Search found 970 matches

by PeteOlcott
Mon Jun 29, 2020 4:30 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V15

1. You ignored the first question. 2. I asked "what is proof?" not "what is a formal system?". Regardless, what is a finite string input and output other than a tautology where one thing is expressed under a new variation as a string of truth values? The formal proof in such a formal system would s...
by PeteOlcott
Sun Jun 28, 2020 7:53 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V15

1. Does your system requires P=P as a foundational axiom? 2. Define "proof". The most generic example of a formal system is finite string input produces Boolean output indicating that a decision has been made. 1. You ignored the first question. 2. I asked "what is proof?" not "what is a formal syst...
by PeteOlcott
Sun Jun 28, 2020 7:37 am
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V15

Each respective framework needs to be defined by a framework beyond it for the isomorphism to occur. Dually each framework needs to be assumed. In each framework, P and Q, the Munchauseen trillema occurs. P=P and Q=Q is not only circular but each assertion is assumed. Third, each framework both as ...
by PeteOlcott
Sun Jun 28, 2020 12:46 am
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V15

Each respective framework needs to be defined by a framework beyond it for the isomorphism to occur. Dually each framework needs to be assumed. In each framework, P and Q, the Munchauseen trillema occurs. P=P and Q=Q is not only circular but each assertion is assumed. Third, each framework both as ...
by PeteOlcott
Sun Jun 28, 2020 12:17 am
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V15

You would have to then defined soundness by an outside framework which is unsound. For soundness to describe proof would require proof to describe soundness and a circularity occurs. This circularity expands when you add in "incompleteness". Within the isomorphism between formal proofs and valid de...
by PeteOlcott
Sat Jun 27, 2020 11:45 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V15

You would have to then defined soundness by an outside framework which is unsound. For soundness to describe proof would require proof to describe soundness and a circularity occurs. This circularity expands when you add in "incompleteness". Within the isomorphism between formal proofs and valid de...
by PeteOlcott
Sat Jun 27, 2020 10:59 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness and Tarski Undefinability away V15
Replies: 14
Views: 475

Simply defining Gödel Incompleteness and Tarski Undefinability away V15

Defining Gödel Incompleteness Away We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of ...
by PeteOlcott
Mon Jun 22, 2020 10:25 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

For physically existing things that are a measurable distance apart you can simply count them, if you count above one then you have distinct things. For conceptually existing things if they have an identical set of properties then you really only have one thing with two different words pointing to ...
by PeteOlcott
Mon Jun 22, 2020 8:53 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

If two distinctly different things have all of their properties identical then is was a mistake to call these two distinctly different things. You aren't fucking hearing a word of what I am saying. Either you have TWO things; or you have ONE thing. FIRST you have to decide HOW MANY THINGS you have ...
by PeteOlcott
Mon Jun 22, 2020 8:24 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

Yes and that justifies "the identify of indiscernibles": This is often referred to as ‘Leibniz's Law’ and is typically understood to mean that no two objects have exactly the same properties. It doesn't justify anything. You are stuck in a tautology. Even if TWO objects had exactly the same propert...
by PeteOlcott
Mon Jun 22, 2020 7:46 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

"If you have TWO DIFFERENT ENTITIES which are identical with respect to all their properties" then that already includes that their spacetime properties are also identical, therefore "The identify of indiscernibles contradicts itself." is false. Pete, either you have TWO THINGS e.g objects with dif...
by PeteOlcott
Mon Jun 22, 2020 7:31 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. https://en.wikipedia.org/wiki/Identity_of_indiscernibles Likewise two separate objects are distinguished as separate objects on the basi...
by PeteOlcott
Mon Jun 22, 2020 6:02 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. https://en.wikipedia.org/wiki/Identity_of_indiscernibles Likewise two separate objects are distinguished as separate objects on the basi...
by PeteOlcott
Mon Jun 22, 2020 5:58 pm
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

There is no object or identity which holds all the same properties in common thus the principle is useless. You are contradicting yourself. Previously you said: "Goats are dump trucks" now you are saying: "There is no object or identity which holds all the same properties" nothing is the same as an...
by PeteOlcott
Mon Jun 22, 2020 3:40 am
Forum: Logic and Philosophy of Mathematics
Topic: Simply defining Gödel Incompleteness away V8
Replies: 38
Views: 774

Re: Simply defining Gödel Incompleteness away V8

False, both goat and dump truck share the same property of material carrying or removal (dump truck carries x and goat carries what it consumes). Both seemingling different contexts share a context which equates. It is called a middle term. There is no context which is completely equal to another c...