Question: What is Math?

[Byblos]

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.

It's not a matter of opinion, it is a mathematical certainty that the different methods (or bases, or languages) are representative of the same exact underlying reality. You can differ and disagree all you want, you're still wrong.

[Nicki]

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 )

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).

Thanks, mate, but I just meant what the non-Christians on here have said Interesting though. I suppose I agree with moderate realism but not extreme - that's just not realistic to me! I don't see why God's existence implies the existence of all sorts of airy-fairy independent-of-mind ideas floating around.

[1over137]

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

Ken,
do you agree with this: there are universal laws of nature?
(like for example gravity, limiting speed of light)

[Nicki]

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.

It's not a matter of opinion, it is a mathematical certainty that the different methods (or bases, or languages) are representative of the same exact underlying reality. You can differ and disagree all you want, you're still wrong.

Kenny, you're quibbling about the possible 'languages' of mathematics used to describe the same reality - but I think the whole discussion is quibbling in a way. There are two ideas here of what mathematics is - the science used to describe and predict reality, compared to the underlying size, shape, speed, number and so on of things in the universe. Speaking of prediction, don't the other sciences predict things, or do they only use mathematics to do so? (Sorry, can't bring myself to say 'math' - seems so American - we called it 'maths' at school; including the 's' on the end of 'mathematics', I suppose.)

[RickD]

Maybe you guys can explain to Kenny how math(s) predict things. As opposed to people using math to predict things. Maybe that way, Kenny can see how your definition of math is applied.

[Kenny]

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

Ken,
do you agree with this: there are universal laws of nature?
(like for example gravity, limiting speed of light)

I agree.

K

[1over137]

Great.
That may be a starting point toward understanding each other. Let me think on how to continue.

[1over137]

Maybe it would be good to ask you this Kenny:

How would you call a set of maths that describe the universal laws?
I mean, in one math (e.g. base 10) the speed of light would be one number and in different math (e.g. base 12) the speed of light would be different number. But always there would be a limiting speed of light. The universal law of things not being able to cross the limit.

Under one name, how would you call these maths?

[Kenny]

Maybe it would be good to ask you this Kenny:

How would you call a set of maths that describe the universal laws?
I mean, in one math (e.g. base 10) the speed of light would be one number and in different math (e.g. base 12) the speed of light would be different number. But always there would be a limiting speed of light. The universal law of things not being able to cross the limit.

Under one name, how would you call these maths?

If I understand you correctly, but are you referring to the laws of physics?

Ken

[1over137]

physics needs math, right?

edit: I talk about math that helps to describe the nature. And that is theoretical physics.

[Kenny]

physics needs math, right?

edit: I talk about math that helps to describe the nature. And that is theoretical physics.

Yes. But before we go any further, just to be clear, I hold the position that people using math predicts things, and you hold the position that it is math that is actually predicting these things. Please explain the difference.

Ken

[Kurieuo]

Thanks, mate, but I just meant what the non-Christians on here have said Interesting though. I suppose I agree with moderate realism but not extreme - that's just not realistic to me! I don't see why God's existence implies the existence of all sorts of airy-fairy independent-of-mind ideas floating around.

That wasn't just for you really, but for everyone here including myself, it was also a good exercise to put together.
It's quite relevant I think to help people frame their responses, since things can get confusing.

I'm not sure anyone agrees really with Platonic realism off the bat, it is also called an exaggerated realism.
But, then add God into the picture, who is an eternal mind possessing aseity, then mechanism for how such "ideas" could exist albeit not on their own do start making sense.

[Kurieuo]

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.

It's not a matter of opinion, it is a mathematical certainty that the different methods (or bases, or languages) are representative of the same exact underlying reality. You can differ and disagree all you want, you're still wrong.

Kenny, you're quibbling about the possible 'languages' of mathematics used to describe the same reality - but I think the whole discussion is quibbling in a way. There are two ideas here of what mathematics is - the science used to describe and predict reality, compared to the underlying size, shape, speed, number and so on of things in the universe. Speaking of prediction, don't the other sciences predict things, or do they only use mathematics to do so? (Sorry, can't bring myself to say 'math' - seems so American - we called it 'maths' at school; including the 's' on the end of 'mathematics', I suppose.)

Oh, so that's it? An American spelling thing?
I use to always write maths -- even on my notebooks actually, I recall it being written Maths.
Just looked it up and both are acceptable. I thought it was more an illiteracy thing on my part so adopted math. Should have known!

[Kenny]

Just to be clear, I hold the position that it is people using math who predicts things; and you guys are holding the position that it is actually math that is predicting these things, and people gained the knowledge by discovering math thus obtaining all the knowledge math provided. Please explain the difference.

Ken

[Byblos]

Just to be clear, I hold the position that it is people using math who predicts things; and you guys are holding the position that it is actually math that is predicting these things, and people gained the knowledge by discovering math thus obtaining all the knowledge math provided. Please explain the difference.

Ken

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Subject: Question: What is Math?