What is religion ?

[godelian]

My point was to answer to Godelian about natural religion, who believes (as i interpret it) that they do not make distinction between God and World. Actually they do.

My point is rather that the belief in an eternal physical universe is not a viable religious doctrine. According to Tennenbaum's theorem, arithmetic is not possible in such eternal physical universe. Computation does not work and therefore computers don't work either.

https://en.wikipedia.org/wiki/Natural_religion

Natural religion most frequently means the "religion of nature", in which God, the soul, spirits, and all objects of the supernatural are considered as part of nature and not separate from it. Conversely, it is also used in philosophy to describe some aspects of religion that are said to be knowable apart from divine revelation through logic and reason alone, for example, the existence of the unmoved Mover, the first cause of the universe.[1]

This "religion of nature" is unsustainable. Computations and computers don't work in this kind of "nature".

The model-theoretical signature of the universe implied by the "religion of nature", i.e. its set of non-logical symbols, contains a nonstandard number, i.e. an actual infinity. That is not our universe. It may be another universe that exists somewhere else, but it is not the universe that we live in.

[Skepdick]

When a person hallucinates 'something X' and claims there is "something X" which is very "real", the logic from that perspective is the the origin "incoming date" must be from that external something X or from somewhere external which is independent from the observer.

"Incoming" from where? "Originating" from where?

[Skepdick]

Well on the fact that things are distinguished for a purpose, I already realized it. On the fact that they are arbitrary distinguished, i disagree.

How is it non-arbitrary? You are "distinguishing" using collective nouns. That's not distinguishing - that's erasing distinctions.

[Skepdick]

What did you do then when you pointed out a purpose of distinction between religion and non religion as a tribal warfare, assuming it was mine or maybe a generic person designated by "you" ?

You gave indirectly a definition of religion, not yours I guess.

Where is this "definition"? I merely observed the act of distinguishing. The distinction criteria are unspecified.

People can draw the line wherever they feel like; and for whatever prupose they choose.
Or they can choose to erase the line.

Actually religion is a term that has a social use. this term is used to refer to distinct things.

It's not used to refer to distinct things. It's used to distinguish uniform things.

But I think that this category as it is usually understood cannot really be applied to all cultures. However, it is also considered as a universal anthropolgic category. My objective here is to note the fact that this category is lacking in the understanding of human cultures.

The category is ephermal and can be stretched to include everyone; or exclude everyone.

It depends on why you are drawing the line.

[Veritas Aequitas]

When a person hallucinates 'something X' and claims there is "something X" which is very "real", the logic from that perspective is the the origin "incoming data" must be from that external something X or from somewhere external which is independent from the observer.

"Incoming" from where? "Originating" from where?

When a person hallucinates 'something X' and claims there is "something X" which is very "real", the logic from that perspective is the the origin "incoming data" must be from that external something X or from somewhere external which is independent from the observer.

But the reality is the "incoming data" is from his self and not something that is absolutely independent from the hallucinator's self.

If we in the ordinary empirical world are also hallucinators of different degrees [normal humans] then the "incoming data" must be coming from us.

This obviously defies common sense but there must be something to it, else it would not an alternative to common and conventional sense.
How to understand it, that is another issue.

[godelian]

When a person hallucinates 'something X' and claims there is "something X" which is very "real", the logic from that perspective is the the origin "incoming date" must be from that external something X or from somewhere external which is independent from the observer.

This similar to the brain-in-the-vat thought-experiment.
In this case, there is a supposed 'incoming data' but the overall reality is grounded to the brain-in-the-vat.

In the case of humans, the origin of the incoming data of reality is somehow grounded to humans themselves. Somewhat circular but not fully.

It is just that humans cannot make an absolute claim there is an absolutely 100% certainty there is a human/mind independent reality; the most humans can claim is the human/mind independence is relative to the humans themselves.
This sort of skepticism and suspension of judgment is very rational and reasonable.

If we blindly surrender to an absolute claim there is an absolutely 100% certain human/mind independent reality, we open a pandora box to all sorts of irrational and delusional supernatural claims that lead to great evils as evident in the past and at present.

This claims the opposite of Plato's allegory of the cave, in which physical reality is deemed to be just a shadow of the truth.

