You are speaking a bunch of incoherent nonsense. Logical inference is just a simplification of proper Bayesian inference. There are no problems you can model with logic that can't be modeled by Bayesian logic. You just take a set of logical premises and set their probabilities to be 0 or 1.

But this is only an approximation, and is fundamentally wrong in principle for any real world problem. You can never be 100% certain of anything, even mathematical proofs. After all, errors are found in published mathematical proofs all the time. And people regularly make mistakes doing even simple arithmetic.

That's the thing, we live in an uncertain world and can never have true certainty about anything. Especially in most real world problems that we care about. All forms or reasoning and inference are part of the mind, not reality. Reality doesn't have to respect your axioms or logical inferences. At any time reality can bite back and say your logic was wrong. And you must change your map, not argue that the territory is incorrect.

Bayesian inference is the process of drawing maps of a territory. And realizing that they are just maps. That we can make more and more accurate maps, but we can never have maps that are 100% perfect and certain. Reality doesn't grant us certainty, and that's ok.

> There are no problems you can model with logic that can't be modeled by Bayesian logic.

"Socrates is a man, therefore Socrates is mortal". Please explain to us, speaking a bunch of incoherent nonsense, how Bayesian logic will prove the necessary "all men are mortal". Notice, that just saying "100% of a sample died" proves nothing. I am not asking about why the sun will rice in the east next morning.

> You can never be 100% certain of anything, even mathematical proofs.

This is some pseudo-intellectual hipster's bullshit, I am sorry to say. One can be 100% certain that DNA is the genetic material and bunch of other things, like for an external observer one and another one constitutes a structure - a pair and a pair introduces the notion of an ordering, etc. This is the good-enough basis of the DNA encoding, (and a Lisp). Notice, that the DNA encoding relies only on exact pattern matching on concrete physical structures - there are no numbers anywhere. The Mother Nature does not count. And this is logic, my friend.

Now take your canonical map-territory metaphor a bit further. The structure of a brain which makes mind possible, and all the other body's organs, of course, including an eye, reflects the physical environment it has been evolved within. A brain is an "implicit map" of the territory, it reflects what is, like a print, or using modern terminology a trained neural network.

The mind is bound by the brain and its sensory and evolutionary conditioning, which is bound by the environment (no matter what idealists, humanists and theologians would say). Everything the mind is capable of, including a valid reasoning (and excluding socially constructed bullshit and sectarian beliefs for a moment) is bound by the structure of the brain which is a representation of reality or so to speak a "map" of the territory. Consulting this map makes logic (and intuitions!) possible, the very same way a correctly trained model could give a reasonable predictions. It is just a form of pattern-matching.

This kind of map is more "valid" than any Bayesian map. There is no objection about uncertainty part as long as it refers to a process of "unfolding" of reality.

>"Socrates is a man, therefore Socrates is mortal". Please explain to us, speaking a bunch of incoherent nonsense, how Bayesian logic will prove the necessary "all men are mortal".

Exactly the same way regular logic does! You can have logical statements like "For all x, 'x is a man', implies 'x is mortal'". Bayesian logic doesn't take anything away from regular logic, it adds to it. It gives you the option of adding probabilities to statements. So you can do:

Socrates is a man, 99.999%

Men are mortal, 99%

->

Socrates is mortal, 98.99901%

>One can be 100% certain that DNA is the genetic material

No, you can't. Scientists could discover something completely different tomorrow. I'll grant you that it's very unlikely, but not literally impossible. It's a common mistake to confuse the two, but they are not the same.

>The Mother Nature does not count.

Take two apples, add two more apples, you have four apples. Nature definitely counts.

>The structure of a brain which makes mind possible, and all the other body's organs, of course, including an eye, reflects the physical environment it has been evolved within. A brain is an "implicit map" of the territory, it reflects what is, like a print, or using modern terminology a trained neural network.

I don't disagree. And what does this have to do with anything? The brain is (approximately) bayesian and weighs different probabilities. The brain is never 100% certain of anything. It can never know reality completely, just become a better map.

> Take two apples, add two more apples, you have four apples.

To whom? To other apples? Intelligent observer which is required to relate absolutely unrelated apples together is a most recent innovation. Atomic structures, to the contrary, are self-sufficient and could be matched without any observer whatsoever. Do you realize the subtle difference?

Molecular biology does not count, have no timers and obviously does not compute probabilities. It relies on pattern matching and message passing so to speak and feed back loops. It is an analog universe, like a clock.

One more time. There is no way to establish proper causation from​ mere observations without a proper rigorous scientific method. The whole human knowledge is based on this statement. Religions​ has been overthrown by it. This is the most important achievement of whole human philosophy. And Bayesians ​is just a sect. ;)

A friend of mine asked me to clarify a bit and to cut out my silly jokes.

The main question of Eastern philosophy (What is real? What is?) is way too far away from being answered adequately. One very old and very naive view is that nothing is real, everything is constructed by the mind. The question is - what is mental and what is real and how​ to get them apart.

Out of this comes a few simple notions, such that, while math and probabilities in particular could be used to produce a model of what is, nevertheless they cannot be the causes of phenomena because math and probabilities does not exist outside people's minds.

Of course there are certain physical constants - an angle between atoms in a water molecule, but there is no way a cell could measure it. It happens that other molecules assume certain positions in a water solution, but there is no notion of an angle anywhere. It requires an intelligent observer, which isn't here.

Same logic applies to numbers. Yes, of course, two apples and two apples would he be four apples, but there is no one to notice this at a molecular level. So, cells does not count. They pattern match, because it requires no observer and interpreter.

These notions could be generalised to a simple rule of thumb - do not try to establish causation with mere abstractions of the mind - they aren't here. Numbers, leave alone probabilities, are abstractions. Out of abstractions one construct simulations. But simulation is not reality the same way a map is not the territory.

Now about logic. It is a path from what is real to what is real, each step of which is validated by all the previous steps. It is a result of a domain-specific heuristic-guided search process, where a heuristic not choices the next step, but validates the current position by tracing it back to what is real.

Nothing much to see here. Just applied Eastern philosophy. To arrive at what is an observer with all his mental constructs has to be removed, similar to removal of the illusory self which obstructs reality. It is an ancient hack.

> Socrates is a man, 99.999% > Men are mortal, 99% > Socrates is mortal, 98.99901%

From where these numbers came from and why?