Question: What is Math?

Healthy skepticism of ALL worldviews is good. Skeptical of non-belief like found in Atheism? Post your challenging questions. Responses are encouraged.
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Re: Question: What is Math?

Postby Byblos » Sat Apr 23, 2016 5:05 pm

1over137 wrote:Byb,
please teach me, b/c right now my view is closer to Ken's.
2+2 = 1 e.g. in math where base is 3 and not 10

So, chimps would have their 'chimp math'.
What I view as existing independent of humans is not math but the rules behind the nature.
Math and Physics help to describe them.

P.S. warning: am philosophically not much educated.


This is not philosophy 1over it is really simple math. Whether binary or base 3 or 10 or even kenny's silly base 12, the resulting answers are not contradictory but equivalent. 7x2=12 in kenny's base 12 is exactly equivalent to 7x2=14 in base 10. Both (all, rather) systems represent the same exact quantity written in different languages (in this case bases). It is exactly the same as what Jac was referring to in language constructs. The word 'sky' in english and 'ciel' in french and 'sama' in arabic all are difftent words in different languages but they refer to the same exact thing, i.e sky. The problem is that kenny thinks he discovered a discrepancy in math whereas he points out that 7x2=12 in base 12 is somehow different than 7x2=14 in base 10. I hope you see how dead wrong he is because I have no faith whatsoever that he will see it.

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And to address your point regarding math and physics as they relate to nature, kenny's contention is that math is a construct created only in the human mind. I repeatedly asked him to explain how then math can be used to preditct things in reality such as the higgs boson and how it is that math is so remarkably consistent in describing the reality we live in. A satisfactory answer is yet to come and I won't hold my breath.
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Re: Question: What is Math?

Postby Kenny » Sat Apr 23, 2016 7:37 pm

So if Math, and Physics have an actual existence other than in the context of human thought, what are they? Are they a force? Material? Spiritual? What are they?

Ken

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Re: Question: What is Math?

Postby Byblos » Sat Apr 23, 2016 7:56 pm

Kenny wrote:So if Math, and Physics have an actual existence other than in the context of human thought, what are they? Are they a force? Material? Spiritual? What are they?

Ken


The laws of physics, chemistry and biology are descriptive. They describe reality in a way we, humans, can relate to and understand. Our understsnding of such does not change the underlying reality they describe.

Math is more than that. It is not only descriptive, it is also predictive. It not only corresponds to the reality we observe but also allows us to make predictions about reality we don't even observe or know about. Think about this kenny, as sophisticated and extremely complex as math can get, that it took 14 billion years of evolutionary processes to produce intelligent beings capable of rational thought, to only discover this reality we live in is perfeftly describable in the most intelligently sophisticated mathematical system that is remarkably applicable from the beginning, i.e. long before hunan intelligence ever existed. The unreasonable effectiveness of mathematics indeed. You can try to discount it all you want but just so you know, for millenia some of the most brilliant minds haven't been able to do come to grips with the concept.
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Re: Question: What is Math?

Postby Kenny » Sat Apr 23, 2016 8:14 pm

Byblos wrote:
Kenny wrote:So if Math, and Physics have an actual existence other than in the context of human thought, what are they? Are they a force? Material? Spiritual? What are they?

Ken


The laws of physics, chemistry and biology are descriptive. They describe reality in a way we, humans, can relate to and understand. Our understsnding of such does not change the underlying reality they describe.

Math is more than that. It is not only descriptive, it is also predictive. It not only corresponds to the reality we observe but also allows us to make predictions about reality we don't even observe or know about. Think about this kenny, as sophisticated and extremely complex as math can get, that it took 14 billion years of evolutionary processes to produce intelligent beings capable of rational thought, to only discover this reality we live in is perfeftly describable in the most intelligently sophisticated mathematical system that is remarkably applicable from the beginning, i.e. long before hunan intelligence ever existed. The unreasonable effectiveness of mathematics indeed. You can try to discount it all you want but just so you know, for millenia some of the most brilliant minds haven't been able to do come to grips with the concept.

Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?

Ken

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Re: Question: What is Math?

Postby Byblos » Sat Apr 23, 2016 8:49 pm

Kenny wrote:Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?


Math is the language of nature. Whether or not there are rational beings to discover it is besides the point.
Let us proclaim the mystery of our faith: Christ has died, Christ is risen, Christ will come again.

Lord I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed.

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Re: Question: What is Math?

Postby Kenny » Sat Apr 23, 2016 9:01 pm

Kenny wrote:Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?


Byblos wrote:Math is the language of nature.

Language does not exist by itself, it only exist within the context of those who use it. Or are you gonna start claiming language has a physical existence as well?
Byblos wrote:Whether or not there are rational beings to discover it is besides the point.

No; that IS the point. That is the point I've been making, and you guys have been trying to refute for half a dozen pages already.

Ken

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Problem of Universals

Postby Kurieuo » Sat Apr 23, 2016 9:03 pm

Nicki wrote:
Kurieuo wrote:I guess there was no motion if no one saw or measured it.
Maybe you can try and understand what my wife posted.


I'm inclined to agree with the non-Christians - maths and physics are the study and measuring of the natural world, not part of the natural world itself. Things still move if no one measures their speed, it's just that no one knows how fast they're going. A certain kind of plant may have grown to a certain height before anyone came along and said it was ten inches high, then someone else said it was 25 centimetres, and another person three hand-widths. God made (one way or another) the plant to grow as it did and I suppose he knew people would be able to measure it in different ways, but that's not a quality of the plant in itself.

Hi Nicki,

To be clear this is dabbling in philosophy, in particular what is known as the problem of universals or abstract objects. So there is no official "non-Christian" position really, although most do often associate with what is called Nominalism (read below).

Christians have different answers themselves, if they've ever thought about the existence of universals at all and their nature thereof. Though Realism scenarios are where Christians, or anyone else who believes their god is God, should stick to.

So then, on the problem of universals, which the nature of math is encompassed by, there are various positions and they can be quite hard to explain. After carefully reading to accurate apprehend and re-describe them here, there are perhaps 4 foundational positions to consider (if anyone sees anything wrong with what I’ve written, feel free to correct or add clarity):

1) Realism says “ideas” exist independent of mind. There is an 'extreme realism' associated with Plato, and 'moderate realism' associated with his student Aristotle.

  • a) Extreme Realists after Plato believe an “idea” exists absolutely stable and by itself isolated from the world we experience that is distinct from Divine and human intellect.

    For example, with cats there exists a universal idea of “cat” that qualifies cats as having their “catness” and therefore actually be a cat. Independent of though, or even if there were no cats, the idea of "cat" would nonetheless exist somewhere in an immaterial form.

    With each abstract representation we have, whether of natural creatures (human, cat, dog), of objects (bed, chair, bridge), of properties (red, blue) or the like, there exists an actual corresponding “idea” beyond the world we experience.

    Furthermore, it follows from Plato’s Realism that although such representations might be referred to in different terms and ways, the actual representation in “idea” has universal applicability. Therefore, whether or not someone mistakes blue for red, that both colours actually do exist is universally true.

  • b) Moderate Realists following Aristotle break with Plato’s thinking where individuals in the material world are instantiated from some universal idea, instead believing the universality is found in a representation abstracted from the world we experience. This abstracted idea we then universally multiply across all instances of that particular thing.

    For example, when we experience "cats", we have the power to abstract a representation of “catness” and define what a cat is. That is, we comprehend an abstract type "catness" from the particular "cats", and then universally apply this to identify all creatures that are "cats".

