# Tag Info

Accepted

### 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-...
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### 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 ...
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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(...
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### 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 ...

### 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 ...

### 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 ...

### "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 ...

### 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 ...
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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"...

### 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 ...
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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.

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 "...
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### 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 ...
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### In what work did Venn use his diagrams to analyze syllogisms?

John Venn (1834-1923), Symbolic Logic (1881), ch. 5 "Diagrammatic Representation", pp. 100-125. For an earlier Venn's pubblication, see: On the diagrammatic and mechanical representation ...

### 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 ...
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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 ("...
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### 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 ...

### 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 ...
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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 ...
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### 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 ...
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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 (...

### 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 ...
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### 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; ...
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### 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 “...
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