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- Dictionaryvacuous/ˈvakjʊəs/
adjective
- 1. having or showing a lack of thought or intelligence; mindless: "a vacuous smile" Similar Opposite
- 2. empty. archaic
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If we defined vacuous statements as false, then the conditional/ → / IF operation would be logically equivalent to the conjunction/ ∧ / AND operation. Saying that p→q≡p∧q would make it useless in the logical context, as there is no point in equivalent operators. So that is a practical reason why we define the conditional operation ...
Jun 12, 2022 · Vacuous truth is not the same as vacuous logic: 1 is not consistent with 2, 3 contradicts 5 and 4 contradicts the original consideration (the empty set does exist, that's precisely the starting point, both statements depend not on vacuity). Metaphysically, this is a trivial contradiction, not an issue of vacuous truth. Share. Improve this answer.
Jan 15, 2024 · 0. Apparently a vacuous truth is a conditional statement P ⇒ Q where it is known a priori that P can NEVER be true. This obviously includes conditionals, but also a universal statement that can be converted to a conditional statement. That Wikipedia article also lists some examples of that: ∀x:P(x) ⇒ Q(x), where ∀ x: ¬P(x) ∀x: x∈ A ...
Feb 12, 2022 · Vacuous truths assert that an entire proposition is true even if the antecedent is false. Take the following proposition.. "If I am a toilet paper roll then I am a flying guitar" The antecedent is false, I am not a toilet paper roll. Therefore, how could the entire proposition be true?
Sep 26, 2024 · The “definition” of the material conditional A->B as ~A v B is very useful in connecting implicational statements to conjunctions and disjunctions. Also, vacuous truth is quite useful in set theory, wherein it can be used to define the empty set. Also, I didn’t downvote. – PW_246.
0. One possible meaning of "vacuous tautology" is for those tautologies where there is no line in the truth table where all of the premises are true. This would not include all tautologies. So maybe that was the intent. However, the phrase "vacuous tautology" should raise questions.
There is a a more complicated relationship in the switch configuration that is not captured by the logical statements. as to an intuition for 'material implication' or the logical 'if-then' P -> Q, consider the truth-valuation and how upset you might be given the values of P and Q. So suppose I claim P->Q. How upset will you be, how trustworthy ...
Sep 12, 2024 · These are not contradictory: (3) If someone is not blonde, then they can do logic. (4) If someone cannot do logic, then they are not blonde. Because the set referred to in (4) is always null (per 1 and 2). Assuming no unicorns exist, all of these statements are true and noncontradictory: All unicorns are blue. No unicorns are blue.
Apr 19, 2016 · 3. In classical Boolean logic at least, logical connectives can be completely understood semantically through their actions as truth-functions of Boolean values. In other words, the truth table associated with a particular logical operator provides a complete description of that operator. The standard truth table for the material conditional ...
Apr 24, 2014 · Whereas statement is language specific and always contain the same proposition of what it is saying though it differs grammar, word usage etc. For Ex 1. The fact that "unicorns are fake" can be written as "ยูนิคอร์นเป็นของปลอม" in thai. In both the languages the propositions are the same but the ...