    Where the universality for Platonic thinking was found in a universal “idea” existing upon which the nature of something is founded, in Aristotelean thinking we abstract ideas from particular things in the world, and then universalise these ideas when re-applying them to represent the particular:

      “The abstract type when the intellect considers it reflectively and contrasts it with the particular subjects in which it is realised or capable of being realised, is attributable indifferently to any and all of them. The applicability of the abstract type to the individuals is its universality.” (Mercier, "Critériologie", Louvain, 1906, p. 343)


2) Nominalists are anti-Realists, denying the actual existence of universals and also normally abstract objects. Most nominalists believe only physical particulars in space and time are real, although some allow for “abstract entities” such as numbers part of such.

Wikipedia on Nominalism talks of the distinction between Plato’s Realism along with the main concerns Nominalists have with universals:

    "Nominalism arose in reaction to the problem of universals, specifically accounting for the fact that some things are of the same type. For example, Fluffy and Kitzler are both cats, or, the fact that certain properties are repeatable, such as: the grass, the shirt, and Kermit the Frog are green. One wants to know in virtue of what are Fluffy and Kitzler both cats, and what makes the grass, the shirt, and Kermit green.

    The Platonist answer is that all the green things are green in virtue of the existence of a universal; a single abstract thing that, in this case, is a part of all the green things. With respect to the color of the grass, the shirt and Kermit, one of their parts is identical. In this respect, the three parts are literally one. Greenness is repeatable because there is one thing that manifests itself wherever there are green things.

    Nominalism denies the existence of universals. The motivation for this flows from several concerns, the first one being where they might exist. Plato famously held, on one interpretation, that there is a realm of abstract forms or universals apart from the physical world (see theory of the forms). Particular physical objects merely exemplify or instantiate the universal. But this raises the question: Where is this universal realm? One possibility is that it is outside space and time. ....
    .... However, naturalists assert that nothing is outside of space and time."


Nominalists take particulars they experience in the physical world as only existing in that reality. We merely ascribe to groups and individual things names (nomen). These abstract terms exist, but universal and abstract objects do not exist.

So then, in virtue of what would Nominalists say that Fluffy and Kitzler are both cats? Like Realists, there are various nominalist groups ranging from extreme up to almost realist.

Some realist-leaning Nominalists would say, "'cat' applies to both cats because Fluffy and Kitzler resemble an exemplar cat closely enough to be classed together with it as members of its kind, or that they differ from each other (and other cats) quite less than they differ from other things, and this warrants classing them together." Some concede this "resemblance relationship" as a type of universal, although others will try to distance themselves and reason away from admitting to any universal.

Other nominalists would reason that some “class membership” forms the metaphysical backing for relationships. So Fluffy and Kitzler are both cats because they share properties in that they are both members of a classes corresponding to their properties—that of four legs (quadrupedals), tail (caudates), claws and sharp teeth (carninorans), fur (mammalian) and the like. So as far as I can understand, shared classes are identified that Fluffy and Kitzler fit within, and for simplicity we name them "cats".

Whether there is just a lot of smoke being blown trying to complicate and get away with a response, I sense there is an issue of infinite regress. For example, finer particulars of classes now need explaining what’s a tail, what are teeth, what are claws, what are legs according to classes, and then even finer particulars like what are incisors, what are canines, what are molars and the like. Not much is being explained at all it seems, but rather just throwing in unnecessary complications with classes to make the problem seem covered (i.e., blowing smoke).


3) Conceptualists believe in the existence of abstract and universal objects, but holds that we do not know whether or not the mental objects have any foundation outside our minds in the actual physical work.

The Matrix movie plays with a very conceptual philosophy in certain ways. Or the brain in a jar that is stimulated into perceiving this or that, when in actuality everything we experience are just electric impulses without any real foundation outside of our brain (if we accept brains have a 1:1 correlation with our minds ;)).

___________________


So then, according to the above, we can clearly see Kenny wanting to ascribe to Nominalism of some sort. He can be forgiven I guess since he is only sticking to his bias, even if his words are at times imprecise. (sorry to talk of you in third person Ken, actually no I'm not :P)

On the "problem of universals", Christians obviously would adopt a Realism approach which many modern Naturalists would not like to entertain since such acknowledges a reality that exists outside of the physical world. There is also Neo-Platonic (New Platonic Realism) where universals are said to exist in the mind of God (or more theologically proper I believe God’s existence, that is, they simply rest upon God).
"Whoever will call on the name of the Lord will be saved." (Romans 10:13)

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Re: Question: What is Math?

