For all you Philosophy buffs out there...answer this!?

Question

Suppose that p and q are sentences (they can be any sentences whatsoever). If p implies q and q implies p, then p and q are equivalent. Your task is to explain why this is...good luck!

Answer 1

It is simply this: you should mind your p's and q's, just to be sure you keep track of how many you can fit in a can.

Answer 2

there are 3 possible combinations for p's and q's

1) niether implies the other;

if the sentence p states, "I am man"
and the sentence q states "I am not a man"

then p implies not q and vice versa (neither implies)

2) one implies the other while the other does not imply the first;

now if p states "I am a man"
and q, "I am a male"

then p implies q
but q does not neccessarily imply p

finally
3)both imply each other {as your question poses}
the only way this is possible is if they both say the same thing
(ie: equivalent or identical)

so p would state. "I am a man"
and q must state "i am a man"

note: the words and syntax used are irrelevant as it is what the are 'saying' that matters.

so q may well state , "j'me suis un homme" {pardon my french}


hopefully there is no flaw in this logic. and I believe there is your explanation.

Answer 3

fortunately, one does not need good luck to answer this. Anyway,

p implies q means the information content of p is greater than or equal to that of q.

q implies p means the information content of q is greater than or equal to that of p.

Both the above can be true only if the information content of p and q are exactly the same.

If the information content of 2 statements are EXACTLY the same, it means you are saying exactly the same thing in 2 diff ways, ie., the 2 statements are equal.
QED.

ps: no one forbids the use of the language of algebra in philosophy. Philosophy need not always be vague abstract stuff!
& eric (below), i think ur answer is erroneous because ur p does not imply q. i.e., if i knew p alone, i can never deduce q from it.

Answer 4

it type of feels as though St. Augustine is installation reminiscence as something idealized, that the two works completely or fails thoroughly. yet what if it constantly works imperfectly, remembering some issues jointly as forgetting others? Or remembering in basic terms specific components of something, jointly with "I undergo in recommendations her call starts off with a 'T'..." As yet another occasion, I some time past forgot what the capital of Bulgaria is. yet of direction, I nonetheless comprehend that Bulgaria is a rustic, and subsequently ought to have a capital. St. Augustine looks unnecessarily hung up on how reminiscence works. possibly we purely have the income of living in a greater scientific age, the place we greater ideal comprehend the way those issues artwork? no longer a philosophy expert, so i ought to be lacking the factor here....

Answer 5

"Implies" does not mean 'equals'. Therefore, there is a real probability they are not equivalent. Thus, the premise of your question is invalid.

Answer 6

p---Art is beauty.
q---Beauty is art.

then both are the same.

but if

p---The second sentence is true.
q---The first sentence is true.

In this case, the p implies q and q implies p, but there are not the same!

Answer 7

Yin Yang

Different yet not separate taking up equal parts of the whole.

Answer 8

This isn't philosophy, it's algebra.

Answer 9

PUCK YQU

p = f

q = o