“0 < 0.5 is a statement about the numerical value indicating nothing. “Nothing is greater than X” is a statement about the size of the set containing things greater than X. You are using “nothing” with two different meanings.
So you mean to say … supposing there are no dogs and 3 cats and n(x) returns the numerical value of x that what 0 < 3 means is n(dogs) < n(cats) i.e. n({ }) < n({cat 1, cat 2, cat 3})? There must be some quality (in this case quantity :puzzled:) on the basis of which a comparison (here quantitative) can be made.
Do you also mean that we can’t compare nothing to something, like I was doing above? Gracias. Non liquet, but gracias.
Just a thought, but what if our ancestors had used an infinitesimal (sensu amplissimo) wherever they had to deal with n(nothing) = 0. They could’ve surmounted their philosophical/intuitionistic objections to treating nothing a something. For example if they ran into the equation 3 men−3 men, they could’ve used s (representing a really, really, small number) and “solved” the equation thus: 3−3=s. It would’ve surely made more sense to them than 3−3=0, oui?
No.
“0 < 0.5 is a statement about the numerical value indicating nothing. “Nothing is greater than X” is a statement about the size of the set containing things greater than X. You are using “nothing” with two different meanings.
So you mean to say … supposing there are no dogs and 3 cats and n(x) returns the numerical value of x that what 0 < 3 means is n(dogs) < n(cats) i.e. n({ }) < n({cat 1, cat 2, cat 3})? There must be some quality (in this case quantity :puzzled:) on the basis of which a comparison (here quantitative) can be made.
Do you also mean that we can’t compare nothing to something, like I was doing above? Gracias. Non liquet, but gracias.
Just a thought, but what if our ancestors had used an infinitesimal (sensu amplissimo) wherever they had to deal with n(nothing) = 0. They could’ve surmounted their philosophical/intuitionistic objections to treating nothing a something. For example if they ran into the equation 3 men−3 men, they could’ve used s (representing a really, really, small number) and “solved” the equation thus: 3−3=s. It would’ve surely made more sense to them than 3−3=0, oui?
There is sometimes a quantity on the basis of which a comparison can be made.
This quantity exists in 0 < 3. It doesn’t in “nothing is bigger than X”.
Do you mean to say “nothing is bigger than X” is nonsensical? We regularly encounter such expressions e.g. “nothing is greater than God”.
That statement is not nonsensical, but “nothing” is not being compared as a quantity either.
What. if I may ask, is the sense in it?