It is illogical to severe empiricism from rationalism, or to think of them as opposing views. Making an observation entails using your eyes and brain - making sense of what it is that you are looking at. It is one process, not two separate ones that can be done without the other. — Harry Hindu

Well, in Critique of Pure Reason, Immanuel Kant pointed out the existence of a type of knowledge that is not empirical. It is synthetic a priori. At the same time, he rejected classical Greek geometry as NOT being synthetic a priori, because it is highly visual, as it is an exercise in fiddling with visual puzzles.

In the meanwhile, mathematics has changed. It has migrated from visual fiddling to pure symbol manipulation. Nowadays, its essence is language only. We no longer follow visual procedures in mathematics.

Therefore, I disagree with relying on empiricism in mathematics. The progress in mathematics in the last few centuries has only been possible by removing its dependence on visual input. Mathematics has now finally become pure reason only.

Like I said, you weren't born knowing 3+0=3 because you needed to observe this rule in order to know there is a rule and then observe how such a rule is useful in the world. The rule itself stems from our own observations of individual things and the need to quantify those individual things that share similarities. So these "axiomatic" domains themselves require at least two observations - one to learn the rule and the other to learn what the rule is for. — Harry Hindu

For a starters, we simply end up cutting off the real-world origins of mathematical theories, if there were any to begin with:

Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.[1][2][3][4] — Wikipedia on abstraction in mathematics

Secondly, quite a bit of mathematics does not have a real-world origin. For example, where in nature can you find something like look-ahead left-right parsers? Where in nature can you find Turing machines? Von Neumann machines?

These things are abstraction only. They started studying them in mathematics because these at first imaginary devices were potentially useful for computing. If they had limited themselves to what is readily visible in the surrounding universe, we would simply never have had computers. Nature does not have them to begin with.

I other words, it doesn't qualify as software. If it doesn't execute, or do anything, then the programmer didn't follow the rules for writing a program in that particular language. It's merely observable scribbles on a screen. — Harry Hindu

Well, for example, even C/C++ header files contain mostly definitions that are not even meant to ever execute. For example, what is chromium/base/barrier_closure.h supposed to do? Even the source code of something like a web browser such as Google Chrome contains seemingly absurd abstractions that are concept heavy while being low on actual code to execute. In other words, it is not even meant to do anything. It just structures things in one way or another ...

In other words, how would you arrive by computation to possibly the only certain epistemological and ontological true statement: “I think, therefore I know I exist”?

Also, is that realization a thought or a feeling, cognition or intuition? Is it maybe bound to language? And if it is, perhaps by acquiring an understanding of some language, then the logic of such sentence automatically becomes self-evident?

So, how to make an algorithm “understand”, and then to understand words like “I”, “know”, or “exist”? But, what “to understand” actually means? And even before that, what the word “means” really means?

On closer inspection the relation between computation and epistemology seems to be more like the relation between a certain fact and complete mystery.

In practice, a "non-computable" process, that is to say a truly random process, is indistinguishable from an unknown pseudo-random process, since we can only ever observe a finite number of observations generated by an unknown process. For the unknown process to be declared as 'truly random' it can never terminate and it must pass an infinite number of tests that refute each and every conceivable Turing computable algorithm that could have generated it.


The practical impossibility of distinguishing an unknown pseudo-random process from a really random process provides us with ammunition for rejecting an absolute ontological distinction between randomness and lawfulness. In which case, the question as to whether nature is computable or not is meaningless.

Instead we need only invoke a game-theoretic distinction between a controlled process referring to a process we create and control ourselves using an algorithm, versus an uncontrolled process that is part of nature that we only query and make speculative computer models of.

Perhaps you confuse being true with being justified. There are obvious empirical truths - such as that you are reading this post. — Banno

Try solipsisism or syllopsysosm. I can't spell the danged thing, but I know what it is.

Try that. That refutes the entire truth value of observation.

If that won't convince you that I was right, then try the thought that everything you know, and stored as memory, both conscious and unconscious, and both subconscious and super-conscious, in fact your entire life experience and life just started a minute ago. Or this instant. There is no proof for this, but it is conceivable.

