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Post BBCode URL - Right click and save to clipboard to use later in post Post 1: Thu Sep 19, 2019 3:08 pm
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Future Reference: The Logic 100 usergroup

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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! Study Very Happy Cool

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

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Post BBCode URL - Right click and save to clipboard to use later in post Post 2: Thu Sep 19, 2019 3:26 pm
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Re: Future Reference: The Logic 100 usergroup

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[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

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Post BBCode URL - Right click and save to clipboard to use later in post Post 3: Tue Nov 19, 2019 7:13 pm
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An example of logics interpretation

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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 Very Happy Cool

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