- C — "For every x, if x is Italian, then at some point in the
future, x will be rich." Option B is clearly wrong, because it says that
in the future everyone will be both Italian and rich. That's different.
- B — It didn't say only when! Work out the truth tables if
you need more convincing.
- B — Gödel created the statement "I am not provable". If it is true, the system is
incomplete; if false, then it is inconsistent. Note that answer C is absurd ("can't prove
its theorems" ... theorems are defined as that which are proved). Option A and D might be true
statements, but they are NOT what the Incompleteness Theorem says; indeed the Theorem allows
for them to be false, if you take the inconsistency route!
- A — "Strong AI" means minds can be simulated. Searle says no way, man. Option C is
wrong: if there is one thing Searle is adamant about, it is that mental phenomena ARE caused
by brain processes.
- E — Note that he even wrote a follow-up paper as to why he didn't like the argument for B.
The Chinese Room doesn't even address A and C.
- C — C's count for two A's, not the other way around.
- B — Let R mean "turn right" and L mean "turn left" and imagine instructions
to a drawing agent. Note that it's not a (likely) safe combination as there is no
reason to go right multiple times in a row.
- C — All I can say here is generate B0, B1, B2, B3, and B4 systematically, on your own.
- C — Theorems are strings producible from the rule-book. The Tortoise only said
the rules produced strings with Buddha-nature (implying soundness) but he never said
the rule-book produced ALL strings with Buddha-nature.
- B — Goldbach conjecture: Every even number is the sum of two primes.
- B — Straight from the book, pretty much.
- C — "All Cretans are liars" is NOT a paradox! It can be consistently false.
Half of the Cretans could be truth-tellers and half liars, with the sentence uttered
by a liar!
- C — He said, "Lucas cannot consistently assert this statement." Gotcha, Lucas.
- C — Look at the 3 smaller triangles. Each is half the width of the big one, and
half its height as well.
- C — The word "swam" is in category IV, which is not followed by a PP inside a VP.
- A — "If omnipotent and omniscient then not omnibenevolent - AND - if omnipotent
and omnibenevolent then not omniscient - AND - if omniscient and omnibenevolent then
not omnipotent". Alternatively, "Pick any two of three." IF any two are true, then
the third must be false. I know that
~<<p∧s>∧b>
would have worked,
but I didn't want the test to be trivial.
- E — All straight from GEB.
- C — A direct quote from What Is Thought?
- E — Directly from Chapter 13 of What Is Thought? Also, he said several
times that language evolved slowly, not rapidly (technically: why did it take so long
to evolve?)
- D — Note that C is not a quine and E is a finite sequence. A and B don't
even have loops, let alone strange loops.