Under these two possible considerations empirical truths are shmafu. Only a priori truths can exist for a 100 percent degree certainty in any possible arrangement of the physical world.

Well, in Critique of Pure Reason, Immanuel Kant pointed out the existence of a type of knowledge that is not empirical. It is synthetic a priori. At the same time, he rejected classical Greek geometry as NOT being synthetic a priori, because it is highly visual, as it is an exercise in fiddling with visual puzzles. — alcontali

Ay-vey, Immanuel. Just because you can see it, it does not mean it can't be a priori existant. What a narrow-minded little block-head that Immanuel was. Or square head. Or take your choice of synthetic a priori geometrical shape, and apply it to Immanuel Kant's head shape. You can't lose.

And yet we know of unprovable truths. (IN mathematics - ed.)

Epistemology is broader than computability. — Banno

the only unprovable truths I know about math are its axioms and its axiomatic behaviour. (Such as 2+7=4.) Do they, the axioms of math, qualify as being outside of computability? I hardly think so, but I actually can't decide that.

Ay-vey, Immanuel. Just because you can see it, it does not mean it can't be a priori existant. What a narrow-minded little block-head that Immanuel was. Or square head. Or take your choice of synthetic a priori geometrical shape, and apply it to Immanuel Kant's head shape. You can't lose. — god must be atheist

Even though I very much appreciate Immanuel Kant's Critique of Pure Reason, I am still not one of his cheerleaders. On the one side, Kant says that pure mathematics has the potential for being pure reason:

Mathematics gives us a shining example of how far, independently of experience, we can
progress in a priori knowledge.

If this be demurred to, I am willing to limit my statement to pure mathematics, the very concept of which implies that it does not contain empirical, but only pure a priori knowledge.

Mathematics presents the most splendid example of the successful extension of pure reason, without the help of experience. — Kant in Critique of Pure Reason on mathematics

But Kant denies that the visual puzzles in classical Greek geometry are pure reason:

The mathematician meets this demand by the construction of a figure, which, although produced a priori, is an appearance present to the senses ... but their employment and their relation to their professed objects can in the end be sought nowhere but in experience, of whose possibility they contain the formal conditions. — Kant on geometry and its visual puzzles

At some point, Kant engages in infinite regress by demanding a justification for the axioms in mathematics from "transcendental philosophy". Of course, that will never work:

In the Analytic I have indeed introduced some axioms of intuition into the table of the principles of pure understanding ... For the possibility of mathematics must itself be demonstrated in transcendental philosophy. Philosophy has therefore no axioms, and may never prescribe its a priori. — Kant demanding a justification for axioms

Kant believes in metaphysics, i.e. in infinite regress, while I absolutely don't:

Now if in the speculative employment of pure reason there are no dogmas, to serve as its special subject-matter, 1 all dogmatic methods, whether borrowed from the mathematician or specially invented, are as such inappropriate. All knowledge arising out of reason is derived either from concepts or from the construction of concepts. The former is called philosophical, the latter mathematical. — Kant insisting on dogma-less views, i.e. insisting on infinite regress

Since its very beginning, 2500 years ago, metaphysics has never produced anything of value or anything actually worth knowing. The reason for that, is, that the method of infinite regress is faulty. It literally leads to nowhere.

Well, in Critique of Pure Reason, Immanuel Kant pointed out the existence of a type of knowledge that is not empirical. It is synthetic a priori. At the same time, he rejected classical Greek geometry as NOT being synthetic a priori, because it is highly visual, as it is an exercise in fiddling with visual puzzles. — alcontali

We are visual creatures. We think in mostly visual forms. Our thoughts have form and those forms are the same as all of the sensory impressions we are capable experiencing. Mathematics is just different puzzles using different visual scribbles.

