# on 26-Dec-2018 (Wed)

#### Flashcard 3711673437452

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#chapter-1 #jaynes_probability_theory
Question
A -> B. Does a logical statement imply that A physically cause B?
This example shows also that the major premise, ‘if A then B’ expresses B only as a logical consequence of A; and not necessarily a causal physical consequence, which could be effective only at a later time.
The rain at 10 am is not the physical cause of the clouds at 9:45 am. Nevertheless, the proper logical connection is not in the uncertain causal direction (clouds =⇒ rain), but rather (rain =⇒ clouds), which is certain, although noncausal

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#### Flashcard 3713104481548

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#chapter-1 #jaynes_probability_theory
Question
one would take ‘A implies B’ to mean that B is logically deducible from A.
What's wrong?
"A implies B" really does not mean that there is a chain of arguments so you can derive B from what's inside the statement A. "A implies B" indeed only means "whenever A, then B". You can say "the fact that the number 3 is odd implies that the number 100 is bigger than the number 50". "Implies" here really doesn't mean that you can derive size relations of numbers from the oddness of other numbers by looking at the concepts of "size" and "oddness". These statements haven't anything special to do with each other, they just happen to be both true.

And every true statement "follows from" / "is implied by" every other true statement in the sense of formal logic.
every statement (be it true or false) "is implied by" / "follows from" any false statement.

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Note carefully that in ordinary language one would take ‘A implies B’ to mean that B is logically deducible from A. But, in formal logic, ‘A implies B’ means only that the propositions A and AB have the same truth value.

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#### Flashcard 3713171590412

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#chapter-1 #has-images #jaynes_probability_theory

#chapter-1 #jaynes_probability_theory

Question
This is just an example of a function. C = f(A, B)
How large is the class of new propositions thus generated?
two propositions, although they may appear entirely different when written out in the manner, are not different propositions from the standpoint of logic if they have the same truth value.
For A and B there 4 different inputs. TT, TF, etc. Size of the function: 2 -> 4, therefore there are 4^2 functions. A fixed number.
This easily generalizes to greater dimensions.

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#### Flashcard 3713173425420

Tags
#chapter-1 #jaynes_probability_theory
Question
Example of "reduction to disjunctive normal" method in logic
Hint: size