Search found 20 matches

by ProfAlexHartdegen
Mon Sep 11, 2017 10:40 pm
Forum: Logic and Philosophy of Mathematics
Topic: If...Then as element of a superset
Replies: 8
Views: 3731

Re: If...Then as element of a superset

I think it is a great idea, averroes! I recommend subforums for Philosophy of Science, Philosophy of Language and Philosophy of History also. :D
by ProfAlexHartdegen
Sat Sep 09, 2017 5:19 am
Forum: Logic and Philosophy of Mathematics
Topic: If...Then as element of a superset
Replies: 8
Views: 3731

Re: If...Then as element of a superset

Thanks again for your time and effort and willingness to help, sorry for the slow reply it took me time to read your post carefully to see if I could understand. I think that I do. One point to thank you especially because my book did not discuss The transposition/contraposition rule: (P ≡ Q) ≡ (~Q ...
by ProfAlexHartdegen
Sun Sep 03, 2017 1:19 am
Forum: Logic and Philosophy of Mathematics
Topic: If...Then as element of a superset
Replies: 8
Views: 3731

Re: If...Then as element of a superset

Thanks again for your detailed replies -they are very helpful. I am still developing my understanding of the Proofs. I will try to do the Proofs for the remaining parts and present them here for you to evaluate. The Logic Book does discuss maximal consistency. It describes it as: "A maximally c...
by ProfAlexHartdegen
Wed Aug 30, 2017 4:47 pm
Forum: Logic and Philosophy of Mathematics
Topic: If...Then as element of a superset
Replies: 8
Views: 3731

Re: If...Then as element of a superset

I was thinking about that after I published my original post. The conditional is true for only three cases: When both P and Q are true, when P is false and Q is true, or when P is false and Q is false. The fourth case is when P is true and Q is false. If the truth of the conditional is all that's ne...
by ProfAlexHartdegen
Wed Aug 30, 2017 2:11 pm
Forum: Logic and Philosophy of Mathematics
Topic: If...Then as element of a superset
Replies: 8
Views: 3731

If...Then as element of a superset

okay, again from the Logic Book there is something I don't understand - I'll quote the discussion with the part that confuses me bolded: "6.4.11: If Γ* is maximally consistent in SD and P and Q are sentences of SL, then: a. ~P ∈ Γ* if and only if P ∉ Γ* b. P & Q ∈ Γ* if and only if both P ∈...
by ProfAlexHartdegen
Wed Aug 30, 2017 2:01 pm
Forum: Logic and Philosophy of Mathematics
Topic: need help understanding when a Proof is a Proof
Replies: 3
Views: 1345

Re: need help understanding when a Proof is a Proof

thanks! :D I have a new question but I think I must create a new thread - give me a few minutes and I'll post it! thanks again for your willingness to help!
by ProfAlexHartdegen
Wed Aug 30, 2017 2:40 am
Forum: Logic and Philosophy of Mathematics
Topic: need help understanding when a Proof is a Proof
Replies: 3
Views: 1345

Re: need help understanding when a Proof is a Proof

Let me try to rephrase the question ..... When you see a 'Proof' in a book about Logic - does it mean more that it is more of an argument with as many possible aspects discussed, defined, and answered with a possible outcome? Or is a 'Proof' what most people would consider it - evidence for an asser...
by ProfAlexHartdegen
Tue Aug 29, 2017 3:43 am
Forum: Logic and Philosophy of Mathematics
Topic: need help understanding when a Proof is a Proof
Replies: 3
Views: 1345

need help understanding when a Proof is a Proof

okay, I'm rather confused by the discussion in the section of my book 'The Logic Book' about the section The Completeness of SD and SD+. I will write a portion of the discussion verbatim here; if it is not enough information to help you explain to me then I could try to write some of the earlier or ...
by ProfAlexHartdegen
Tue Aug 22, 2017 11:38 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 4170

Re: need clearer explanation of mathematical induction.

Actually, I do have another question that involves the concepts of Mathematical Induction and Truth Functional Completeness. In that section of the Logic Book there is another example of Mathematical Induction that discusses a minor point in passing that confuses me. The example involves showing tha...
by ProfAlexHartdegen
Tue Aug 22, 2017 10:03 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 4170

Re: need clearer explanation of mathematical induction.

thank you so much for your willingness to help, I think I might understand now - I am reading farther along the book. I'm just finishing the section about Truth Functional Completeness. :)
by ProfAlexHartdegen
Sun Aug 20, 2017 7:15 am
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 4170

Re: need clearer explanation of mathematical induction.

thanks again for your detailed replies. Just a slight clarification request, so in mathematics and mathematical induction: are you hypothesizing a general principle and trying to prove as many cases as possible are applicable?
by ProfAlexHartdegen
Sat Aug 19, 2017 5:41 pm
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 4170

Re: need clearer explanation of mathematical induction.

My example comes directly from the textbook The Logic Book, Chapter 6 Sentential Logic: Metatheory. The specific example that I cite comes from the second page of that chapter and is prefaced with the words: "We introduce mathematical induction with an example. It seems obvious that in each sen...
by ProfAlexHartdegen
Sat Aug 19, 2017 5:05 am
Forum: Logic and Philosophy of Mathematics
Topic: need clearer explanation of mathematical induction.
Replies: 11
Views: 4170

need clearer explanation of mathematical induction.

Okay, so I'm reading a book called The Logic Book and I just started the chapter about Metatheory. The topic of Mathematical Induction is being discussed by an example using the recursive definitions of Symbolic Logic. So, they say how can you prove for every sentence the number of left parenthesis ...
by ProfAlexHartdegen
Sun Aug 13, 2017 8:02 pm
Forum: Logic and Philosophy of Mathematics
Topic: help understanding Negation Introduction
Replies: 17
Views: 6924

Re: help understanding Negation Introduction

Thank you that was a very helpful post. I think that I understand a fair bit better about Negation Introduction now! :)
by ProfAlexHartdegen
Sun Aug 13, 2017 6:32 am
Forum: Logic and Philosophy of Mathematics
Topic: help understanding Negation Introduction
Replies: 17
Views: 6924

Re: help understanding Negation Introduction

thanks for the serious reply and the tip. As for the others, I don't appreciate them hijacking my thread. I am trying to learn an academic subject and the notation and discussion is rather challenging for me too. Although I have a decent aptitude for math, advanced mathematics has been difficult for...