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### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 12:03 am**

by **Univalence**

PeteOlcott wrote: ↑Tue May 14, 2019 11:56 pm
All that I am saying is that whenever you transmit anything from one place to another place that (by definition) it actually gets to that other place.

And I am pointing out that your definition is incomplete and does not describe all that actually happens in practice.

It omits details which renders your conclusion approximately true, but precisely - false. It's called

model error.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 12:48 am**

by **PeteOlcott**

Univalence wrote: ↑Wed May 15, 2019 12:03 am
PeteOlcott wrote: ↑Tue May 14, 2019 11:56 pm
All that I am saying is that whenever you transmit anything from one place to another place that (by definition) it actually gets to that other place.

And I am pointing out that your definition is incomplete and does not describe all that actually happens in practice.

It omits details which renders your conclusion approximately true, but precisely - false. It's called

model error.

Ah so you are unable to distinguish the difference between a stochastic process and deterministic one. In other words you don't know the difference between induction and deduction. Not knowing these key distinctions is the reason for the title of this thread. Only people that already understand formal proofs of mathematical logic as per Mendelson, will be able to understand what I am saying.

When the premises of any conventional (Mendelson) formal proof of mathematical logic are true the consequence of this same proof is necessarily true.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 12:57 am**

by **Univalence**

PeteOlcott wrote: ↑Wed May 15, 2019 12:48 am
Ah so you are unable to distinguish the difference between a stochastic process and deterministic one. In other words you don't know the difference between induction and deduction. Not knowing these key distinctions is the reason for the title of this thread.

Another argument from ignorance.

What you seem to be unaware of is the fact that you live in a stochastic, not a deterministic universe.

End even if it were deterministic, to somebody with incomplete knowledge it appears stochastic either way.

Using deterministic models in a stochastic universe is precisely the Ludic fallacy I pointed out.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 1:13 am**

by **PeteOlcott**

Univalence wrote: ↑Wed May 15, 2019 12:57 am
PeteOlcott wrote: ↑Wed May 15, 2019 12:48 am
Ah so you are unable to distinguish the difference between a stochastic process and deterministic one. In other words you don't know the difference between induction and deduction. Not knowing these key distinctions is the reason for the title of this thread.

Another argument from ignorance.

What you seem to be unaware of is the fact that you live in a stochastic, not a deterministic universe.

End even if it were deterministic, to somebody with incomplete knowledge it appears stochastic either way.

Using deduction in an inductive context is precisely the Ludic fallacy I pointed out.

I was not ever referring to any inductive context. Godel does not say that his G is not provable some of the time. His claim is that G is never provable this is not any sort of stochastic claim or inductive context.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 1:16 am**

by **Univalence**

PeteOlcott wrote: ↑Wed May 15, 2019 1:13 am
I was not ever referring to any inductive context. Godel does not say that his G is not provable some of the time. His claim is that G is never provable this is not any sort of stochastic claim.

Godel was talking about formal/axiomatic systems. You were talking about pouring 8 ounces of water from one cup into another.

The one is an abstract context. The other is a context in which the laws of physics apply.

The one is subject to formalism. The other is subject to empiricism.

The one is a closed system. The other is an open system.

The one is deterministic. The other is stochastic.

Can you even tell which is which?

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 1:24 am**

by **PeteOlcott**

PeteOlcott wrote: ↑Wed May 15, 2019 1:13 am
Univalence wrote: ↑Wed May 15, 2019 12:57 am
PeteOlcott wrote: ↑Wed May 15, 2019 12:48 am
Ah so you are unable to distinguish the difference between a stochastic process and deterministic one. In other words you don't know the difference between induction and deduction. Not knowing these key distinctions is the reason for the title of this thread.

Another argument from ignorance.

What you seem to be unaware of is the fact that you live in a stochastic, not a deterministic universe.

End even if it were deterministic, to somebody with incomplete knowledge it appears stochastic either way.

Using deduction in an inductive context is precisely the Ludic fallacy I pointed out.

I was not ever referring to any inductive context. Godel does not say that his G is not provable some of the time. His claim is that G is never provable this is not any sort of stochastic claim or inductive context.

I only used that as an example because you were refusing to acknowledge the sound deductive inference model. I have actually only been talking about the subset of conventional formal proofs having a sets of entirely true premises. All of these have necessarily true consequences. You didn't seem to grasp that.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 1:26 am**

by **Univalence**

PeteOlcott wrote: ↑Wed May 15, 2019 1:24 am
I only used that as an example because you were refusing to acknowledge the sound deductive inference model. I have actually only been talking about the subset of conventional formal proofs having a sets of entirely true premises. All of these have necessarily true consequences. You didn't seem to grasp that.

I have acknowledged it as being just that - a model.

All models are wrong.
Knowing when to use a particular model, and more importantly - when not to use it. That's not something you seem to grasp.

You also fail to grasp why using a deterministic model in a stochastic domain leads to conclusions which are not "necessarily true".

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 1:50 am**

by **PeteOlcott**

Univalence wrote: ↑Wed May 15, 2019 1:26 am
PeteOlcott wrote: ↑Wed May 15, 2019 1:24 am
I only used that as an example because you were refusing to acknowledge the sound deductive inference model. I have actually only been talking about the subset of conventional formal proofs having a sets of entirely true premises. All of these have necessarily true consequences. You didn't seem to grasp that.

