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/sci/ - Science & Math

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11659551 No.11659551 [Reply] [Original]

Explain vacuous truth to me.
I just conceptualise it in my head.

>> No.11659564

>>11659551
Anything follows from a false premise. The members of the empty set have all properties.

How is this hard to understand?

>> No.11659568 [DELETED] 

>>11659551
I can tell that none of the dogs in your image pissed on the floor in their lives.

>> No.11659573

>>11659551
I can tell that none of the dogs in your image have pissed on the floor in their lives.

>> No.11659593

>>11659551
It comes from 2 valued logic. If you were to prove that for all y there is x is a false statement you would find an example of y that not x. But if there is no y at all, you cannot find an counterexample, cannot conclude that the for all y statement is false. So you are left with that it must be true.

>> No.11659610

>>11659564
>Anything follows from a false premise. The members of the empty set have all properties.
Those two notions should not be conflated

>> No.11660268

>>11659551
If 0=1, then 2+2=5.
Second statement is vacuously true.

>> No.11660602

>>11659551
"all of my dogs can speak english"
I don't have no dogs, man :^)

>> No.11660900

>>11659564
>How is this hard to understand?
Because it's nonsensical.
>The members of the empty set have all properties.
Say you have a collection of subsets of Z satisfying the property that for every element U in this collection, if n is in U, then -n is in U. Is the empty set a member of this collection? Yes: there is no element in the empty set to witness that the empty set fails to satisfy the aforementioned property. Although this may be what you meant by "The members of the empty set have all properties", don't pass that statement off as being obvious because it really isn't.

>> No.11661078

>>11660900
>here is no element in the empty set to witness that the empty set fails to satisfy the aforementioned property.
what kind of gay ontology grounds properties in their being witnessed by elements
mathematicains just can't get it right lmao

>> No.11661134

>>11659564
>The members of the empty set have all properties.
On second thought, this may actually a valid statement. For if not, then there must exist an element in the empty set which fails to satisfy the property that it has all properties, which cannot be, for the empty set contains no elements.
>>11661078
It's a figure of speech.