Wikipedia:Reference desk/Archives/Mathematics/2023 April 24

= April 24 =

Logic question
I was under the impression that, if I am human, and, for example, Kathy Griffin is human, logically, I must be Kathy Griffin (though that assumption would be invalid)? Thanks in advance. Cessaune  [ talk ]   21:45, 24 April 2023 (UTC)


 * I don't know if there is a name for that particular fallacy, but yes that is quite obviously invalid. Basically, for it to be valid it would have to be logically impossible for two objects to have any properties in common. -- Random person no 362478479 (talk) 22:55, 24 April 2023 (UTC)


 * It looks like you're trying to use a syllogism, but you can just make them up willy-nilly; some combinations are valid, most are not. --RDBury (talk) 04:07, 25 April 2023 (UTC)
 * The syllogism "(assumption) 2 + 2 is 4. (assumption) 2 × 2 is 4. (conclusion) Therefore 2 + 2 is 2 × 2." is valid. The syllogism "(assumption) 1 is positive. (assumption) 2 is positive. (conclusion) Therefore 1 is 2." is invalid. Even if its assumptions are valid, its conclusion is not. The difference rests on a dual function of the verb to be. If A and B are names that have entities as referents, the assertion "A is B" asserts that A and B are different names for the same entity. In more formal notation this can be expressed as A = B". However, if B does not refer to an entity, but to a property that entities such as A may have, the assertion "A is B" merely expresses that A is a name for one of several entities that have property B. An assertion of having a property "is B" is also known as a predicate; a notation used in formal logic is "B(A)". The predicate "is positive", applied to a name A referring to a number, can also be expressed as A > 0. So, to wrap this up, 2 + 2 = 4 and 2 × 2 = 4 together imply 2 + 2 = 2 × 2. But 1 > 0 and 2 > 0 do not imply 1 = 2. --Lambiam 07:25, 25 April 2023 (UTC)


 * Is this maybe affirming the consequent? -- Jayron 32 12:08, 25 April 2023 (UTC)


 * @Cessaune The phrase "I am human" does not mean "I = human(s) (or I = humanity)"; it means "I am a member of the set of humans".  Others are also members of the same set, without being equal to each other.
 * Once you accept that "am" doesn't always mean "is the same as", the weirdness falls away.
 * This reminds me of my favorite logic thing: "All crows are black.  Therefore, all non-crows are not black."  :-) David10244 (talk) 04:44, 30 April 2023 (UTC)
 * This reminds me of my favorite logic thing: "All crows are black.  Therefore, all non-crows are not black."  :-) David10244 (talk) 04:44, 30 April 2023 (UTC)