Philosophy Now Forum

so in mathematics and mathematical induction: are you hypothesizing a general principle and trying to prove as many cases as possible are applicable? Concerning mathematical induction, in my understanding, what can appropriately be said to be a general principle is the inductive step, and the latte...

They talk about proving the basis clause of the first premise then use the second premise as the inductive step which you need to prove is true I'm not clear - is the inductive hypothesis the first premise? - the basis clause? They say it's the antecedent of the inductive step. If you consider the ...

I can't understand the use of each individual rule. I mean I know you could apply that rule but I don't see why you use the rule. The 'plan' or the 'forest from the trees' if you will. In the example you provided, it was required to prove (U & M) ⊃ S, M & ~S ⊢ ~U The letters are complete se...

Sorry for the crude representation but as you know the forum isn't conducive to writing symbolic logic. The subderivation is offset a bit to clarify what it is: As has already been explained one can use the code tags of the post editor to include white spaces and format the proof accordingly. It de...

Can someone help me to understand and clarify this? I do not know but I can try share some thoughts with you. It states: A set Γ of sentences of symbolic logic truth functionally entails a sentence P if and only if there is no truth value assignment on which every member of Γ is true and P is false...

Yes, the one snafu was a typo. But I tried to do it without DeMorgan's. I thought that (C & D) and (notC & notD) produced the contradiction for my RAA. For (C & D) reduces to C by separation and then (notC & not D) reduces to notC. So C & notC is the contradiction (the same with...

WHY make an assumption in the first place? Why not? Why not just look at what IS, already an actual fact? And what would that be? 'The sky is blue on a sunny day', expresses a fact in the English language. In formal logic, there is no such fact. In the problem in the OP, what would you consider as ...

It depends on what your professor is requiring of you. Do you have axioms and rules of inference or are less formal proofs allowed? If you are working with only modus ponens (including conditional proof): Assume A (whatever follows from assuming A will create a conditional, If A then....) Assuming ...

I am a “bit” late on this, but some people say, better late than never! If one can find some wisdom in that saying then here goes. One thing to bear in mind in any logical and/or mathematical proofs, is that the first strategy to attempt to prove anything is the reductio ad absurdum. As the mathemat...

I do. In fact that pattern is one of the famous series in math. But before you can see it, factor out the 8. So now we have: 8•1 = 8 8•3 = 24 8•6 = 48 8•10 = 80... Do you recognize the series 1, 3, 6, 10...? This is the famous triangular series and the process I used which led to those numbers I ca...