Postby Byblos » Sat Apr 23, 2016 9:14 pm

Kenny wrote:
Kenny wrote:Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?


Byblos wrote:Math is the language of nature.

Language does not exist by itself, it only exist within the context of those who use it.


You might want to alert nature to that little nugget of wisdom. Perhaps it didn't know that and somehow got by on random chaos until humans came along to invent math.

kenny wrote:
Byblos wrote:Whether or not there are rational beings to discover it is besides the point.

No; that IS the point. That is the point I've been making, and you guys have been trying to refute for half a dozen pages already.


You keep saying that to yourself kenny. Perhaps one day you'll even believe it.
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Lord I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed.

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Re: Question: What is Math?

Postby Kenny » Sat Apr 23, 2016 10:08 pm

Kenny wrote:
Kenny wrote:Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?


Byblos wrote:Math is the language of nature.

Language does not exist by itself, it only exist within the context of those who use it.


Byblos wrote: You might want to alert nature to that little nugget of wisdom. Perhaps it didn't know that and somehow got by on random chaos until humans came along to invent math.

Nature isn't making any claims; you are. I'll continue to direct my nuggets of wisdom at you.

kenny wrote:
Byblos wrote:Whether or not there are rational beings to discover it is besides the point.

No; that IS the point. That is the point I've been making, and you guys have been trying to refute for half a dozen pages already.


Byblos wrote: You keep saying that to yourself kenny. Perhaps one day you'll even believe it.

If you go to page 1 you will see that is the point I was making. That's okay; nothing wrong with agreeing with me, it was bound to happen eventually; after all, even a broken clock can be right twice a day; right?

Ken

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Re: Question: What is Math?

Postby Byblos » Sun Apr 24, 2016 5:41 am

Kenny wrote:
Kenny wrote:
Kenny wrote:Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?


Byblos wrote:Math is the language of nature.

Language does not exist by itself, it only exist within the context of those who use it.


Byblos wrote: You might want to alert nature to that little nugget of wisdom. Perhaps it didn't know that and somehow got by on random chaos until humans came along to invent math.

Nature isn't making any claims; you are. I'll continue to direct my nuggets of wisdom at you.

kenny wrote:
Byblos wrote:Whether or not there are rational beings to discover it is besides the point.

No; that IS the point. That is the point I've been making, and you guys have been trying to refute for half a dozen pages already.


Byblos wrote: You keep saying that to yourself kenny. Perhaps one day you'll even believe it.

If you go to page 1 you will see that is the point I was making. That's okay; nothing wrong with agreeing with me, it was bound to happen eventually; after all, even a broken clock can be right twice a day; right?

Ken


I am well aware of your claim. You also claimed that math would be different if humans had 12 digits. Your claims are baseless at best.

As for me agreeing with you, your delusions are mathematically challenged. And make no mistake about it, they are in fact mathematically discoverable, your delusions that is.
Let us proclaim the mystery of our faith: Christ has died, Christ is risen, Christ will come again.

Lord I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed.

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Re: Question: What is Math?

Postby 1over137 » Sun Apr 24, 2016 6:52 am

Byb, thanks.
Am starting to see it from your point of view.
Whether it be math of humans (or e.g. base 10) or chimps (or e.g. base 12) they would both come to the reality that things fall down (gravity) that there is a limiting speed - the speed of light (electromagnetism), etc, etc. They would both come to the same realities that are objective, independent of us.

So, there are subjective maths (Kenny's view probably) but they all fall under one universal math (Byb's view probably). And this universal Math is property of nature. And the more we understand this Math (universal language) the more we can predict about the nature.

You guys probably use different definitions of math. Your views on what math is differ.