I have acknowledged it. It's exactly that - a model. All models are wrong.

Knowing when to use a particular model, and more importantly - when not to use it. That's not something you seem to grasp.

You also fail to grasp why using a deterministic model in a stochastic domain leads to conclusions which are not "necessarily true".

I always make sure to make it clear that I am never ever referring to anything besides deductive inference because I am accutely aware of the limitations of the problem of induction. I am only referring to those things that can be known to be certainly true entirely on the basis of the meaning of their words.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 1:53 am**

by **Univalence**

PeteOlcott wrote: ↑Wed May 15, 2019 1:50 am
I always make sure to make it clear that I am never ever referring to anything besides deductive inference.

Yet you keep committing the Ludic fallacy by blurring the lines between the world of games (formal systems) and reality.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 2:00 am**

by **PeteOlcott**

Univalence wrote: ↑Wed May 15, 2019 1:53 am
PeteOlcott wrote: ↑Wed May 15, 2019 1:50 am
I always make sure to make it clear that I am never ever referring to anything besides deductive inference.

Yet you keep committing the Ludic fallacy by blurring the lines between the world of games (formal systems) and reality.

Univalence wrote: ↑Wed May 15, 2019 1:53 am
PeteOlcott wrote: ↑Wed May 15, 2019 1:50 am
I always make sure to make it clear that I am never ever referring to anything besides deductive inference.

Yet you keep committing the Ludic fallacy by blurring the lines between the world of games (formal systems) and reality.

I have never ever been talking about reality (a continuous stream of physical sensations). I have only been talking about truth (a set of interconnected semantic tautologies).

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 2:11 am**

by **Univalence**

PeteOlcott wrote: ↑Wed May 15, 2019 2:00 am
I have only been talking about truth (a set of interconnected semantic tautologies).

And I already pointed you to Quine's argument demonstrating the circularity of analytic truths.

Tautologies contain zero bits of information and trivialise the notion of truth.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 2:20 am**

by **PeteOlcott**

Univalence wrote: ↑Wed May 15, 2019 2:11 am
PeteOlcott wrote: ↑Wed May 15, 2019 2:00 am
I have only been talking about truth (a set of interconnected semantic tautologies).

And I already pointed you to Quine's argument demonstrating the circularity of analytic truths.

Tautologies contain zero bits of information.

I looked it up Quine's view is simply incoherent. The set of knowledge is an acyclic (not cyclic) directed graph. This can be verified by graphing any part of it. Cycles are not any part of this graph. I created a whole formal language to show that the error of many paradoxes is cycles that are specified by their graphs, thus specifying these paradoxes to be infinitely recursive.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 2:33 am**

by **Univalence**

PeteOlcott wrote: ↑Wed May 15, 2019 2:20 am
This can be verified by graphing any part of it. Cycles are not any part of this graph.

I created a whole formal language to show that the error of many paradoxes is cycles that are specified by their graphs, thus specifying these paradoxes to be infinitely recursive.

Then how do you explain the

**bachelor ⇔ not-married** dipole?

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 3:30 am**

by **PeteOlcott**

Univalence wrote: ↑Wed May 15, 2019 2:33 am
PeteOlcott wrote: ↑Wed May 15, 2019 2:20 am
This can be verified by graphing any part of it. Cycles are not any part of this graph.

I created a whole formal language to show that the error of many paradoxes is cycles that are specified by their graphs, thus specifying these paradoxes to be infinitely recursive.

Then how do you explain the

**bachelor ⇔ not-married** dipole?

All of knowledge is organized as a directed acyclic graph inheritance hierarchy.

The otherwise meaningless finite string "bachelor" inherits its semantic meaning from its parent: Marital_Status Boolean.False.

The Cyc project has 700 labor years into this stuff over the last 34 calendar years.

### Re: Does anyone here actually understand formal proofs of mathematical logic?

Posted: **Wed May 15, 2019 4:12 am**

by **Scott Mayers**

PeteOlcott wrote: ↑Tue May 14, 2019 3:11 pm
http://liarparadox.org/Provable_Mendelson.pdf
Introduction to Mathematical logic Sixth edition Elliott Mendelson (2015) Page 27-28

**Introduction to Mathematical logic Sixth edition Elliott Mendelson (2015) Page 28 **
A wf C is said to be a consequence in S of a set Γ of wfs if and only if there is a

sequence B1, …, Bk of wfs such that C is Bk and, for each i, either Bi is an axiom

or Bi is in Γ, or Bi is a direct consequence by some rule of inference of some of

the preceding wfs in the sequence. Such a sequence is called a proof (or deduction)

of C from Γ. The members of Γ are called the hypotheses or premisses of the proof.

**We use Γ ⊢ C as an abbreviation for “C is a consequence of Γ”... **

Thank you. I'll have to look up this text to participate fairly. Were you still trying to disprove the Incompleteness theorems or is this something else?

This is a metalogic for proving some system closed closed on its domain and consistent among its axioms. It might be good to go step by step here to lay out what your ideal goal is (rather than 'lead' without others knowing what you are aiming for). I thought you intended to USE proofs within some system or other.