h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

<'Two' is a mathematical concept, and apart from any conceptual baggage built up around it is still independent of human thought.>

George Lakoff was asked a question covering very nearly the same ground as this discussion. I shan't try to put the case myself, as I would only be parrotting what I learned from Lakoff. Of course, he isn't right *because* he's Lakoff, but I believe he's right: <"How can we understand the fact that such complex and precise mathematical relations inhere in nature?" - They don't inhere in nature. Mathematics makes use of the same conceptual apparatus used by the human mind generally, which allows for mathematical ideas — ideas grounded in our bodies and that mostly make use of metaphor. Mathematical ideas, like other ideas, don't go floating around in the air. Those ideas arise from human brains that evolved to run human bodies and don't exist outside those brains. >



*Organised* religion is not necessary to support a belief in God(s).

It is our general understanding - and has been for some time, even though it is not verifiable - that man had some form of religious belief right from the very beginning, probably before or at the time we were developing speech. OK, this isn't proveable.

I still think that you can't have a non-Catholic until Catholicism exists, and this applies to atheism too, I think.

Pattern-chaser

"Who cares, wins"

Catholicism is very specific, it refers to one particular religion. Theism refers to a potentially huge and open-ended category.

There's the difference, I think.

"Mathematical ideas, like other ideas, don't go floating around in the air."

Um. I disagree. Base 10 has no objective grounding, but numbers are purely objective. Even with a hypothetical alien intelligence radically different from ours, our mathetmatical structures would stand up to scrutiny.

Of course there may be other, equally valid equivalents but ours would still work.

Axiomatic mathematics is at the level now where the only assumption left is the existance of the empty set. Everything else, from simple addition to analysis, follows.

I think the causation runs the other way round; our brains work like that because mathematics does. Thought is, after all, a structured random process.

Show me "two" somewhere in the Real World, outside of a human's head. And I don't mean one cow in a field standing beside another cow; I mean "two". If numbers are objectve - independent of the conceptions or opinions of humans - then they must exist in the Real World, independent of us. Where are they?

Pattern-chaser

"Who cares, wins"

Two is an abstract concept. However, even abstract concepts can have objective reality. The atomic number of helium is 'two'. It was 'two' long before life evolved on earth, and it will remain 'two' long after humanity has gone.

Abstraction is a vital part of consiouness, but it does not follow that all abstraction is subjective.

Besides, what axiomatic maths tells us is that all we need to do is show that it is potentially possible to categorise the Real World in such a way that you can have a category with no elements. Notice that this does not require any conciousness in the Real World, just that it could be done were there one. Once you have that, you get all the rest of mathematics for freem, 'two' included.

<...abstract concepts can have objective reality. The atomic number of helium is 'two'. It was 'two' long before life evolved on earth, and it will remain 'two' long after humanity has gone.>

No, I don't think so. Helium, I agree, is unchanged by humans and whatever they might (not) know about it. But where is "atomic number", and where is "two"? Are they written on or near a helium atom? Is there a sign describing or defining the atomic number of the atom? A helium atom has the structure it always has, but "two" is not there, nor is it necessary for helium to continue being what it always has been.

So (setting aside "atomic number", and staying with a single example), I ask again () where is the "two"? [I know it's nowhere to be seen, I'm just waiting for you to say it! ]

Pattern-chaser

"Who cares, wins"

'Two' is abstract. It doesn't have to be substance, and indeed it isn't.

BUT it is still independent of our particular conciousness, or conciousness in general.

Maths is an entirely abstract logic sequence; and as such it 'exists', inasmuch as it exists at all, independently of us. Maths is, in fact, nothing but a huge class of internally consistent structures. It stays perfectly valid regardless of how much we know or explore of it, and will be exactly the same no matter type of consciousness considers it. It stays the same even if there is no conciousness considering it.

I say again: out thought processes are a product of mathematics, not vice versa.

<'Two' is ... independent of our particular consciousness, or consciousness in general.>

Then it must exist somewhere outside the mind of a human. Show me where that is, or withdraw your assertion.



Then it must exist somewhere outside the mind of a human. Show me where that is, or withdraw your assertion.

While you're at it, please also find "logic" for me in the Real World. Where does it reside? If it *exists*, it exists *somewhere*; please tell me where that is....

All of the things you ascribe existence to are human inventions or conventions, are they not? As such, don't they dwell - quite properly - in the human mind, and nowhere else?



Please explain to me how this can be?

Pattern-chaser

"Who cares, wins"

"Then it must exist somewhere outside the mind of a human. Show me where that is, or withdraw your assertion."

Over *there*, in the abstract realm. See? Unlike concepts such as 'good' or 'funny', some abstract concepts have absolutely no reliance on subjectivity. As human beings we are quite used to delaing with abstractions. Not all of them are subjective. Those that are not subjective are objective, and as such independent of conscious thought. You could blast the human race flat and replace it with whatever you wanted, and the new consciousness would arrive at exactly the same mathematics.

The reason maths is made abstract it to make it constant and unchanging. If some assertions about physics are correct, mathematics is more fundamental and unchanging than physical laws.

"All of the things you ascribe existence to are human inventions or conventions, are they not?"

