## Search found 705 matches

Fri Apr 26, 2019 12:01 am
Forum: Logic and Philosophy of Mathematics
Topic: Tarski Undefinability Theorem Succinctly Refuted
Replies: 100
Views: 1077

### Re: Tarski Undefinability Theorem Reexamined

If I understand your concern re: Cartesian closed spaces, it's basically the same concern all of Quantum Mechanics have been complaining about. Infinities break the mathematics - lets renormalise everything! And renormalization is effectively turning everything into a Cartesian closed space. Which ...
Wed Apr 24, 2019 5:28 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (greatly simplified)
Replies: 54
Views: 482

### Re: Transforming formal proof into sound deduction (greatly simplified)

One is true on a plane and the other is true on a sphere. On a sphere is triangle actually has more than 180 degrees. http://mathworld.wolfram.com/SphericalTriangle.html This is fudging with truth a little bit because an actual triangle is only on a plane. A spherical triangle would actually be an ...
Wed Apr 24, 2019 5:09 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (greatly simplified)
Replies: 54
Views: 482

### Re: Transforming formal proof into sound deduction (greatly simplified)

That was what was great about your question and my subsequent research. I was previously assuming that only the first was true and the second was false. Then I found out that the first assumes geometry on a plane and the second assumes some other non-plane basis. This means that they are both equal...
Wed Apr 24, 2019 4:16 am
Forum: Logic and Philosophy of Mathematics
Topic: Tarski Undefinability Theorem Succinctly Refuted
Replies: 100
Views: 1077

### Re: Tarski Undefinability Theorem Reexamined

You are mistaken Conceptually the fields of computation, physics and mathematics are isomorphic. You know anything about Cartesian closed categories? I dabble in a little category theory and watched a video with Steve Awodey describing how the lambda calculus can be interpreted as a Cartesian close...
Wed Apr 24, 2019 4:13 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (greatly simplified)
Replies: 54
Views: 482

### Re: Transforming formal proof into sound deduction (greatly simplified)

PeteOlcott wrote:
Wed Apr 24, 2019 4:06 am
Axiom(1) ∀F1 ∈ Formal_System ∀x ∈ Closed_WFF(F1) (True(F1, x) ↔ (F1 ⊢ x))
Axiom(1) ∀F2 ∈ Formal_System ∀x ∈ Closed_WFF(F2) (True(F2, x) ↔ (F2 ⊢ x))

F1 is Euclidean geometry
F2 is non-Euclidean geometry
But which is true?
Wed Apr 24, 2019 3:20 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (greatly simplified)
Replies: 54
Views: 482

### Re: Transforming formal proof into sound deduction (greatly simplified)

\ That took me almost five minutes to figure out. Then explain it to me. In English. It's perfectly clear (and has been since 1840) that no axiomatic system can reveal -- or even express -- truth. Truth is an empirical matter. Are you telling me that you never heard of non-Euclidean geometry before...
Wed Apr 24, 2019 2:49 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (rewritten)
Replies: 78
Views: 585

### Re: Transforming formal proof into sound deduction (rewritten)

Logik wrote:
Tue Apr 23, 2019 4:32 pm
Stanford has been paying you a salary for 22 years.
I must have missed that. Is PeteOlcott an employee of Stanford university? In what capacity? Just curious.
Wed Apr 24, 2019 2:20 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (greatly simplified)
Replies: 54
Views: 482

### Re: Transforming formal proof into sound deduction (greatly simplified)

Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) unlike the formal proofs of symbolic logic provability cannot diverge from truth. Aren't there mutually exclusive but independently self-consistent axiomatic system...
Sun Apr 21, 2019 5:24 am
Forum: Logic and Philosophy of Mathematics
Topic: Transforming formal proof into sound deduction (rewritten)
Replies: 78
Views: 585

### Re: Transforming formal proof into sound deduction (rewritten)

Stipulating that formal systems are Boolean: Axiom(3) ∀F ∈ Formal_System ∀x ∈ Closed_WFF(F) (True(F,x) ∨ False(F,x)) How can a wff have a truth value without a model? In fact Wikipedia is in on THIS conspiracy as well. Here's what they have to say about WFFs: A formula is a syntactic object that ca...
Sun Apr 21, 2019 2:37 am
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems
Replies: 62
Views: 651

### Re: Eliminating Undecidability and Incompleteness in Formal Systems

elif person.surname.lower() == "bachelor": You have to check all possible alternate spellings too, like "batchelor". a young knight serving under another's banner Which illustrates my point that you can't axiomatize natural language. And when Carl Sandburg wrote that the fog creeps in on little cat...
Sun Apr 21, 2019 1:23 am
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems
Replies: 62
Views: 651

### Re: Eliminating Undecidability and Incompleteness in Formal Systems

The trivial counter-example is the married bachelor of sciences. LOL. Good one! But then again I don't believe natural language can be axiomatized. PeteOlcott does, if I understand him correctly. ps -- How about this guy? http://johnbatchelorshow.com/ How critical is the exact spelling of a word? T...
Sat Apr 20, 2019 11:21 pm
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems
Replies: 62
Views: 651

### Re: Eliminating Undecidability and Incompleteness in Formal Systems

You are only giving the same word another meaning, the meanings themselves remain distinct. No, I used the original meanings. A circle is a set of points equidistant from a given point. You agree, right? And a square is a 4-sided quadrilateral with all sides equal and all angles equal. Right? Right...
Sat Apr 20, 2019 10:55 pm
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems
Replies: 62
Views: 651

### Re: Eliminating Undecidability and Incompleteness in Formal Systems

The fact that the same finite string is associated with different meanings does not coherently combine the [geometric object of a circle] with the {geometric object of a square} such that a [geometric square circle] is formed. This is TOTALLY IMPOSSIBLE because they are mutually exclusive classes. ...
Sat Apr 20, 2019 10:29 pm
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems
Replies: 62
Views: 651

### Re: Eliminating Undecidability and Incompleteness in Formal Systems

PeteOlcott wrote:
Sat Apr 20, 2019 10:14 pm
I tried and tried and tried to make a square circle to test this concept.
The unit circle is a square in the taxicab metric. The Wiki page has a picture of it.

https://en.wikipedia.org/wiki/Taxicab_geometry
Thu Apr 18, 2019 7:02 pm
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems
Replies: 62
Views: 651

### Re: Eliminating Undecidability and Incompleteness in Formal Systems

The elementary statements which belong to T are called the elementary theorems of T and said to be true. Right. They are SAID to be true. Like in chess, the fact that the knight can jump over other pieces is SAID to be true. It's not a law of nature. It's colloquially said to be true to get the gam...