Platonic realism is the dominant ontology in mathematics. Skepticism, i.e. antirealism, is not considered "rational and reasonable" but rather incompetent and untalented:

https://en.m.wikipedia.org/wiki/Philoso ... athematics

Kurt Gödel's Platonism[34] postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly.

If you are not able to see the abstract, Platonic world, it does not mean that it does not exist. It just means that you lack the talent and intuition to see it. Claiming skepticism is just a way to cope with one's incompetence.

Physicalism is popular with people who lack the capacity to abstraction. They cannot see abstract things and therefore they try to convince other people that these things do not exist. It is like claiming that a complicated formula must be wrong, simply because you do not understand it.

[Skepdick]

Platonic realism is the dominant ontology in mathematics. Skepticism, i.e. antirealism, is not considered "rational and reasonable" but rather incompetent and untalented:

https://en.m.wikipedia.org/wiki/Philoso ... athematics

Kurt Gödel's Platonism[34] postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly.

If you are not able to see the abstract, Platonic world, it does not mean that it does not exist. It just means that you lack the talent and intuition to see it. Claiming skepticism is just a way to cope with one's incompetence.

Here you go... https://philosophynow.org/issues/46/New ... aser_Sword

This pretty much does for Platonism as far as mathematicians are concerned. Axioms stopped being self-evident truths as soon as the work was read and understood. Instead they were simply postulates, and they might be interpreted as true statements about the world, perhaps in several different ways. Or they might not be interpreted at all. Platonism died for mathematicians some centuries ago, and simply looks silly. Mathematics doesn’t give truths, it gives consequences. The axiom of parallels is merely the postulate that the space in which we are working is flat. This tells us nothing about whether the space we live in really is flat – maybe it is and maybe it isn’t. We would need to find out by observation, and Gauss, who grasped the point immediately, suggested putting three telescopes on different mountain peaks and measuring the sum of the angles of the triangle so formed. If it came to 180 degrees, space was flat, at least up to the limits of accuracy of the measurements. If more, we lived in Riemannian space, if less then in a Lobachevskian space. Reason alone couldn’t possibly tell us which.

Maybe you want to catch up on developments in the last 60 years. Grothendieck universes and topological spaces would be a good start.

[Veritas Aequitas]

When a person hallucinates 'something X' and claims there is "something X" which is very "real", the logic from that perspective is the the origin "incoming date" must be from that external something X or from somewhere external which is independent from the observer.

This similar to the brain-in-the-vat thought-experiment.
In this case, there is a supposed 'incoming data' but the overall reality is grounded to the brain-in-the-vat.

In the case of humans, the origin of the incoming data of reality is somehow grounded to humans themselves. Somewhat circular but not fully.

It is just that humans cannot make an absolute claim there is an absolutely 100% certainty there is a human/mind independent reality; the most humans can claim is the human/mind independence is relative to the humans themselves.
This sort of skepticism and suspension of judgment is very rational and reasonable.

If we blindly surrender to an absolute claim there is an absolutely 100% certain human/mind independent reality, we open a pandora box to all sorts of irrational and delusional supernatural claims that lead to great evils as evident in the past and at present.

This claims the opposite of Plato's allegory of the cave, in which physical reality is deemed to be just a shadow of the truth.

Platonic realism is the dominant ontology in mathematics. Skepticism, i.e. antirealism, is not considered "rational and reasonable" but rather incompetent and untalented:

https://en.m.wikipedia.org/wiki/Philoso ... athematics

Kurt Gödel's Platonism[34] postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly.

If you are not able to see the abstract, Platonic world, it does not mean that it does not exist. It just means that you lack the talent and intuition to see it. Claiming skepticism is just a way to cope with one's incompetence.

Physicalism is popular with people who lack the capacity to abstraction. They cannot see abstract things and therefore they try to convince other people that these things do not exist. It is like claiming that a complicated formula must be wrong, simply because you do not understand it.

Do you know what are the limitation of abstraction?
In abstraction one is ignoring the real world of particulars and continuity but rather deal with polished universals which are unreal.
This is a matter of convenience and practicality in sacrificing reality.
This is driven by the faculty of pattern recognition to facilitate basic survival it is not effective for modern time and our awareness of greater complexities.

In observing a group of people,
you may conclude there are 10 men and 9 women on a universal basis based on direct observation.
This view may be sufficient for basic survival but it is really real in terms of particular?
In reality, some 'men' and 'women' may be of mixed gender with very fine distinction.
Some of the so called men may have XY Chromosomes, and some women has XX chromosomes. One or two may be hermaphrodites.
To be most realistic we should detain the complex details of each individual.

