Intelligence test

[brewer]

Can we have the arrogance test next, PLEASE?

[Alex K]

Something I cooked up to test your logical thinking skills. Ask any question you feel you need to pertaining to the question.

Two brothers walk up to you.

Man 1 says "One of us tells lies"

Man 2 says "And one of us tells the truth".

Man one states an undeniable fact.

Which one lies, and which one tells the truth?

Determine all of what you know, don't think one has to tell lies and one has to tell the truth.

I read "one of us" as "exactly one of us". The wording is ambiguous. (edit: and I for now ignore the additional comment, c.f. Pyrrho) (edit: I also read them as meaning "always, consistently" c.f. Losty)

Hypothesis TT contradicts the first statement, the hypothesis is rejected

TL is compatible with the first statement, but not with negation of statement 2 (none or two of us tell the truth). Therefore the hypothesis is rejected.

LT is compatible with statement 2, but not with the negation of statement 1 (none or two of us tell lies)

LL is compatible with the negation of  statement 1 (none or two of us tell lies) and with the negation of statement 2 (none or two of us tell the truth).

Both are liars therefore is the only consistent constellation. (edit: however, this constellation is not compatible with the additional comment about the undeniable fact. The riddle in this reading is inconsistently written, c.f. Pyrrho)

---

Now, if "one of us" is read as "at least one of us" it gets more interesting.

TT is again contradicted by statement 1
TL is contradicted by the negation of statement 2 (none of us tells the truth)
LT is contradicted by the negation of statement 1 (none of us tell lies)
LL is again contradicted by the negation of statement 1 (none of us tell lies).

None of the possibilities remain.

Therefore, we have a Paradox akin to the Barber [Russell] who shaves everyone except those who shave themselves. Such a barber cannot exist, or there is a limitation of the language used in which no truth value can be assigned to some sentences.

[Angrboda]

Something I cooked up to test your logical thinking skills. Ask any question you feel you need to pertaining to the question.

Two brothers walk up to you.

Man 1 says "One of us tells lies"

Man 2 says "And one of us tells the truth".

Man one states an undeniable fact.

Which one lies, and which one tells the truth?

Determine all of what you know, don't think one has to tell lies and one has to tell the truth.

I read "one of us" as "exactly one of us". The wording is ambiguous.

Hypothesis TT contradicts the first statement, the hypothesis is rejected

TL is compatible with the first statement, but not with negation of statement 2 (none or two of us tell the truth). Therefore the hypothesis is rejected.

LT is compatible with statement 2, but not with the negation of statement 1 (none or two of us tell lies)

LL is compatible with the negation of  statement 1 (none or two of us tell lies) and with the negation of statement 2 (none or two of us tell the truth).

Both are liars therefore is the only consistent constellation.

Liar!

[Homeless Nutter]

Something I cooked up to test your logical thinking skills. Ask any question you feel you need to pertaining to the question.[...]

OK - who the f*** are you?

It seems to me that in order to be able to "test" other people's "logical thinking skills" you'd need some knowledge of logic yourself. And - judging by your clumsily worded riddle - you lack it.

[Pyrrho]

Something I cooked up to test your logical thinking skills. Ask any question you feel you need to pertaining to the question.

Two brothers walk up to you.

Man 1 says "One of us tells lies"

Man 2 says "And one of us tells the truth".

Man one states an undeniable fact.

Which one lies, and which one tells the truth?

Determine all of what you know, don't think one has to tell lies and one has to tell the truth.

I read "one of us" as "exactly one of us". The wording is ambiguous.

Hypothesis TT contradicts the first statement, the hypothesis is rejected

TL is compatible with the first statement, but not with negation of statement 2 (none or two of us tell the truth). Therefore the hypothesis is rejected.

LT is compatible with statement 2, but not with the negation of statement 1 (none or two of us tell lies)

LL is compatible with the negation of  statement 1 (none or two of us tell lies) and with the negation of statement 2 (none or two of us tell the truth).

Both are liars therefore is the only consistent constellation.

---

Now, if "one of us" is read as "at least one of us" it gets more interesting.

TT is again contradicted by statement 1
TL is contradicted by the negation of statement 2 (none of us tells the truth)
LT is contradicted by the negation of statement 1 (none of us tell lies)
LL is again contradicted by the negation of statement 1 (none of us tell lies).

None of the possibilities remain.

Therefore, we have a Paradox akin to the Barber who shaves everyone except those who shave themselves. Such a barber cannot exist.

Your analysis is good, except that you forgot:

"Man one states an undeniable fact."

With that, both cannot always lie, and so with your first interpretation, none of the options are possible either.

It does not seem to be a well-worded problem.  It seems that they are not both consistent in their answers.

[Losty]

They're both lying that's easy.

Eta: hmmm

Ok

Everyone lies and everyone tells the truth, not at the same time but everyone does both.

So I thought they were both lying at first because I was assuming "only one of us" but neither says only. So I think they're actually both telling the truth.

[Alex K]

Very good, Pyrrho. I ignored that comment in my analysis. (I edited my post accordingly)

[Alex K]

The question which remains is now - did the poster understand the implications of their own riddle?

[Losty]

Now, if "one of us" is read as "at least one of us" it gets more interesting.

TT is again contradicted by statement 1
TL is contradicted by the negation of statement 2 (none of us tells the truth)
LT is contradicted by the negation of statement 1 (none of us tell lies)
LL is again contradicted by the negation of statement 1 (none of us tell lies).

Under "at least one of us", why can't statement one and two be true at the same time?

What I mean is, you are assuming an "always" or a "right now" that isn't actually written in either statement.

[Alex K]

Now, if "one of us" is read as "at least one of us" it gets more interesting.

TT is again contradicted by statement 1
TL is contradicted by the negation of statement 2 (none of us tells the truth)
LT is contradicted by the negation of statement 1 (none of us tell lies)
LL is again contradicted by the negation of statement 1 (none of us tell lies).

Under "at least one of us", why can't statement one and two be true at the same time?

If both always told the truth, we'd have to believe the first guy, who claims that one of them always lies. This contradicts the original assumption that both tell the truth

Edit: I indeed assume an "in this conversation, consistently", which is not written but traditionally assumed in such Paradoxes which have a long tradition going back to ancient Greece (The lying guy from Crete comes to mind). If we drop this restriction, the problem tends to become simply undeterminable from the existing information.