quote:And Tres, Dr. M says that in order to establish the sentences as truth-functionally equivalent, you need to find equivalent truth values on every line of the truth table, not just the lines where the both sentences are true.
> now the negation of P>Q and thereforenot the case, is P>~Q Right???
Wrong!!!
The negation of P>Q is P&~Q. If you construct a truth table, you'll find that P>Q and ~(P>~Q) have different truth conditions. In light of that, I guess the paradox unravels.
quote:Not quite. Just answer me this. What is P&~Q the logical equivalent of? In words? ("if P then possibly or possibly not Q"? No... that doesn't work...)
The negation of P>Q is P&~Q. If you construct a truth table, you'll find that P>Q and ~(P>~Q) have different truth conditions. In light of that, I guess the paradox unravels.
quote:Sorry, the "&" connective is used to form a conjunction, i.e., "&" means "AND." Many logic texts use a dot or an inverted "V" to signify "AND", but the ampersand (&) is also acceptable.
What was I thinking! good lord. Just somebody please tell me what P&~Q means in english.
quote:Well, I was going for implication, not equivalence. For A to imply B all that needs to be true is for B to be true whenever A is true.
And Tres, Dr. M says that in order to establish the sentences as truth-functionally equivalent, you need to find equivalent truth values on every line of the truth table, not just the lines where the both sentences are true.
quote:Incompleteness of arithmetic.
See, I just never see the POINT of symbolic logic. What can it do that regular, everyday logic cannot?
quote:"Regular everyday logic" tends to be whatever anyone wants to call logic. People will say stuff like "logic dictates that evolution is true" or "logic says we should invade Iraq" when really it isn't logic at all.
See, I just never see the POINT of symbolic logic. What can it do that regular, everyday logic cannot?
quote:Ah! That's a good point. It's a rather drastic way of achieving this end, though. I'm quite sure that precise use of language does the same thing, and while there are precious few people who use language precisely, the numebr can't be much smaller than the number of people who understand symbolic logic.
Symbolic logic forces you to actually use logic to prove things, because there is a fixed set of rules, a fixed way of using them, and you can quickly tell when someone is using them wrongly.
quote:Yes - symbolic logic has the added bonus that you can program machines to follow the simple rules and solve problems far faster than a human could. That way you can find the best move in checkers far quicker than you could normally deduce it.
I've never seen any real-world issue answered by symbolic logic that couldn't be answered FASTER without it. Do you have an example?
quote:Actually, using English precisely will still be vague. You get things like "Joe's friend waited while he was changing his shirt." Is the "he" Joe or the friend? There's tons of stuff like that. Symbolic logic is designed to be a language that doesn't have that sort of vague stuff.
I'm quite sure that precise use of language does the same thing, and while there are precious few people who use language precisely, the numebr can't be much smaller than the number of people who understand symbolic logic.
quote:Oops, not neccessary, and I understood all of the above already... sorry to put you through the trouble Mrs. M, I guess I worded my question wrong.
Okay, here's what Dr.M wrote:
quote:
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What was I thinking! good lord. Just somebody please tell me what P&~Q means in english.
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Sorry, the "&" connective is used to form a conjunction, i.e., "&" means "AND." Many logic texts use a dot or an inverted "V" to signify "AND", but the ampersand (&) is also acceptable.
P&~Q means "P AND NOT Q"
Here is the complete deduction:
quote:First of all, keep in mind that P and Q stand for sentences. So, if you're still looking for an example, let P = "Dean is president", and let Q = "hell is freezing over." Then "P and not Q" = "Dean is president and hell is not freezing over."
Really, what I should of asked, I suppose:
what would "P and not Q" mean if you translated it out of symbolic logic and in to written english by using some sort of example.
quote:Come on, man! Is that actually a sentence in our language? "If a dog, then red"? What in the world does that even mean?
Like for the case of P>Q, you could say, if a dog, then red. That pretty much sums up "if P then Q".
quote:
Is symbolic logic actually worth spending time on? I've never been convinced
quote:Well, skimmed it before , Read it now. I try to skim pretty thoroughly, though, and I meant no disrespect. I do not know, however, why you think your statements are insightful with regard to my last comments.
Did you perchance read my explanation of the many uses of symbolic logic?
code:If that's an outcome for a rectangular game, for instance, I can see at a glance that the third row dominates the fourth row, which means we can quickly simplify the matrix into one with equivalent optimal strategies and value. That relationship is not so immediately noticeable when the matrix is written out by english.|| 5 3 8 7 ||
|| 2 9 1 4 ||
|| 6 6 3 5 ||
|| 1 2 3 2 ||
|| 9 7 5 3 ||