If you look at a forest and upon counting you may conclude there are 202 trees based on the concept of what is a tree.
But is that precisely real?

It is the same with all things which we ignore the particularity of each thing.
In addition we sacrifice continuity for discreteness.

My point is that we should NOT focus on merely one aspect, i.e. abstraction, but understand both views while taking into account their limitations.

For your focus on abstractions, you are too focused in falsehoods in a way and ignoring what is really real, i.e. the particularity in continuity.

[godelian]

Maybe you want to catch up on developments in the last 60 years. Grothendieck universes and topological spaces would be a good start.

It's not just mathematicians that tend to be Platonists:

https://en.wikipedia.org/wiki/Philosophy_of_mathematics

Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers.

Mathematical ontology is multifaceted, though. Platonism is usually balanced with formalism:

Davis and Hersh have suggested in their 1999 book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position carefully, they may retreat to formalism.

I agree with Gödel's take on the matter. Without Platonic talent, you cannot comprehend mathematics.

[godelian]

For your focus on abstractions, you are too focused in falsehoods in a way and ignoring what is really real, i.e. the particularity in continuity.

In my opinion, physicalism reflects a certain lack of intelligence. If you cannot understand abstract, Platonic concepts, then you end up denying them. Physicalism is fuelled by a lack of intellectual capacity.

[Skepdick]

Maybe you want to catch up on developments in the last 60 years. Grothendieck universes and topological spaces would be a good start.

It's not just mathematicians that tend to be Platonists:

https://en.wikipedia.org/wiki/Philosophy_of_mathematics

Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers.

Mathematical ontology is multifaceted, though. Platonism is usually balanced with formalism:

Davis and Hersh have suggested in their 1999 book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position carefully, they may retreat to formalism.

I agree with Gödel's take on the matter. Without Platonic talent, you cannot comprehend mathematics.

Mathematical ontology is an oxymoron. Any ontological view of mathematics is a religion.

In computation everything's a space-time trade-off. If you assume infinite data structures are decidable you are pre-supposing some time complexity. On an infinite object.

What's the time-complexity of defining the naturals using unfold? It has to have one - because it supposedly terminates.

Can you say "bullshit"?

[godelian]

Mathematical ontology is an oxymoron. Any ontological view of mathematics is a religion.

The ontology of X is simply the question: What exactly is X?
Everything has an ontology, not just mathematics.

ChatGPT: What is the ontology of mathematics?

The ontology of mathematics refers to the study of the nature and existence of mathematical entities, such as numbers, sets, functions, geometric objects, and other abstract structures. Essentially, it seeks to answer the question: What is the true nature of mathematical objects?

1. Platonism (Mathematical Realism)
...
2. Nominalism
...
3. Intuitionism
...
4. Formalism
...
5. Constructivism
...
6. Fictionalism
...
7. Structuralism
...
8. Empiricism (Mathematical Instrumentalism)
...

The question "What exactly is X?" cannot be avoided when dealing with X. This does not mean that we always have a definitive answer to the ontological question of X. Still, the question itself is certainly legitimate. Seriously, what would there be wrong in asking the question, "What exactly is mathematics?".

[Skepdick]

Mathematical ontology is an oxymoron. Any ontological view of mathematics is a religion.

The ontology of X is simply the question: What exactly is X?
Everything has an ontology, not just mathematics.

Yes. That's your religious belief. The onto-theological tradition is a persistent delusion...

What's the ontology of

Code: Select all

unfoldr (\n -> Just (n, n+1)) 0

Go ahead and define it in Linear logic.

Is that infinite time, infinite space? Both? Neither?

Tell me something about the computational complexity of that computation!

[godelian]

Mathematical ontology is an oxymoron. Any ontological view of mathematics is a religion.

The ontology of X is simply the question: What exactly is X?
Everything has an ontology, not just mathematics.

Yes. That's your religious belief. The onto-theological tradition is a persistent delusion...

What's the ontology of

Code: Select all

unfoldr (\n -> Just (n, n+1)) 0

Go ahead and define it in Linear logic.

Is that infinite time, infinite space? Both? Neither?