In the meanwhile, mathematics has changed. It has migrated from visual fiddling to pure symbol manipulation. Nowadays, its essence is language only. We no longer follow visual procedures in mathematics. — alcontali

It hasn't changed. Languages are visual scribbles and sounds. If the procedures you follow aren't visual, then how do you know you're following a procedure? What form does your mathematical procedure take? How would you describe the experience of performing a mathematical procedure? In describing it you will be using visual scribbles on a screen to reference the visuals in your head. If you say the experience is more like talking it out - talking to yourself in your mind, then it is taking an auditory form rather than a visual form. It seems to me that you are saying that mathematics is done unconsciously.

Therefore, I disagree with relying on empiricism in mathematics. The progress in mathematics in the last few centuries has only been possible by removing its dependence on visual input. Mathematics has now finally become pure reason only. — alcontali

I don't know what pure reason is unless it takes some form for me to know that I am engaged in pure reasoning. How do you know that you are engaged in pure reason as opposed to relying on empiricism if they both don't appear differently to you in your mind - visually.

Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.[1][2][3][4] — Wikipedia on abstraction in mathematics

What form do these underlying structures, patterns, properties, phenomena take? Structure, pattern, phenomena and properties are all visual terms.

Secondly, quite a bit of mathematics does not have a real-world origin. For example, where in nature can you find something like look-ahead left-right parsers? Where in nature can you find Turing machines? Von Neumann machines?

These things are abstraction only. They started studying them in mathematics because these at first imaginary devices were potentially useful for computing. If they had limited themselves to what is readily visible in the surrounding universe, we would simply never have had computers. Nature does not have them to begin with. — alcontali

Well, I don't see humans, or their inventions, as being separate from nature. So abstractions are natural products of our minds and our minds are products of natural selection (evolutionary psychology and computational theory of mind). Our minds are the software and our bodies are the hardware. The computer is the best analogy for the mind that we've had in our history of thinking about the mind and its relationship with the world.

Well, for example, even C/C++ header files contain mostly definitions that are not even meant to ever execute. For example, what is chromium/base/barrier_closure.h supposed to do? Even the source code of something like a web browser such as Google Chrome contains seemingly absurd abstractions that are concept heavy while being low on actual code to execute. In other words, it is not even meant to do anything. It just structures things in one way or another ... — alcontali

Definitions are not executed. Functions are executed and reference those definitions. No programmer would put code that isn't used somewhere in the program as code takes up memory. It would be a waste of memory space and programmers try their best to streamline their code so that it runs efficiently and isn't a memory hog. Any other "code" that isn't executed would be remarks for us humans to be able to understand what the code is used for.

f the procedures you follow aren't visual, then how do you know you're following a procedure? What form does your mathematical procedure take? How would you describe the experience of performing a mathematical procedure? — Harry Hindu

By visual procedures, I mean a procedure in which the use of circles, lines, triangles, polygons, graphs, and similar visual representations are essential. Nowadays, only the algebraic symbol manipulations are essential. Mathematics is now essentially language only. For example, you do not need to create any drawing to solve the roots of a quadratic equation. In fact, that was the first non-visual, language-only procedure that appeared in the Middle Ages, in the Liber Algebrae by Algorithmi. Nowadays, mathematics has completely algebraized, including geometry.

In describing it you will be using visual scribbles on a screen to reference the visuals in your head. — Harry Hindu

You can represent language visually with written letters but you can also represent it verbally with sounds. You cannot do that with a line, triangle, circle, or polygon. In algebra, the visual aspect is not essential.

What form do these underlying structures, patterns, properties, phenomena take? Structure, pattern, phenomena and properties are all visual terms. — Harry Hindu

Their canonical description is in language only; while language is not necessarily visual. Language also has an isomorphic auditory representation. Language is not considered an empirical input.

By visual procedures, I mean a procedure in which the use of circles, lines, triangles, polygons, graphs, and similar visual representations are essential. Nowadays, only the algebraic symbol manipulations are essential. Mathematics is now essentially language only. For example, you do not need to create any drawing to solve the roots of a quadratic equation. In fact, that was the first non-visual, language-only procedure that appeared in the Middle Ages, in the Liber Algebrae by Algorithmi. Nowadays, mathematics has completely algebraized, including geometry. — alcontali

:confused:
And algebraic symbols have curves and circles and lines. 6 + 0 = 6

You draw the symbols on paper, or repeat them with auditory symbols in your head. The spoken word, "six" is the same as the visual 6. How is it that we can represent the same idea with two different empirical forms?