No. They are processes and internally consistent structures. We did not invent them (any more than we 'invented' gravity). Rather, we discovered them. They were always there, waiting to be discovered. Stuff is still there, waiting to be discovered. And if it is lost and discovered again it will be unchanged.

"
Please explain to me how this can be?"

In many respects learning and decision-making follows a pattern of Bayesian statistics. Such systems are well-defined in terms of mathematics and certain qualities of their behaviour are determined by mathematics. The brain is not an engine of logic (a computer is), it is a naturally evolved decision-making machine, with a heavy emphasis on randomness. As such, it is impossible to predict its behaviour precisely. This woolliness is what gives it its power; it allows thought processes to adapt. However, it is still in the realm of statistics. Mathematics governs how the brain works, and the tohught processes in the brain are a product of that.

"All of the things you ascribe existence to are human inventions or conventions, are they not? As such, don't they dwell - quite properly - in the human mind, and nowhere else?"

Are they really? I suspect that you would find it difficult to proove that statement.

PC: <"Then it must exist somewhere outside the mind of a human. Show me where that is, or withdraw your assertion.">

QQ:

No, I don't see. I'm not being facetious. Mine is a serious question. If something exists in the Real World, you *must* be able to say where it is.

So where in the real world is "two", or does it exist somewhere other than the Real World, for example, the "abstract realm"?

Pattern-chaser

"Who cares, wins"

PC:<"All of the things you ascribe existence to are human inventions or conventions, are they not? As such, don't they dwell - quite properly - in the human mind, and nowhere else?"

Madent:

First, let me confirm that I'm not trying to say that anything and everything is a product of the human mind. The example we've used is that "two" is a product of the human mind, with no existence independent of humans. "Two" does not exist in the Real World. If it does, where is it?

Yes, I'm aware that this isn't 'proof', as "two" could be hiding somewhere we haven't looked yet. I can no more provide *that* kind of proof than I can prove the existence of God.

Although I realise I'm shifting the burden of proof onto you, I would like to ask where in the Real World (but outside the minds of humans! ) you think "two" might be found? I'm not insisting on an actual location, just where you *think* it might be. Do you have an answer?

Pattern-chaser

"Who cares, wins"

No, but it might be worth asking a dolphin.

Pattern-chaser

"Who cares, wins"

I don't think you can say that mathematics is objective and independent of human activity. Axiomatic mathematics is about what you could "in principle" write down and agree upon. It is a set of rules that all mathematicians have to adhere to. It is a subjective matter whether two mathematicians agree with a proof or not, although in practice there is general agreement among mathematicians.

I'm not simply saying that mathematics in practice is subjective and error prone, that would be an obvious point. I'm saying that mathematics is defined in terms of human relationships and cannot then be said to be independent of human activity. The whole point about axioms is that they provide a final arbiter in an argument between two mathematicians (at least in principle). Without the humans and their argument, axiomatic mathematics is meaningless.

You can say that "two" is an objective concept, but that makes two mistakes. First of all, there is the mistake above. Secondly, even ignoring that problem, there is nothing that connects the mathematical "two" to empirical reality. The connection with reality is empirical and hence again defined by human activity. To be more explicit, the connection is as follows: mathematicians have a definition of two which is used to define a language and provide a final arbiter in mathematical discussions, physicists model the world in the language of mathematics, and finally it seems (subjectively) that these models are accurate (in other words, they rarely produce a subjective feeling of contradiction).

It's also incorrect to say that mathematics has reduced all problems to the existence of the empty set. Most modern mathematics uses the Zermelo-Fraenkel axiom set which consists of 9 (or 10 depending on whether you include the axiom of choice) axioms, one of which is the existence of the empty set. See http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html for more details. If you do look at that site you'll see that the axioms are about what can be written, they are about symbols. It is possible to interpret those symbols as having meaning (and in practice mathematics would be impossible for humans if we couldn't do so, and useless to boot), but really they are just rules about what can be written down.

I see we have a mathematical Platonist in our midst.



Thereis an element of truth in this. The question is, WHERE were they waiting to be discovered?
Small children (and many animals) have the ability to track changes in small numbers. It's non verbal, and there are (presumably) no defined concepts like 'two'. But without this ability a procedure like counting would be impossible. Rare individuals who don't have it NEVER make sense of arithmetic, let alone maths.
This ability presumably evolved, and presumably it did so because it tracked (or mapped) changes in the real world in a useful way. But the concepts exist only in the human mind.

Noggin

I have decided to ask permission to join this (humble) forum, and ask the title Atheos

wonders why the subject is give the witch chocolate!

>>> wonders why the subject is give the witch chocolate!

That's because it was 'Burn the witch!' earlier, but I didn't like that very much, given that I'm a witch and being burned doesn't sound like much fun.

You say that like it's normal

Ok

Right, I've added our two newest to the list: a girl called Ben, with no chair title (she's always been iconoclastic like that ), and Jodan, under the title 'Atheos'.

Care to tell us what that means, Jodan?

Welcome to both of you!


GTB

Atheos is greek, theos is god (And the -ism put at the end, making it theism implies a belief system) and the a- prefix to theism implies a neglect of a belief system. So logically (as far as my logic goes) Atheos would be the atheist god

I'm neat like that!