Let's see what ChatGPT says about that:

ChatGPT: What is the ontology of the expression "unfoldr (\n -> Just (n, n+1)) 0"?

The expression you're asking about, unfoldr (\n -> Just (n, n+1)) 0, is from Haskell and utilizes the unfoldr function, which is part of the Data.List module. To fully understand the ontology of this expression, let's break it down step by step:
Key Concepts:

unfoldr:
The unfoldr function generates a list from a seed value by repeatedly applying a function that returns a Maybe value. The function produces the next element of the list and a new seed value, or Nothing to stop the process.
The type of unfoldr is:

unfoldr :: (b -> Maybe (a, b)) -> b -> [a]

The first argument is a function that takes a seed of type b and returns Maybe (a, b). This means it either produces a value of type a and a new seed b (wrapped in a Just), or it returns Nothing to terminate the list.
The second argument is the initial seed of type b.
The result is a list of type [a].

(\n -> Just (n, n+1)):
This is the function provided to unfoldr. It takes a value n and produces a tuple (n, n+1) wrapped in Just. The first element of the tuple is n, which will be included in the list, and the second element n+1 becomes the new seed for the next iteration.

The initial seed (0):
The function starts with 0 as the seed, and in each step, it generates the current value of n and updates the seed to n+1.

Execution Process:

Step 1:
The function (\n -> Just (n, n+1)) is applied to the initial seed 0. This results in:

Just (0, 1)

So the first element of the list is 0, and the next seed for the next iteration is 1.

Step 2:
Now, the function is applied to the new seed 1. It produces:

Just (1, 2)

The next element of the list is 1, and the new seed for the next iteration is 2.

Step 3:
The function is applied to the seed 2, producing:

Just (2, 3)

The next element of the list is 2, and the new seed for the next iteration is 3.

Continuation:
This process continues indefinitely, producing elements 0, 1, 2, 3, 4, ....

Since unfoldr does not know when to stop unless the function produces Nothing, this particular function (\n -> Just (n, n+1)) will generate an infinite list of integers starting from 0.
Result:

The result of the expression unfoldr (\n -> Just (n, n+1)) 0 is an infinite list of integers, specifically:

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...]

Ontology:

The ontology of this expression can be seen as the construction of an infinite, lazily evaluated list of integers, beginning from 0 and incrementing by 1 at each step. It is generated by a process of "unfolding," where the current value and next seed are calculated recursively, and the next value of the list is determined by the previous one.

From a type-theoretical perspective:
The function (\n -> Just (n, n+1)) maps each integer n to a pair (n, n+1), which means that for each iteration, it produces an element of the list (the first element of the pair) and a new seed for the next iteration (the second element of the pair).
The infinite list is represented lazily, meaning that it is not fully computed at once, but rather each element is generated only when needed.

Summary:

In summary, the expression unfoldr (\n -> Just (n, n+1)) 0 defines an infinite sequence of integers starting from 0, where each integer n is followed by n+1. This sequence is generated lazily by repeatedly applying the function (\n -> Just (n, n+1)) and is an example of a lazy list in Haskell.

That does not look particularly interesting.

For a starters, I do not program in Haskell. The furthest I go in functional programming is by using something like the underscore or lowdash (or similar) library, which is in fact just a collection of set-theoretical macros. I admit that they are often useful. However, I do not think that the entire language should push you into functional programming mode. I personally prefer to default to simple imperative mode because I usually find it more straightforward. I consider set-theoretical operations to be just an add-on.

[Skepdick]

That does not look particularly interesting. For a starters, I do not program in Haskell. The furthest I go in functional programming is by using something like the underscore or lowdash (or similar) library, which is in fact just a collection of set-theoretical macros. I admit that they are often useful. However, I do not think that they entire language should push you into functional programming mode. I personally prefer to default to simple imperative mode because I usually find it more straightforward. I consider set-theoretical operations to be just an add-on.

Oh, the programming language is getting in the way? You can't translate it into Javascript?

Code: Select all

function* unfoldr(fn, seed) {
    let current = seed;
    while (true) {
        const result = fn(current);
        if (result === null) break;
        const [value, next] = result;
        yield value;
        current = next;
    }
}

const naturals = unfoldr(n => [n, n + 1], 0);

Imperatively - tell me when the above computation terminate? Tell me something about its computational complexity.

If even the process of defining the naturals fails to terminate, then what is left of Mathematics?