(March 24, 2015 at 8:38 am)Nestor Wrote:

(March 24, 2015 at 7:54 am)The Reality Salesman Wrote: @Nester

Are you suggesting that abstract things, like the number 6, have their own transcendental properties beyond the conceptual application to the physical universe? As if the number 6 would still mean something within an alternate reality that did not contain discrete objects capable of being counted? Do I smell a tag argument coming along here?!

Ha! You'll get no TAG argument from me, but don't numbers mean something in an 'alternate' reality of sorts that does not contain discrete objects? Otherwise, how else could we do pure mathematics? I've been having an email exchange with my philosophy professor the last few days on the subject, and though he's told me that in full disclosure he's an anti-realist with respect to numbers, he's filled my head with all kinds of reasons to suspect that any debate about their nature is far from concluded!

(Bolded by me) First...I don't know. Now for the fun part-what I think:

It's seems to me that for numbers to have any meaning at all, the numbers must represent something. And if there were no thing that was distinct from another thing, then there would be no number that could be distinguishable from any other number. If any alternate reality existed, it would be distinct from the one we live in now, wouldn't it? So could any reality be said to exist in which no thing is distinct from any other thing? For the value of numbers to even vary, it seems to require a reality that supports the assumption that things are distinct from other things, and within that reality, each thing that may exist has the properties it has and not the properties of that which it is not. Otherwise, how could math have any utility as a descriptive tool? My head is starting to hurt...

I'm certainly not qualified to truly comment on the topic, but I've always leaned ever so slightly towards the idea that mathematics is an underlying property of the cosmos, not just a human classification.

I do know enough, however, to know that anyone claiming to know just what math is is full of shit.

(March 24, 2015 at 2:55 pm)Mezmo! Wrote: Anyone can see that things preserve their identity throughout change. This the basic observation analysed by means of reason.

Ah yes, the argument from "everyone knows that I'm right!"

The idea that objects have an "identity" to be retained? Your assertion. The idea that it can't change? Your assertion, and even if you appeal to all the available data- not that you provided any- you're still making a huge argument from ignorance by doing so.

Besides, in a basic sense- and god knows I can't have anything other than that since you're so vague with what your terminology actually means- the claim that things preserve their identity through change is simply false; coal becomes diamonds, sand becomes glass, all kinds of objects change form into something unrecognizeable. No doubt I'll get some form of assertion-as-clarification shifting the goalposts so I'm not talking about what you are, but if you're going to appeal to the same airy Forms stuff you usually do, then all you've got there is another assertion.

Quote:I don't know...maybe you haven't made any personal observations that things that exist or noticed any process of change. In either case you would have no content about which to reason.

All the observations I have of things that exist and change are of physical things, undergoing physical changes without any need for the kinds of things you insist are necessary for all that to happen. That's kinda the reason why I keep asking you for evidence of those things; I don't see them, and whenever I request that they be pointed out to me the people saying that they're there just fumble through some presuppositional nonsense about how they're obviously there and everyone can see them.

(March 24, 2015 at 3:53 pm)Faith No More Wrote: I'm certainly not qualified to truly comment on the topic, but I've always leaned ever so slightly towards the idea that mathematics is an underlying property of the cosmos, not just a human classification.

I do know enough, however, to know that anyone claiming to know just what math is is full of shit.

Yeah but I've always said that I...

Oh.

(March 24, 2015 at 3:44 pm)The Reality Salesman Wrote: (Bolded by me) First...I don't know. Now for the fun part-what I think:

It's seems to me that for numbers to have any meaning at all, the numbers must represent something. And if there were no thing that was distinct from another thing, then there would be no number that could be distinguishable from any other number. If any alternate reality existed, it would be distinct from the one we live in now, wouldn't it? So could any reality be said to exist in which no thing is distinct from any other thing? For the value of numbers to even vary, it seems to require a reality that supports the assumption that things are distinct from other things, and within that reality, each thing that may exist has the properties it has and not the properties of that which it is not. Otherwise, how could math have any utility as a descriptive tool? My head is starting to hurt...

(Bold mine)
It seems to me like numbers represent themselves. Or when you say they must represent some thing, is that what you mean---that 2 represents the value of... 2? And doesn't this abstract object, which we call "2," exist eternally and unchanged regardless if there were only a "single" entity that comprises reality?

Hopefully my question doesn't sound silly and misguided... indeed my brain hurts too... What are abstractions that seem intrinsic properties to the physical world whether or not conscious minds are present to conceptualize their value?

(March 24, 2015 at 4:25 pm)Nestor Wrote:

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(March 24, 2015 at 3:44 pm)The Reality Salesman Wrote: (Bolded by me) First...I don't know. Now for the fun part-what I think:

It's seems to me that for numbers to have any meaning at all, the numbers must represent something. And if there were no thing that was distinct from another thing, then there would be no number that could be distinguishable from any other number. If any alternate reality existed, it would be distinct from the one we live in now, wouldn't it? So could any reality be said to exist in which no thing is distinct from any other thing? For the value of numbers to even vary, it seems to require a reality that supports the assumption that things are distinct from other things, and within that reality, each thing that may exist has the properties it has and not the properties of that which it is not. Otherwise, how could math have any utility as a descriptive tool? My head is starting to hurt...

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(Bold mine)
It seems to me like numbers represent themselves. Or when you say they must represent some thing, is that what you mean---that 2 represents the value of... 2? And doesn't this abstract object, which we call "2," exist eternally and unchanged regardless if there were only a "single" entity that comprises reality?

Hopefully my question doesn't sound silly and misguided... indeed my brain hurts too... What are abstractions that seem intrinsic properties to the physical world whether or not conscious minds are present to conceptualize their value?