In fact, that was the first non-visual, language-only procedure that appeared in the Middle Ages, in the Liber Algebrae by Algorithmi. Nowadays, mathematics has completely algebraized, including geometry. — alcontali

How did we learn that "the first non-visual, language-only procedure that appeared in the Middle Ages, in the Liber Algebrae by Algorithmi" if we didn't see it written out on paper? When I ask you for evidence for your claim, how would you show it?

You can represent language visually with written letters but you can also represent it verbally with sounds. You cannot do that with a line, triangle, circle, or polygon. In algebra, the visual aspect is not essential. — alcontali

Their canonical description is in language only; while language is not necessarily visual. Language also has an isomorphic auditory representation. Language is not considered an empirical input. — alcontali

I already pointed this out. Auditory forms are still empirical forms. Language and math take the form of visual or auditory symbols. How did you learn your native language without eyes and ears, or tactile sensations if you are blind? How do you use language without making sounds or visual scribbles?

It seems to me that you are saying that mathematics is done unconsciously. — Harry Hindu

Do you turn into a p-zombie when you perform mathematical calculations in your head?

And algebraic symbols have curves and circles and lines. — Harry Hindu

Language-only communication also uses visual representations but of text and symbols only. It is not considered empirical input.

The computer is the best analogy for the mind that we've had in our history of thinking about the mind and its relationship with the world .

Yes, but what is computer without display screen? All the electrons moving around electronic components is like electrochemical signaling in our brains. Information without inherent meaning, something that needs to be decoded or integrated in some way, at some place where it all comes together to form subjective experience or qualia - that parallel to a computer screen which displays the mental content and at the same time perceives it, somehow.

The problem with computers is that it is all mechanical actually, in a sense that in principle you could make a PC powered on water instead of electric current and replace electronic components with wooden contraptions to produce the same kind of computation. Imagining this computer makes it more obvious why many say it is impossible computation could ever explain mind phenomena such as subjective experience and mental content.

Yes, but what is computer without display screen? — Zelebg

A server. They run the Internet. This website runs on a server in some datacenter. There's no display connected to it. When the IT folks need to access it they log in remotely over the network.

Haven't followed the discussion but just happened to notice this. Computers without display screens are extremely common.

Language-only communication also uses visual representations but of text and symbols only. It is not considered empirical input. — alcontali

You're not reading my entire post. I asked how you learned and use language without using your eyes and ears. When you read instructions on how to assemble your new bicycle, you use your eyes and the instructions are the input and your actions in assembling the bicycle is the output.

Try reading the rest of my post (the input) with your eyes closed, and then reply (the output) with your eyes closed.


















Betelgeuse will go supernova in 2 years and obliterate the Earth.

You can't escape being both empirical and rational in using language or mathematics.

Yes, but what is computer without display screen? — Zelebg

A server.

A display screen is only one type of output that a computer can use. They can also produce sound, printing on paper, 3-D printing, tactile sensations in VR gloves, etc. As long as you have an electronic device processing information (input to output), you have a type of computer.

All the electrons moving around electronic components is like electrochemical signaling in our brains. Information without inherent meaning, something that needs to be decoded or integrated in some way, at some place where it all comes together to form subjective experience or qualia - that parallel to a computer screen which displays the mental content and at the same time perceives it, somehow. — Zelebg

Yes, but what is looking at the computer screen in your brain? This is the infinite regress of the homoculus in your head - the cartesian theater. There is no screen being looked at. There is only the working of your short-term memory. That is what consciousness is - this work getting done of processing information coming in through the senses and producing output with your intent and actions.

