Uwe
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5 answers
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Real World Example to break the logic of this Syllogism
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7 votes

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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1 answers
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Language Logic Proof Q
4 votes

You can combine the expressions for ¬ and v, as suggested by MarkOxford, but that yields a rather complicated expression. You get an easier solution if you start by developing an expression for ¬(P ∧ ...

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2 answers
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Can you Define Something in Terms of What is True About it?
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You give the example yourself: Yes, algebraic structures, such as groups, rings, fields, or lattices are defined in exactly this way. The definition of, say, a group does not specify what the set of ...

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4 answers
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When do descriptions of objects qualify as "known" vs "unknown"?
1 votes

There are boundary cases where one may argue whether some number is "known" or not, but this is not one of them. Note that the number 2^(43112609)-1 is represented in binary by 43112609 consecutive 1'...

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3 answers
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Is ¬(a = b) the same as (a ≠ b) in logic
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Noah Schweber already explained that constructive mathematics makes a difference between both formulas. But even in classical logic, we have a choice: a ≠ b can be the same formula as ¬ (a = b). Then ...

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