Theists Equivocating the Empirical with the Transcendental

[Iwannaplato]

It is impossible for an absolutely non-empirical thing like a square-circle to exists.

Here VA is conflating two very different things. Transcendance and self-contradicion.
There is no empirical thing that is a geometric circle. The line of that circle has no width and all the points are exactly equidistant from the center. There would be no quantum shifts of position in whatever widthless substance makes up that circle. So, saying that a square circle exists is more than redundant. And it's geometric qualities or lack of certain qualities make it transcendant or perhaps Platonic. The fact that a square and a circle have different definitions that contradict each other is the problem with a square circle.
His 'argument' is also assuming that God must be transcendant, a word very few theists use and one that does not AT ALL fit some theists' ideas about God, and then to a lesser degree ALL versions of the deity (or deities) have been to a degree empirical. People talk all the time about intervention in the empirical world (without using the word 'empirical' usually) about feeling God's presence, about Jesus being in their hearts, about miracles and other kinds of interventions and so on.
The mathematically pure idea of a transcendant deity is more the stuff of some theologians analyses, and often theists feel duty bound to defend a concept that is not in the Bible, Koran, Bhagavad Gita and so on. Atheists especially like to turn to an idea, make it infinite or total and then come up with a paradox. But then most theists do think of Heaven, for example, as somewhere, a real place, though, one might say, not in the same dimension or with the same rules. An alternate universe might be a scientific category with some similar characteristics - note that's not an argument that Heaven is real. My point is that this immaculate separate between God or spiritual beings is not actually how most theists conceive of it. It's a strawman, though one that many theists feel bound to defend, just like the omni- nouns which are also not in the bible and are interpreting the Bible, say, as a mathematical text having no expressive components.

And let's be humble in relation to paradoxes. Particles and waves had contradictory definitions. So, for something to be both a wave and a particle was thought to be impossible. And then it was no longer thought to be impossible.

[Skepdick]

There is no empirical thing that is a geometric circle.

Errr, what?

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

Maybe it's your intention to speak about the abstract idea of a geometric circle divorced from any particular realisation, instead of the various empirical realisations of a geometric circle.

Either way - both exist and both are empirical. Unless you are trying to convince me you don't experience your ideas.

So, saying that a square circle exists is more than redundant. And it's geometric qualities or lack of certain qualities make it transcendant or perhaps Platonic. The fact that a square and a circle have different definitions that contradict each other is the problem with a square circle.

VA is confused about the whole thing, despite it having been explained to him.

If you choose a particular geometry which constrains you to using a particular non-Euclidian distance-metric there is indeed such a thing as a square circle.

https://en.wikipedia.org/wiki/Taxicab_g ... Properties

[Iwannaplato]

Maybe it's your intention to speak about the abstract idea of a geometric circle, instead of the empirical construction of a geometric circle.

Yes.

Either way - both exist.

I looked at the link, but didn't see where we have/made an empirical geometric circle. Can you explain this to someone not familiar with synthetic geometry.

VA is confused about the whole thing, despite it having been explained to him.

If you choose a particular geometry which constrains you to using a particular distance-metric there is indeed such a thing as a square circle.

https://en.wikipedia.org/wiki/Taxicab_g ... Properties

I opted not to bring this up. Perhaps a bad choice on my part but I imaged the dismissive response on his part in advance. Glad you did. Also there are so often so many errors in his posts that one must pick and choose where to focus.

For example, from the OP....

Whatever the fine-tuning claims they are scientific facts conditioned upon the human-made framework and system [FSR].
BUT, whatever are scientific facts based on human made FSR, at best they are polished conjectures and entangled with the human conditions.
The fine tuning principles fundamental based on the Big Bang is not the most credible of scientific facts in contrast the very repeatable 'water is H2O'.

I've read enough of his posts to be able to read what someone new might take to be gibberish. However there are a wealth of issues one could dive into here.

[Skepdick]

I looked at the link, but didn't see where we have/made an empirical geometric circle. Can you explain this to someone not familiar with synthetic geometry.

Synthetic geometry is about constructing geometric objects "out in the real".

Every construction external to your mind is empirical. It's realised - out in the world for everyone else to experience.

This is how reification (or if you want - creation) works. You take the contents of your mind and you bring them into existence.

