Future Reference: The Logic 100 usergroup - And, perhaps, the Logic 101 usergroup...

Aetixintro

Location: Metropolitan-Oslo, Norway, Europe

Age: 44

Gender: Male

109.08 tokens

Post 1: Thu Sep 19, 2019 3:08 pm Future Reference: The Logic 100 usergroup
Like this post
Here we go! We discuss all forms of Logics, Propositional, Predicate, Quantitative, Informal reasoning and Dialectic (huh???!), Modal, etc. But also Logicians like Gödel and Smullyan and all the others. Have fun! Logic100 usergroup link ref:Logic100 - How the Usergroup unfolds in interest... Wildly ordered, Kurt Gödel, Wikipedia: https://en.wikipedia.org/wiki/Kurt_G%C3%B6del Raymond Smullyan, Wikipedia: https://en.wikipedia.org/wiki/Raymond_Smullyan Alonzo Church, also Wikip.: https://en.wikipedia.org/wiki/Alonzo_Church Warren Goldfarb, Wikip.: https://en.wikipedia.org/wiki/Warren_Goldfarb Gottlob Frege, Wikip.: https://en.wikipedia.org/wiki/Gottlob_Frege Alan Turing, Wikip.: https://en.wikipedia.org/wiki/Alan_Turing Bertrand Russell, Wikip.: https://en.wikipedia.org/wiki/Bertrand_Russell Richard Jeffrey, Wikip.: https://en.wikipedia.org/wiki/Richard_Jeffrey .
Last edited by Aetixintro on Fri Sep 20, 2019 8:13 am; edited 1 time in total

Goto top, bottom

Aetixintro

Location: Metropolitan-Oslo, Norway, Europe

Age: 44

Gender: Male

109.08 tokens

Post 2: Thu Sep 19, 2019 3:26 pm

Re: Future Reference: The Logic 100 usergroup

Like this post

[Replying to post 1 by Aetixintro]

Just for putting it back here so that Logic 100 isn't so crucial:

Aetixintro wrote:

Now that Logic100 is here "I reiterate a bit":

Description:
This is the group for people who are interested in logics and who want to know more of it! We start with the 1st order logic, move up with Predicate logic, Modal logic and Quantified logic. The first book to read: The Logic Book by M. Bergmann et al. (McGraw-Hill Higher Education, any edition, 3rd, 4th, 5th).

The recommended reading for now:
The Logic Book by M. Bergmann et al., highly recommended to all people here, religious people...

+ others:
W. Goldfarb, Deductive Logic, Hackett, 2003.
R. Jeffrey, Formal Logic, Its Scope and Its Limits, 3rd ed., McGraw-Hill (Higher Educ.), 1991.
G. E. Hughes, M. J. Cresswell, A New Introduction to Modal Logic, Routledge, 1996. (Not entirely recommended, but possible choice, watch up for "frame logics".)
----
some Gödel logics, for both background, being a fellow religious person, but also for the Incompleteness notions:
P. Smith, An Introduction to Gödel's Theorems, Cambridge Univ. Press, 2007, 4th printing (apart from the editions).

Background of mine, heavier than you think, special circumstances of North Europe:
Connected earlier on 100 points, but not... that they are listening, that the Logician considered, with LPOV from Quine to go... Wink

Goto top, bottom

Aetixintro

Location: Metropolitan-Oslo, Norway, Europe

Age: 44

Gender: Male

109.08 tokens

Post 3: Tue Nov 19, 2019 7:13 pm

An example of logics interpretation

Like this post

I'd like to present an example of logical analysis and interpretation because the arguments can sometimes be reformulated and perhaps made differently too as you like:

Aetixintro wrote:

Gödel's ontological proof can be questioned, however I've contributed with a version that makes it stand out as splendid and at the same time being accepted without a question outside the logical soundness objections to a "necessary God".

Here is:

UoD: Everything.

Gx: x is God-like
Ex: x has essential properties.
Ax: x is an essence of A.
Bx: x is a property of B.
Px: property x is positive.
Nx: x is a General property.
Xx: x is Positive existence.
Cx: x is consistent.

The final argument by my interpretation is presented below in 4 parts:

1.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ □Ex A
3 │ ◊Px ≡ □Px A
4 │ ◊Px A
------------------
5 │ □Px ≡ □Gx 1, 2 ≡E
6 │ □Px 3, 4 ≡E
------------------
7 │ □Gx 5, 6 ≡E

...

4.

