4 ms·

I'm a bit confused by this: > “All stonemen are made of stone” is true by definition, but “no men are made of stone” is also true and seems to contradict it.

I'm a bit confused by this: > “All stonemen are made of stone” is true by definition, but “no men are made of stone” is also true and seems to contradict it. I don't see how “no men are made of stone” contradicts “All stonemen are made of stone”. "stonemen" are not the same as "men". English isn't my first language so maybe I don't know what a stoneman is (and google failed me), but I assumed it is a statue?

assbuttbuttass 3y ago
I'm guessing, a stoneman means a man made out of stone
Smaug123 3y ago
The originator of that quote was writing in the 12th century. The quote is cited without a source at https://en.wikipedia.org/wiki/Square_of_opposition https://en.wikipedia.org/wiki/Square_of_opposition , where the phrase is "Omnis homo qui lapis est" ("every man who is a stone"). I haven't dug any further than that. But the phrase literally is intended to indicate a contradiction.
Jtsummers 3y ago
A stoneman would be a man made of stone, not a stone shaped like a man. It comes down to a philosophy of logic issue. A universal quantifier ("for all x P(x)") is ambiguous when there are no x's. You can take it as false, true, or indeterminant, your system of logic will determine which interpretation should be used. In modern predicate logic, that statement is true if there are no x's. In syllogistic logic it's considered false because there's a second presumption which must be satisfied: That there are any x's to talk about.
- ptx 3y ago
  Shouldn't this question fail at the parsing stage then, before it has even been asked? Q: All stonemen are ... A: ERROR: Undefined operation. Stonemen do not exist.
  - Jtsummers 3y ago
    That's certainly one option. In a way, that's what the colloquial understanding of the expression would entail. In colloquial use if you were to say, "All unicorns are blue" no one can meaningfully contradict nor confirm the statement, the statement is neither true nor false because there are no unicorns (this all assumes we're not discussing in a context where unicorns "exist", like about a particular fantasy setting or animated series). In syllogistic logic it becomes false because of the foundation of that logic (centered on reality, what exists and can be defined, not on fiction). Nothing true can be said about all of some non-existent thing because, well, it doesn't exist, so the statement must be false. In modern predicate logic it's considered true, because even though there are no unicorns we (someone) decided that it should be true by convention when the set is empty (turns out to have useful properties if we permit this). These are just the rules that we've used for our logic, a choice we made. We're generally, in programming, operating under the modern logical rules, using neither colloquial rules nor syllogistic rules, so our programs are consistent with that last interpretation.

assbuttbuttass 3y ago

I'm guessing, a stoneman means a man made out of stone

Smaug123 3y ago

The originator of that quote was writing in the 12th century. The quote is cited without a source at https://en.wikipedia.org/wiki/Square_of_opposition https://en.wikipedia.org/wiki/Square_of_opposition , where the phrase is "Omnis homo qui lapis est" ("every man who is a stone"). I haven't dug any further than that. But the phrase literally is intended to indicate a contradiction.

Jtsummers 3y ago

A stoneman would be a man made of stone, not a stone shaped like a man. It comes down to a philosophy of logic issue. A universal quantifier ("for all x P(x)") is ambiguous when there are no x's. You can take it as false, true, or indeterminant, your system of logic will determine which interpretation should be used. In modern predicate logic, that statement is true if there are no x's. In syllogistic logic it's considered false because there's a second presumption which must be satisfied: That there are any x's to talk about.

ptx 3y ago
Shouldn't this question fail at the parsing stage then, before it has even been asked? Q: All stonemen are ... A: ERROR: Undefined operation. Stonemen do not exist.
- Jtsummers 3y ago
  That's certainly one option. In a way, that's what the colloquial understanding of the expression would entail. In colloquial use if you were to say, "All unicorns are blue" no one can meaningfully contradict nor confirm the statement, the statement is neither true nor false because there are no unicorns (this all assumes we're not discussing in a context where unicorns "exist", like about a particular fantasy setting or animated series). In syllogistic logic it becomes false because of the foundation of that logic (centered on reality, what exists and can be defined, not on fiction). Nothing true can be said about all of some non-existent thing because, well, it doesn't exist, so the statement must be false. In modern predicate logic it's considered true, because even though there are no unicorns we (someone) decided that it should be true by convention when the set is empty (turns out to have useful properties if we permit this). These are just the rules that we've used for our logic, a choice we made. We're generally, in programming, operating under the modern logical rules, using neither colloquial rules nor syllogistic rules, so our programs are consistent with that last interpretation.