[Iwannaplato]

I looked at the link, but didn't see where we have/made an empirical geometric circle. Can you explain this to someone not familiar with synthetic geometry.

Synthetic geometry is about constructing geometric objects "out in the real".

Every construction external to your mind is empirical. It's realised - out in the world for everyone else to experience.

This is how reification (or if you want - creation) works. You take the contents of your mind and you bring them into existence.

OK, so has someone made a geometric circle? IOW something that is perfectly round (or all points are equidistant from the center? How do they control atomic shifting or quantum effects that slightly change measurements? Is it a round thing or a circle? If the latter does the circumfrance have no width?

[Skepdick]

OK, so has someone made a geometric circle? IOW something that is perfectly round (or all points are equidistant from the center? Is it a round thing or a circle? If the latter does the circumfrance have no width?

Show me your two decision procedures please.

One decision procedure for roundness; and one for perfect roundness. If you can't do that I am not sure what mathematical meaning you ascribe to the English word "perfect".

Also, if you are assuming zero-width points you are certainly not working in any system with infinitesimals (numbers which are potentially zero, but not zero). A rather arbitrary choice of axioms...

Here's a blog post that might help you along... http://math.andrej.com/2008/08/13/intui ... r-physics/

[godelian]

The fact that you can explain the verification procedure makes it empirical and 100% mechnical.

We have a problem here with the term "empirical".

Definition of empirical

1 : originating in or based on observation or experience empirical data
2 : relying on experience or observation alone often without due regard for system and theory an empirical basis for the theory
3 : capable of being verified or disproved by observation or experiment empirical laws

The term "empirical" always requires sensory input ("observation") en provenance from the physical universe: vision, sound, touch, smell, or taste. Therefore, your input data must be the encoding of observations from the real world. Otherwise, it is not empirical.

So, a verification procedure can only be empirical, if you use visual input or sound input or any other sensory input. Constructivism in mathematics does not require any sensory input. That is not what it is about. Constructivism merely requires that you produce an example, i.e. a witness, for a set of which you claim the existence. That witness does not need to come from sensory input. An abstract non-physical mathematical object such as a number is also perfectly fine. In my previous example, the number "45" is not empirical, because it does not represent anything that I would have observed in the real world. It is not the encoding of something I saw, heard, smelled or tasted.

Mathematical constructivism is not related to sampling observations from the physical universe. Therefore, it is not empirical.

[Skepdick]

The fact that you can explain the verification procedure makes it empirical and 100% mechnical.

We have a problem here with the term "empirical".

Definition of empirical

1 : originating in or based on observation or experience empirical data
2 : relying on experience or observation alone often without due regard for system and theory an empirical basis for the theory
3 : capable of being verified or disproved by observation or experiment empirical laws

The term "empirical" always requires sensory input ("observation") en provenance from the physical universe: vision, sound, touch, smell, or taste. Therefore, your input data must be the encoding of observations from the real world. Otherwise, it is not empirical.

We have a problem? Seems like you have a problem.

You are interacting with me via text right now. Is this interaction not empirical to you?
Are you not receiving input as visual sense-data (in the form of language) from the real world?

As far as I can tell the exact definition you are providing is being satisfied by what is going on here.

Please let us know if you are experiencing this differently to everybody else.

[Skepdick]

Constructivism in mathematics does not require any sensory input. That is not what it is about. Constructivism merely requires that you produce an example, i.e. a witness, for a set of which you claim the existence.

Can you even hear yourself?

How could I posibly produce any example, how could I possible communicate any example from me to without transmitting evidence via your senses?

[godelian]

What I am referring to is the Philosophy of Mathematics, i.e. upon reflection all modern mathematics are reducible to its roots in the empirical, e.g. numbers which are abstracted from the human empirical sense.

Modern mathematics is completely divorced from human empirical sense. It is symbol manipulation only, which does not need any empirical connection. In fact, it is preferable to reject such connection. If we can do pure reason, why would we reason with impurities? In modern mathematics, you must let go of physical reality. It is simply irrelevant:

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."[1] According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all.

