Philosophy Now Forum

You reply deserves a longer considered response and I will do so they evening. But this stood out. Moe did not win the lottery then if Moe did win the lottery then he was never born demonstrates why [ -P ⊢ P → Q ] is a poor form of reasoning. Okay, but I already gave such an example in that original...

If I'm missing your point, perhaps you could state it more clearly and succinctly for simple minds like my own. The counter examples shows (1) is more than a bit paradoxical or counter intuitive or fails to capture "if...then...", the thread was started because (1) allows true premises to...

These implications should be familiar. (1) ⊨ (¬p ⋁ q) → (p → q) (2) ⊨ (p → q) → (¬p ⋁ q) Together (1) and (2) define material implication. They are theorems of propositional logic and not usually included amongst the paradoxes of material implication. On closer inspection that is surprising. (2) is ...

Second, the Modus Ponens comes out not valid as well. If confirmed, that would be terminal. Just remembered why modus ponens is valid. The table written as implication is never false. It is reliable but not a theorem because of the appearance of C and N in the truth function. But Modus poems is not...

The relation of the etymology of "contingent" is 'con-'(with) + 'tangent' (touch), and I believe the past logicians chose it in light of something that is 'touchable' is sometimes and untouchable at other times. So it fits with how you are using it colloquially in the same way. Something ...

Yes. I'm not in doubt of this. The OP was using binary truth values and appeared to confuse the the term, 'contingent' as a value along side of the truth values when the term describes the table's truth values as a whole. In practice contingent truth means the same as probabilistic truth. It means ...

If someone is able to come up with some nasty unwanted results - then back to the drawing board. :shock: Well, bad news, as far as I can tell. First, I don't get the same results at all as you do for ¬(p → q) → p, though it also comes out not valid. Second, the Modus Ponens comes out not valid as w...

I'm confused at what this thread is about other than to state what material implication is. Like all threads they take on a life of their own and people start chasing all sort of rabbits. The thread was started to discuss the paradoxes of material implication, for those who think the paradoxes are ...

P ⊢ Q → P Which begs whether the arbitrary meaning (semantic matter) of Q is or is not valid. If given any P, how can it seem to imply the material reality of some antecedent without affirming that Q exists first? The problem is resolved when we recognize that the conditional is itself true but say...

And so the point I am making is that every time your logical conclusion disagrees with reality Your logic is wrong. Not reality. All I am describing (rather verbosely at that) is the garbage-in/garbage-out problem. Well it depends what threshold you set that means a principle disagrees with reality...

To be complete, this last statement should be: Q → P ⊢ P ∨ -Q If you provide me with truth-tables for your operators I will construct you a temporal system in which the above is false. I realise I'v made a mistake in a previous post. Several of the formula listed as theorems are only found never fa...

def impl(a,b); return ( (not a) or b ); end $toggle = false def p; $toggle = (not $toggle) end def q; true; end impl( ( p and q) , p) => false It's called a Race condition When the truth-value of P changes after you have established it. Ok I don't code so the syntax is strange to me. I think this s...

Since EVERY model has counter-examples which violate the "impossibility" criterion, What counter examples violate modus ponens? p, (p ⇒ q) ⊨ p and simplification? p ⋀ q ⊨ p Some forms of inference are not seriously up for debate for the lack of counter examples. Whilst different logics ha...

If the pipes are blocked -> Will NOT empty If the tank has no water -> Will NOT empty If the taps are above the water line -> Will NOT empty If the tank is full and hermetically sealed at the top -> Will NOT empty If the pipes are blocked the antecedent is false and the inference is proved true. Fa...

So you have the taps before you. You know how they are supposed to work We have the taps before us. We have the formula before us. The formula is telling us the taps do something they don't. It is because we know what to do that we know there is something wrong with 7. All models have edge/corner c...