The problem with computers is that it is all mechanical actually, in a sense that in principle you could make a PC powered on water instead of electric current and replace electronic components with wooden contraptions to produce the same kind of computation. Imagining this computer makes it more obvious why many say it is impossible computation could ever explain mind phenomena such as subjective experience and mental content. — Zelebg

This is more along the lines of direct realism vs. indirect realism. Is it brains "out there", or minds? When I look at you, I see a physical body, not a subjective experience. When I look at myself, I don't just see a body. I experience a body. There is this "subjective experience" - my mind. Is the world like my mind, or like bodies (mental or physical)? Are brains just how minds simulate other minds? I don't like to say what idealists say, and say that everything is mind. Everything is mind-like, or of the same "substance" as mind. But to say that everything is mind, or conscious, would be anthropomorphic. I think a better term would be "information". Not physical or mental. Physical and mental is a false dichotomy that leads to dualism. Everything is information.

A server.

“Computer without monitor” was a metaphor, and the point is that when we look at the brain we see input and processing, but not where or what the result and "output" is.

So again, to understand qualia and mental content, analogy between mind and computer is not complete until we discover a thing that is analogous to computer output, such as display screen, for example.

I think a better term would be "information". Not physical or mental. Physical and mental is a false dichotomy that leads to dualism. Everything is information.

Words refer to things, and that is exactly what the word “physical” and “mental” differentiate - actual things from their abstract representations.

Information carries no inherent meaning, it needs a context or decoding against or within which it can be understood or perceived.

I asked how you learned and use language without using your eyes and ears. — Harry Hindu

So? That does not mean that language can only be used to describe the physical universe. It can also be used to describe imaginary universes. You can use language to write science fiction. You can use language to describe an idea for something that does not exist yet. Your eyes never saw it. Your ears never heard it.

You're not reading my entire post. — Harry Hindu

I don't see how it demonstrates that language would be an empirical input. I reject that point of view.

So? That does not mean that language can only be used to describe the physical universe. It can also be used to describe imaginary universes. You can use language to write science fiction. You can use language to describe an idea for something that does not exist yet. Your eyes never saw it. Your ears never heard it. — alcontali

Are you being purposely obtuse?

I'm not talking about what the words are about. I'm talking about the words themselves. You would never know about those imaginary universes if you didn't have eyes to see the scribbles in the paperback sci-fi novel, or ears to hear a reader read the scribbles.

“Computer without monitor” was a metaphor, and the point is that when we look at the brain we see input and processing, but not where or what the result and "output" is.

So again, to understand qualia and mental content, analogy between mind and computer is not complete until we discover a thing that is analogous to computer output, such as display screen, for example. — Zelebg

Of course we see the output. They are the nerve signals that get sent to the limbs to take action, or to the mouth to speak, etc. I did say that the output was our intent and actions.

Words refer to things, and that is exactly what the word “physical” and “mental” differentiate - actual things from their abstract representations.

Information carries no inherent meaning, it needs a context or decoding against or within which it can be understood or perceived. — Zelebg

Words can refer to imaginary things or illusions. Does "god" refer to something? I think you'll find a lot of disagreement about whether it does or not.

What do you mean by "physical" and "mental"?

Information is meaning. It is the relationship between causes and their effects. Effects carry information/meaning about their causes.

Of course we see the output. They are the nerve signals that get sent to the limbs to take action, or to the mouth to speak, etc. I did say that the output was our intent and actions.

Obviously the output I was talking about is qualia.

Words can refer to imaginary things or illusions.

Yes, and in that case it’s the other way around - mental or abstract existence of ideas is actual, while their representations can become physical.

What do you mean by "physical" and "mental"?

What I said. https://www.merriam-webster.com/

Information is meaning.

Certainly not. https://www.merriam-webster.com/

I'm not talking about what the words are about. I'm talking about the words themselves. You would never know about those imaginary universes if you didn't have eyes to see the scribbles in the paperback sci-fi novel, or ears to hear a reader read the scribbles. — Harry Hindu

That is not sure at all. People who are blind and/or deaf, still think. Sensory input is not a requirement for thought.

