Search found 317 matches

by Averroes
Wed Aug 30, 2017 1:39 pm
Forum: Logic and Philosophy of Mathematics
Topic: need help understanding when a Proof is a Proof
Replies: 3
Views: 638

Re: need help understanding when a Proof is a Proof

Okay, I hope that's enough to clarify my question which is: If the discussion was to develop a Proof, the one I just wrote, then they proceed to tell me that the supposition ( is that the Assumption?) is wrong - then how does that comprize a Proof?!? I think this a case of reductio ad absurdum,i.e....
by Averroes
Wed Aug 30, 2017 1:22 pm
Forum: Aesthetics
Topic: Great Works of Art
Replies: 83
Views: 15116

Re: Great Works of Art

and as you may well know, from the times of Ataturk,Turkey has been a very secular modern society. I think things have been changing for the better for Turkey since 1994 when the actual President Recep Tayyip Erdogan first took a position of political power in Turkey. At that time, the west and the...
by Averroes
Mon Aug 28, 2017 9:45 am
Forum: Aesthetics
Topic: Great Works of Art
Replies: 83
Views: 15116

Re: Great Works of Art

La Alhambra de Granada (Spain) Thank you so much for these wonderful pictures of Alhambra. The story behind it and more generally Muslim Spain, is very interesting. Bettany Hughes, a respected British historian, goes through a detailed and illustrated analysis of this period of history of Al-Andalu...
by Averroes
Mon Aug 28, 2017 9:37 am
Forum: Aesthetics
Topic: Great Works of Art
Replies: 83
Views: 15116

Re: Great Works of Art

Is the Blue Mosque the same as the Hagia Sophia? What a beautiful place. Hagia Sophia is now a museum. According to Google Map, it is within walking distance of the Blue Mosque; less than 500 meters. You can check the following YouTube to learn more about Hagia Sophia and other splendid historic mo...
by Averroes
Sat Aug 26, 2017 8:12 am
Forum: Aesthetics
Topic: Great Works of Art
Replies: 83
Views: 15116

Re: Great Works of Art

This is an interesting and informative thread, and I express my appreciation for the idea to the author of this thread. Some interesting Picassoes were presented. Pablo Picasso once said: "If I had known there was such a thing as Islamic Calligraphy, I would never have started to paint. I have striv...
by Averroes
Wed Aug 23, 2017 7:51 am
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 2063

Re: need clearer explanation of mathematical induction.

thank you so much for your willingness to help In my way of life and frame of mind, the more I share what I have been given and the more I help others in doing beneficial things, the more I am helped and the more good things I get. So, it is a win-win situation for both of us! Case 1: P has the for...
by Averroes
Tue Aug 22, 2017 5:43 am
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 2063

Re: need clearer explanation of mathematical induction.

ProfAlexHartdegen

If you are still having trouble with this, you can ask more questions. If that be the case, tell me where you are stuck.
by Averroes
Sun Aug 20, 2017 6:45 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 2063

Re: need clearer explanation of mathematical induction.

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...
by Averroes
Sat Aug 19, 2017 5:58 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 2063

Re: need clearer explanation of mathematical induction.

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 ...
by Averroes
Sun Aug 13, 2017 12:01 pm
Forum: Logic and Philosophy of Mathematics
Topic: help understanding Negation Introduction
Replies: 17
Views: 3187

Re: help understanding Negation Introduction

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 sentences ...
by Averroes
Sun Aug 13, 2017 11:29 am
Forum: Logic and Philosophy of Mathematics
Topic: help understanding Negation Introduction
Replies: 17
Views: 3187

Re: help understanding Negation Introduction

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...
by Averroes
Tue Aug 08, 2017 8:27 am
Forum: Logic and Philosophy of Mathematics
Topic: need help understanding truth functional entailment
Replies: 2
Views: 1105

Re: need help understanding truth functional entailment

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...
by Averroes
Thu Jul 27, 2017 4:45 pm
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2921

Re: How to construct a formal proof?

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 D and not D). Why i...
by Averroes
Sun Jul 23, 2017 10:36 pm
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2921

Re: How to construct a formal proof?

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 ...
by Averroes
Sun Jul 23, 2017 10:14 pm
Forum: Logic and Philosophy of Mathematics
Topic: How to construct a formal proof?
Replies: 10
Views: 2921

Re: How to construct a formal proof?

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 ...