1 │ □Bx ≡ □Gx A (A is Assumption)
2 │ ◊Ax ≡ □Bx ≡ (◊Ax ⊃ □Bx) A
3 │ ◊Ax A
------------------
4 │ □Bx 3, 2 ≡E
------------------
5 │ □Gx 4, 1 ≡E

Note for the 4th part: Consider (◊Ax ⊃ □Bx) as “added explanation”!
Also, line 2 of the 4th part is Definition 2 from the original argument of Gödel.
Note2: The following lines are taken out for having no use in this interpretation of the argument.
8 │ □Gx ⊃ □Px A
16│ □Gx ⊃ □Cx A
17│ □Gx ⊃ □Ax A.

From:
Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified
Axiom 1: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 2: If a property is positive, then its negation is not positive.
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is positive.
Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified.
Corollary 1: The property of being God-like is consistent.
Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing.
Theorem 3: Necessarily, the property of being God-like is exemplified.

http://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof
http://en.wikipedia.org/wiki/Universe_of_Discourse - UoD from above.
http://en.wikipedia.org/wiki/Logical_consequence - "Entailment"/"entails".

Some of the text is from http://whatiswritten777.blogspot.no/2012/03/presentation-of-my-interpretation-of.html.

Aetixintro wrote:

UoD: Everything.

Gx: x is God-like
Ex: x has essential properties.
Ax: x is an essence of A.
Bx: x is a property of B.
Px: property x is positive.
Nx: x is a General property.
Xx: x is Positive existence.
Cx: x is consistent.

The final argument by my interpretation is presented below in 4 parts:

1.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ □Ex A
3 │ ◊Px ≡ □Px A
4 │ ◊Px A
------------------
5 │ □Px ≡ □Gx 1, 2 ≡E
6 │ □Px 3, 4 ≡E
------------------
7 │ □Gx 5, 6 ≡E

Alt. 1, 1st.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ □Ex A
3 │ ◊Px ⊃ □Px A
4 │ ◊Px A
------------------
5 │ □Px ≡ □Gx 1, 2 ≡E
6 │ □Px 3, 4 ⊃E
------------------
7 │ □Gx 5, 6 ≡E

Alt. 1, 2nd.

1 │ □Ex ≡ □Px ≡ □Gx A (A is Assumption)
2 │ (□Px ⊃ □Nx) ⊃ □Px A
3 │ □Px ⊃ □Nx A
4 │ □Ex A
------------------
5 │ □Px 2, 3 ⊃E
6 │ □Px ≡ □Gx 1, 2 ≡E
------------------
7 │ □Gx 6, 5 ≡E

This alternative, nr. 2, takes care of the former line ”6 │ (□Px ⊃ □Nx) ⊃ □Px A” and adds overall description by this!

2.

1 │ □Px ≡ □Gx A (A is Assumption)
2 │ □Xx ⊃ □Px A
3 │ □Xx A
------------------
4 │ □Px 2, 3 ⊃E
------------------
5 │ □Gx 1, 4 ≡E

3.

1 │ ◊Cx ≡ □Gx A (A is Assumption)
2 │ □Px ∨ ~□Px A
3 │ □Px ⊃ ◊Cx A
------------------
4 ││ □Px A
0 ││-----------------
5 ││ □Px 6 R

6 ││ ~□Px A
0 ││-----------------
7 ││ □Px 6 R
8 │ □Px 4, 6-9 ∨E
9 │ ◊Cx 8, 3 ⊃E
------------------
10│ □Gx 9, 1 ≡E

4.

1 │ □Bx ≡ □Gx A (A is Assumption)
2 │ ◊Ax ≡ □Bx ≡ (◊Ax ⊃ □Bx) A
3 │ ◊Ax A
------------------
4 │ □Bx 3, 2 ≡E
------------------
5 │ □Gx 4, 1 ≡E

Note for the 4th part: Consider (◊Ax ⊃ □Bx) as “added explanation”!
Also, line 2 of the 4th part is Definition 2 from the original argument of Gödel.
Note2: The following lines are taken out for having no use in this interpretation of the argument.
8 │ □Gx ⊃ □Px A
16│ □Gx ⊃ □Cx A
17│ □Gx ⊃ □Ax A.

So there it is. Enjoy logics! Study

Goto top, bottom

Aetixintro

Location: Metropolitan-Oslo, Norway, Europe

Age: 44

Gender: Male

109.08 tokens

Post 4: Sun Dec 15, 2019 8:34 am People in Logics (Philosophy) - J. C. Beall
Like this post
People in Logics (Philosophy) J. C. Beall: Wikipedia, https://en.wikipedia.org/wiki/Jc_Beall World Catalogue, https://www.worldcat.org/identities/lccn-no2003056998/ Phil People, https://philpeople.org/profiles/jc-beall I get some input from Daily Nous and thus I've been presented with JC Beall from there. More will come, surely.

Goto top, bottom

Debating Christianity and Religion

Debating Christianity and Religion

The pursuit of knowledge and truth, through God, through science, through civil and engaging debate

Aetixintro

Aetixintro

Aetixintro

Aetixintro