Obviously the output I was talking about is qualia. — Zelebg

Qualia is not output. It's the input.

Yes, and in that case it’s the other way around - mental or abstract existence of ideas is actual, while their representations can become physical. — Zelebg

I have no idea what this means.

Your links are imply that I should be looking these trends up in a dictionary. I'm contesting those definitions. Why don't you provide some good reasons for continuing to use these philosophically antiquated terms.

That is not sure at all. People who are blind and/or deaf, still think. Sensory input is not a requirement for thought — alcontali

Then what form do their, and your, thoughts take? How do you know you're thinking?

Then what form do their, and your, thoughts take? How do you know you're thinking? — Harry Hindu

Computers do not require empirical input either.

You could learn how to accept a text stream, character by character, through a device that makes a short stroke on your palm to represent a zero, and a long stroke for a one. Every collection of six strokes represent one 6-bit character in base64. That would be your input. Next, you can output what you thought about the input by moving your index finger on a touchpad to produce short and long strokes. The process would be slow, but it would work absolutely fine. No vision nor sound needed.

Stop avoiding the question.

Then what form do their, and your, thoughts take? How do you know you're thinking? — Harry Hindu

I already pointed out that blind people use braille to feel the words. The tactile sensations are empirical and are the input.

The tactile sensations are empirical and are the input. — Harry Hindu

A priori knowledge or justification is independent of experience (for example "All bachelors are unmarried"), whereas a posteriori knowledge or justification is dependent on experience or empirical evidence (for example "Some bachelors are very happy"). The notion that the distinction between a posteriori and a priori is tantamount to the distinction between empirical and non-empirical knowledge comes from Kant's Critique of Pure Reason.[3] — Wikipedia on empirical evidence

If the fact that knowledge is transmitted through sound, vision, or tactile sensations makes it empirical, then non-empirical knowledge cannot exist. I do not subscribe to that kind of view. I prefer to use Kant's characterization of knowledge.

If the fact that knowledge is transmitted through sound, vision, or tactile sensations makes it empirical, then non-empirical knowledge cannot exist. I do not subscribe to that kind of view. I prefer to use Kant's characterization of knowledge. — alcontali

Of course you do, because you keep avoiding this question:

Then what form do their, and your, thoughts take? How do you know you're thinking? — Harry Hindu

What form does "All bachelors are unmarried" take in your mind? How do you know that you're thinking it? Is it just hearing the words in your mind, seeing the words in your mind, or seeing images of bachelor's and married men? You seem to be saying that you were born knowing "All bachelors are unmarried".

What form does "All bachelors are unmarried" take in your mind? How do you know that you're thinking it? Is it just hearing the words in your mind, seeing the words in your mind, or seeing images of bachelor's and married men? You seem to be saying that you were born knowing "All bachelors are unmarried". — Harry Hindu

The common understanding is as following:

Empirical evidence may be synonymous with the outcome of an experiment. In this regard, an empirical result is a unified confirmation. In this context, the term semi-empirical is used for qualifying theoretical methods that use, in part, basic axioms or postulated scientific laws and experimental results. Such methods are opposed to theoretical ab initio methods, which are purely deductive and based on first principles. — Wikipedia on the distinction between empirical and ab initio

You are questioning the validity of very, very basic epistemic principles. I really do not see what you want to achieve by doing that. Frankly, I do not think that it will lead anywhere.

No, I'm not. I'm simply asking you a direct question that you should be asking yourself, but you are unwilling. I'm asking it because it I need to know if you're a human being, bot, or p-zombie.

What form does the thought, All bachelors are unmarried, take in your mind? How do you know when you are thinking it and when you aren't?

What form does the thought, All bachelors are unmarried, take in your mind? How do you know when you are thinking it and when you aren't? — Harry Hindu

It wasn't my example by the way. I was just quoting from a canonical text. You are questioning and rejecting very basic principles in epistemology. That is ok, but I am not the right person to make useful comments in that regard. For once, I am actually happy with the mainstream beliefs in this matter.