P.S. Correct me if I am wrong somewhere
But examine everything carefully; hold fast to that which is good.
-- 1 Thessalonians 5:21

For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus.
-- Philippians 1:6

The LORD is my rock and my fortress and my deliverer, My God, my rock, in whom I take refuge; My shield and the horn of my salvation, my stronghold
-- Psalm 18:2

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Re: Question: What is Math?

Postby Byblos » Sun Apr 24, 2016 7:04 am

1over137 wrote:Byb, thanks.
Am starting to see it from your point of view.
Whether it be math of humans (or e.g. base 10) or chimps (or e.g. base 12) they would both come to the reality that things fall down (gravity) that there is a limiting speed - the speed of light (electromagnetism), etc, etc. They would both come to the same realities that are objective, independent of us.

So, there are subjective maths (Kenny's view probably) but they all fall under one universal math (Byb's view probably). And this universal Math is property of nature. And the more we understand this Math (universal language) the more we can predict about the nature.

You guys probably use different definitions of math. Your views on what math is differ.

P.S. Correct me if I am wrong somewhere


You're absolutely correct. Views differ all the time but the underlying reality doesn't change. Math is discoverable, by intelligence of course, but discoverable nonetheless. The implications are staggering: 1) because it is discoverable, it precedes and predates the discoverer's intelligence in any form or at any time. And most importantly, 2) given 1, it requires far more intelligence as to its source. The law of non-contradiction demands it.
Let us proclaim the mystery of our faith: Christ has died, Christ is risen, Christ will come again.

Lord I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed.

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Re: Question: What is Math?

Postby 1over137 » Sun Apr 24, 2016 7:08 am

Thanks, Byb.

Hope that Ken understands your view as well. :)

Nice Sunday to all.
But examine everything carefully; hold fast to that which is good.
-- 1 Thessalonians 5:21

For I am confident of this very thing, that He who began a good work in you will perfect it until the day of Christ Jesus.
-- Philippians 1:6

The LORD is my rock and my fortress and my deliverer, My God, my rock, in whom I take refuge; My shield and the horn of my salvation, my stronghold
-- Psalm 18:2

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Re: Question: What is Math?

Postby Kenny » Sun Apr 24, 2016 7:29 am

1over137 wrote:Thanks, Byb.

Hope that Ken understands your view as well. :)

Nice Sunday to all.

I think we differ on what is defined as "different". IMO if you have two exact systems except one system has more single digit numbers, more double digit numbers, more triple digit numbers etc. than the other, even though the systems operate the same, I will see those systems as different. Apparently you guys do not. IOW it isn't that I don't understand your position; I just don't agree with it.

Ken

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Re: Question: What is Math?

Postby Kenny » Sun Apr 24, 2016 7:33 am

Byblos wrote:
Kenny wrote:
Kenny wrote:
Kenny wrote:Again; if math has an actual existence, what is it? Is it a force? is it physical? Is it detectable? What is it?


Byblos wrote:Math is the language of nature.

Language does not exist by itself, it only exist within the context of those who use it.


Byblos wrote: You might want to alert nature to that little nugget of wisdom. Perhaps it didn't know that and somehow got by on random chaos until humans came along to invent math.

Nature isn't making any claims; you are. I'll continue to direct my nuggets of wisdom at you.

kenny wrote:
Byblos wrote:Whether or not there are rational beings to discover it is besides the point.

No; that IS the point. That is the point I've been making, and you guys have been trying to refute for half a dozen pages already.


Byblos wrote: You keep saying that to yourself kenny. Perhaps one day you'll even believe it.

If you go to page 1 you will see that is the point I was making. That's okay; nothing wrong with agreeing with me, it was bound to happen eventually; after all, even a broken clock can be right twice a day; right?

Ken


I am well aware of your claim. You also claimed that math would be different if humans had 12 digits. Your claims are baseless at best.

As said before, a system based on the number 12 will have more single digit numbers, more double digit numbers, more triple digit numbers etc. than the system we have now. I see that as different; apparently you do not.

Ken


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