Modern mathematics does not represent "an abstract sector of reality". I do not have a problem that they teach the kids aboriginal mathematics at school. Just like the pre-Aristotelian Egyptian mathematics, it is moderately useful, even though they could also just learn to use a calculator, instead of making endless procedural exercises in manual arithmetic. It simply does not teach them modern mathematics. It is not even a good beginning.

Application to celestial mechanics

Ok. Point conceded. I am not familiar with celestial mechanics, and I didn't know that they have a use for the quintic in it. Subjects such as astronomy are about physical reality, and that is why I am not familiar with them, and why I do not like them particularly much. I am committed to pure abstraction. Therefore, I reject the physical universe as something that would be particularly interesting. That is why I pride myself on ignoring physical reality. I just don't like being too attached to it.

The metre is currently defined as the length of the path travelled by light in a vacuum in
1 / 299 792 458 of a second.
Thus my point again, the fundamentals of mathematics [old or new] is reducible to the empirical.

That is physics. That is not mathematics. Physics is about the physical universe. Mathematics is not.

Even if you can come up with illusory mathematics via pure reason or whatever, the fundamental is still empirical.

Again, you confuse the concept of "abstract" with "illusory".

The fundamentals of Peano Arithmetic Theory are a set of rules that consist of symbols. The fundamentals of Zermelo-Fraenckel Set Theory are a set of rules that consist of symbols. Where did you ever see such symbols in physical form in the physical universe?

These things are Platonic abstractions. They exist but not in the physical universe. They exist in their own separate world.

A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.

[Skepdick]

These things are Platonic abstractions. They exist but not in the physical universe. They exist in their own separate world.

If these Platonic abstractions are causing you to think about them in what way are the universes "separate" ?

[Skepdick]

The fundamentals of Peano Arithmetic Theory are a set of rules that consist of symbols.

That's not true. The rules are not encoded in the symbols.

Trivial way to test this - give the symbols to a computer; or even a human who has never studied mathematics and see if they learn the rules of PA from the symbols alone.

And when you fail you will come to understand that interpreting the axioms requires more than the symbols. Rule-setting and rule-following is a more intricate process.

[godelian]

These things are Platonic abstractions. They exist but not in the physical universe. They exist in their own separate world.

If these Platonic abstractions are causing you to think about them in what way are the universes "separate" ?

A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.

The above is what I also believe about the abstract, Platonic world of mathematics. I cannot particularly much improve on that explanation, really.

I believe that the main ontologies of mathematics, i.e. Platonism, formalism, logicism, and structuralism are simultaneously correct. They merely emphasize another aspect of its nature.

I see constructivism not as an ontology but as a quite legitimate concern. If someone claims that a set of particular abstract objects exists, then it is certainly commendable to give us an example, i.e. a witness.

[Skepdick]

The above is what I also believe about the abstract, Platonic world of mathematics. I cannot particularly much improve on that explanation, really.

I believe that the main ontologies of mathematics, i.e. Platonism, formalism, logicism, and structuralism are simultaneously correct. They merely emphasize another aspect of its nature.

And I believe in falsification. Platonism (if it claims to be separate) cannot be correct. Because it fails to account for causality.

"Separate" universes that are causally interacting are not separate.

I see constructivism not as an ontology but as a quite legitimate concern. If someone claims that a set of particular abstract objects exists, then it is certainly commendable to give us an example, i.e. a witness.

Indeed. Because that's how epistemology works!

[godelian]

And I believe in falsification.

Falsificationism works really well in science.
It is not a philosophy that would be applicable to mathematics, though.

Platonism (if it claims to be separate) cannot be correct. Because it fails to account for causality.

While science is about the physical universe and tries to account for causality, mathematics is not about the physical universe and does not deal with the notion of causality. There simply is no "Theorem of Causality" in arithmetic theory or set theory.

I see constructivism not as an ontology but as a quite legitimate concern. If someone claims that a set of particular abstract objects exists, then it is certainly commendable to give us an example, i.e. a witness.

Indeed. Because that's how epistemology works!

(Mathematical) constructivism is philosophical concern in mathematics. It is not a treatise on general epistemology.

Formally, if we want a witness, we mean:

In mathematical logic, a witness is a specific value t to be substituted for variable x of an existential statement of the form ∃x φ(x) such that φ(t) is true.

That is all it is. It is not possible to transpose this mathematical notion verbatim to epistemology.