It doesn't sound silly! I guess what I'm saying may be harder to convey than I thought because the value of numbers and their meaning seem so self-evident given our predisposition to a reality in which they are so meaningful. Try to imagine what the word "average" would mean in a universe in which there exists only a single entity. Average what? All that exists would be, al that exists. Now imagine what meaning could be found in uttering the word "2". Isn't 2 only a coherent concept in relation to an understanding of something represented by 1 and the comparative observation that 1 can and has been doubled? We feel as though statements such as 1+1=2 are self evident but that's not quite right. It's just that we've seen the truth of it demonstrated so many times that it no longer requires consideration. But proving this statement has any meaning would require some external something to demonstrate its utility. In an alternate reality in which everything and nothing are synonymous, how could you extract any coherent meaning behind even the simplest of equations? What purpose does 1 have? Numbers are abstract in the sense that you can't find one (no pun intended)under a rock, but I don't think that means that the number 1 has any intrinsic nature apart from that which it describes anymore than "stinky" has any meaning in the absence of smell. In a universe that was absent of minds capable of applying logic, putting aside numbers for a moment, the "truth" that we derive from applying it doesn't even mean anything. In my experience of reality, It is in the nature for things to behave in a manner that is consistent with their nature and not in any other manner. This consistency is between objects and their nature within our reality is what gives numbers their utility to us as conceptual tools. If we disappeared, everything would still be what it is, and it would not be what it's not, and it wouldn't matter whether or not anything was around to think that it was true! Lol...I think I've even confused myself.

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I need Whateverist to come in here and clear all this up with 4 sentences. I know he could!

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Somebody needs to make a tagging feature on this forum like on Facebook!

(March 24, 2015 at 4:11 pm)Esquilax Wrote:

(March 24, 2015 at 2:55 pm)Mezmo! Wrote: Anyone can see that things preserve their identity throughout change. This the basic observation analysed by means of reason.

The idea that objects have an "identity" to be retained? Your assertion.

So you believe it mere assertion when someone says that the acorn and the resulting full grown oak are the same tree?

(March 24, 2015 at 4:11 pm)Esquilax Wrote: … the claim that things preserve their identity through change is simply false; coal becomes diamonds, sand becomes glass, all kinds of objects change form into something unrecognizeable…

Of course a thing can stop being one thing when a new thing is created. In the meantime they persist as whatever it is that they are. When a child blows a soap bubble out of soapy water something new with a distinct nature is created. Even though it can change size, direction, and temperature, it nevertheless preserves its existence as a soap bubble despite such changes. But when it pops, the soap bubble ceases to exist. Physical things, to which I refer as sensible bodies, have substance, form, origin, and disposition. By making note of these features anyone can distinguish between a soap bubble and a drop of soapy water…except you, apparently.

(March 24, 2015 at 3:53 pm)Faith No More Wrote: I do know enough, however, to know that anyone claiming to know just what math is is full of shit.

I'm starting to think that Socrates was right and that anyone claiming to know anything is full of shit! [edit] ...but I don't know that for sure.

(March 24, 2015 at 4:57 pm)The Reality Salesman Wrote: Try to imagine what the word "average" would mean in a universe in which there exists only a single entity. Average what? All that exists would be, al that exists. Now imagine what meaning could be found in uttering the word "2". Isn't 2 only a coherent concept in relation to an understanding of something represented by 1 and the comparative observation that 1 can and has been doubled?

I think I get why you're saying. I wrote to my professor:

Quote:...we still only understand the meaning of 2 in the context of some reasoning process such as the following: it is greater than 1 and less than 3, it is 1 doubled, a half of 4, a quarter of 8, etc.

His reply was:

Quote:Here, you're referring only to numbers and their relations. Physical things aren't anywhere, yet you still understand these relations. It is almost certainly the case that humans first came to understand number by thinking about numbers OF THINGS, but that's just a stepping stone to being able to understand number in the abstract. We learn about all kinds of things indirectly like that. Just because we have our first encounters with numbers in relation to numbers of things doesn't mean that's all numbers are.

I don't really know what to make of them. That was about the tenth email between the two of us in three days, so I didn't want to bother him to give a demonstration, as he had already hinted that some background in "first order modal logic and metalogic" were necessary to really delve into the subject.

(March 24, 2015 at 5:19 pm)Mezmo! Wrote: So you believe it mere assertion when someone says that the acorn and the resulting full grown oak are the same tree?

In some senses it isn't, given that the material making up the tree is, by and large, not the material of the acorn. When we say that the tree is the same as the acorn we aren't referring to it in any concrete sense, we're referring to the fact that the tree is a result of physical process begun by the acorn that ends in a tree. They are not the same thing, one resulted in the other.

Quote:Of course a thing can stop being one thing when a new thing is created. In the meantime they persist as whatever it is that they are. When a child blows a soap bubble out of soapy water something new with a distinct nature is created.

But the bubble is just the composition of the soap and water, spread over a different sort of area. Nothing has actually changed but the physical form, and that's largely a matter of space. What is it that you mean when you say the bubble has a distinct nature apart from the water, and how do you intend to demonstrate the existence of that?

Quote:Even though it can change size, direction, and temperature, it nevertheless preserves its existence as a soap bubble despite such changes. But when it pops, the soap bubble ceases to exist. Physical things, to which I refer as sensible bodies, have substance, form, origin, and disposition. By making note of these features anyone can distinguish between a soap bubble and a drop of soapy water…except you, apparently.

So essentially you're taking a collection of physical things and adding all this additional pseudo-mystical weight to it. Why would you do that?