 votes

Why bother with anything else besides Aristotle's syllogistic logic?

From a modern point of view, Aristotle's Logic is a subset of predicate logic, called Monadic predicate logic: monadic predicate calculus (also called monadic first-order logic) is the fragment of ...
Mauro ALLEGRANZA's user avatar
7 votes

Converting a Euclidian proposition to a syllogism format

I think you are wasting your time on this exercise. Aristotle's logic is too weak for the task you propose. Before the invention of predicate logic, some scholars attempted to express Euclid's ...
Bumble's user avatar
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6 votes

"All men are mortal, Socrates is a man, therefore, Socrates is mortal" original quote

Comment on similar example. The example is not from Aristotle. Categorical propositions with singular terms are used in Medieval logic; see Peter of Spain's Summulae logicales (XIII century): I,8 ...
Mauro ALLEGRANZA's user avatar
5 votes
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Why do singular propositions have a universal quantity?

In origin, sllogism was defined with categorical proposition i.e. for proposition like "All men are mortal" with class terms. The extension to singular terms can be managed considering the "singleton"...
Mauro ALLEGRANZA's user avatar
5 votes
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Wendelin, Marcus Friedrich - Logicae Institutiones tironum adolescentum

It seems that the list of categories from Marcus Friedrich Wendelin's book: Logicae institutiones (1654) [see page 14-on] comes from Petrus Ramus's Dialectique (1955). See also: Walter J. Ong, Ramus, ...
Mauro ALLEGRANZA's user avatar
5 votes

Does an implied premise mean a formal fallacy if used in deduction?

See Enthymeme : An enthymeme is a logical fallacy in which a categorical syllogism omits a premise that is necessary for the conclusion to be true or omits the conclusion itself. The missing ...
Mauro ALLEGRANZA's user avatar
5 votes
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Which logical fallacy is this: A is a C, B is a C, therefore A is a B?

It is the Fallacy of the undistributed middle: All Apples are Fruit All Oranges are Fruit Therefore, all Apples are Oranges is clearly invalid.
Mauro ALLEGRANZA's user avatar
5 votes

Questions about categorial propositions

In modern quantifier logic "no A is B" does not imply "some A is not B". That is because "some A is not B" is taken to entail the existence of at least one A, while "...
Bumble's user avatar
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5 votes

Existential import in "No A is B"

The issue is a little bit tricky... Existential import concerns "the question whether a universal or A proposition such as "all buttercups are blue" implies the existence of its ...
Mauro ALLEGRANZA's user avatar
4 votes

Only valid syllogisms are syllogisms?

The term syllogism is due to Aristotle (originally sullogismos). Aristotle defined it as: an argument (logos) in which, certain things having been laid down, something different from what has been ...
E...'s user avatar
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4 votes
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Are "All A is B" and "If A then B" always logically equivalent?

We are talking about expressing statements in two different systems. The first one is the classical syllogistic of Aristotle ("All dogs are mammals"), with categorical syllogisms, whereas the latter ("...
Conifold's user avatar
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4 votes

Is syllogism an inference rule?

Not exactly. We can consider the propositional valid argument called Hypothetical syllogism as a (derived) rule of inference. We call it "derived", because in standard presentations of propositional ...
Mauro ALLEGRANZA's user avatar
4 votes

How many valid categorical syllogisms are there?

See Syllogism: Aristotle's Theory: terms can be combined in different ways to form three figures (skhemata), which Aristotle presents in the Prior Analytics. When the four categorical sentences are ...
Mauro ALLEGRANZA's user avatar
4 votes
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Is Euclid's syllogistic approach to proving mathematical theorems logically insufficient?

You are correct that syllogistic, which corresponds to monadic predicate calculus in modern terms, is insufficient for doing mathematics. Modern formalisms use polyadic calculus. However, Euclid does ...
Conifold's user avatar
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4 votes

Is this an example of Undistributed Middle?

No, it is not. It is a valid argument : The premise : All teenagers are impulsive is equivalent to : for every x, if x is not impulsive, then x is not a teenager. Thus, using the second ...
Mauro ALLEGRANZA's user avatar
4 votes
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Why is there an O type conclusion in modus celaront

Celaront was not in the original Aristotle's list of valid syllogistic figures (or : moods). It was added later (during the Middles Ages ?) as one of the two subalternate moods in the first figure (...
Mauro ALLEGRANZA's user avatar
4 votes

Why does the Principle of Explosion not make Mathematical Logic inconsistent?

Here is the question: How is it that POE [the principle of explosion] does not make mathematical logic inconsistent? If the axioms of mathematical logic were inconsistent then the principle of ...
Frank Hubeny's user avatar
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4 votes

Do you gain further truth from syllogisms

Your criticism of syllogisms was made by John Stuart Mill. He put it slightly differently, but the point is similar. Mill's claim is that the syllogism, "All men are mortal; Socrates is a man; ...
Bumble's user avatar
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4 votes

Which author(s) first talked of Aristotle's syllogistic as a logic of terms?

I'd bring forward some considerations in the spirit of Fermi estimation. Here are the Ngram Viewer graphs for the phrases “term logic,” “logic of terms” and “terminist logic”: A quick browse for “...
Tankut Beygu's user avatar
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4 votes

How do complex propositions and Aristotle's logic work?

Aristotle's syllogistic approach sometimes requires some word-smithing to get it into the right form. It's easier if we rephrase the sentences to use "is." Our English word "is" ...
Cort Ammon's user avatar

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