V_V comments on Assessing Kurzweil: the results - Less Wrong

45 Post author: Stuart_Armstrong 16 January 2013 04:51PM

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Comment author: TheOtherDave 30 January 2013 02:56:08PM *  2 points [-]

Why oughtn't it be? The construction "A, though B" is an independent assertion of A and B. Syntactic linkage is not enough to establish contingency.

It is not like "A, because B" for example, where it's arguably unfair if B and A are both false to count it as two failures... in that case, the claim of A can be seen as contingent on the claim of B, and not independent.

To put this differently, "A, though B" makes the following claims:
A
B
You might (mistakenly) expect -B given A, which is why I mention B explicitly.

Whereas "A, because B" makes the following claims:
B
If B, then A

If A happens in the first case, the first claim is correct. If B happens, the second is correct. If both happen, both claims are correct.

If A happens in the first case but B doesn't, the first claim is correct and the second claim is unevaluatable.

(I suppose one could argue that the second case implicitly claims "if -B, then -A" as well... "because" is somewhat ambiguous in English.)

Comment author: V_V 30 January 2013 05:13:22PM *  0 points [-]

Well, if you analyze the statements in terms of prepositional logic, then all the English language conjunctions "and", "but", "though", etc. map to the only type of logical conjunction ∧.

But natural language is richer than (directly mapped) prepositional logic. I interpret the statement "Local roads, though, are still predominantly conventional." as a clarification of "Intelligent roads are in use, primarily for long-distance travel.".

Formally, if you just claim:
"Intelligent roads are in use, primarily for long-distance travel."
it is equivalent to:
"Intelligent roads are in use, primarily for long-distance travel." ∧ ( "Local roads are still predominantly conventional" ∨ ¬"Local roads are still predominantly conventional" )
which is different from
"Intelligent roads are in use, primarily for long-distance travel." ∧ "Local roads are still predominantly conventional"

However, we can assume that if you claim:
"Intelligent roads are in use, primarily for long-distance travel."
you also wanted to communicate that
"Local roads are still predominantly conventional"
not that you are undecided between
"Local roads are still predominantly conventional", ¬"Local roads are still predominantly conventional"
otherwise you would have probably stated that explicitely.

Therefore, the information content of:
"Intelligent roads are in use, primarily for long-distance travel."
and:
"Intelligent roads are in use, primarily for long-distance travel. Local roads, though, are still predominantly conventional."
is rougly the same.