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Topic: infinities and the mind-dependence of maths (split from Newton etc.) (Read 843 times) previous topic - next topic - Topic derived from Newton, Copernicus, G...

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #50
BD isn't mean.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #51
No need to be mean about it.
True.  Sorry, I was getting frustrated.  The harder I tried to ponder your words, the more unclear they became.
Quote from: Testy
you aren't understanding my issue at all.
Right.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #52
BD isn't mean.
Well, I was having a twinge of conscience about being overly snarky (or something).  So the "no need to be mean" response seems appropriate.  :)

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #53
Testy, when you get around to your response later today, please try to keep straight whether you're talking about the set of all sets or about the set of all "normal" sets (in the sense used in that wiki article you quoted about Russell's Paradox).  That should go at least 1% of the way toward clearing up the confusion between us.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #54
What could we possibly be referring to other than a statement that "the operation of taking 2 and adding 3 produces the result of 5"?
There's the statement, and then there's the underlying truth reflected in the statement.  "Meaning" is the mapping from one to the other.  Of course a "statement" has no meaning without a mind to parse it, but that has no implications about the underlying mathematical truth.
Quote from: Testy
At any rate, you seem to be saying that because an operation produces the same result every time due to the logic of its parameters, that this result exists independently of the operation. I can't even see how that is a sensical statement if that is what you are saying,
I'm not saying that the result exists independently of the operation.  I agree that that would be nonsensical.  I'm saying (among other things) that the operation exists independently of statements of the operation.  And that the "operation" is not best viewed as a physical process that happens in time.

I made no reference to the operation producing the same result every time.  In your narrative, it's not even true that the operation produces the same result every time.  Since you're taking the operation to be nothing but a mental process, the fact is that the mental process of "doing" a mathematical operation can give variable results.  There won't be much variation in 2+3, of course, but there can be a lot of variation when the questions get harder.

It's easy to account for such things in my narrative:  There's a right answer (2+3=5), but sometimes people make errors (2+3=6).  Since you're denying the existence of a mind-independent underlying mathematical truth, I don't see how you can refer to "errors" in your narrative, unless you do something weird like trying to make mathematical truths democratic (e.g. "usually when people contemplate 2+3 they get 5, so we'll take that to be 'right'").  Of course the word "usually" will itself depend on some sort of mathematical understanding as well, so the democracy-as-truth model would probably break down under its own weight.
Quote from: Testy
I am not bothered by it either but it does lead to the qualities of the deity in question. You are making a strong deterministic statement by allowing that particular type of god.
You have to presume what we're disputing (among other things) in order to argue that I'm taking a theistic position at all.  Naturally, I don't accept that.  Now you're intimating that I'm allowing a "particular type" of god, without even hinting at your reasoning.  I'd ask you to show your work, but I'm not sure that I care at this point.
Quote from: Testy
so again, we are back to iterative processes changing the landscape and minds navigating time as if it were malleable thereby applying unwarranted equalities between discrete unequal temporal landscapes.
Did you get this from a random pomo generator?
this is the post I meant to quote when I said there's no need to be mean about it.

Anyway, the God's eye view is really a critical issue for me and the type of God it suggests is important. That isn't any sort of insult because I don't think that it's necessarily a bad position but it does follow from your logic, I think.

You say that 2+3 exists. Where does it exist?
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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #55
Why does existence imply a "where"?

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #56
Why does existence imply a "where"?
Um. Really?

ETA: Can you think of anything else that exists without a where?

I bet that in every single case, that item will be something in a mind.
Love is like a magic penny
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if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #57
Why does existence imply a "where"?
Um. Really?
yes, really
Quote from: Testy
ETA: Can you think of anything else that exists without a where?
many, many things.

Would you have been happier if I had responded to your question with the answer "between 4 and 6"?

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #58
I missed the other edit.
I bet that in every single case, that item will be something in a mind.
The number 5 is represented in my mind, but that doesn't mean it resides there.

You are also represented (less perfectly) in my mind, but that doesn't mean you reside there.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #59
I missed the other edit.
I bet that in every single case, that item will be something in a mind.
The number 5 is represented in my mind, but that doesn't mean it resides there.

You are also represented (less perfectly) in my mind, but that doesn't mean you reside there.
the number 5 independently resides in lots of minds but does it reside anywhere outside of individual minds? I think the answer can only be no.
Love is like a magic penny
 if you hold it tight you won't have any
if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #60
Why does existence imply a "where"?
Um. Really?
yes, really
Quote from: Testy
ETA: Can you think of anything else that exists without a where?
many, many things.

Would you have been happier if I had responded to your question with the answer "between 4 and 6"?
please name one.
Love is like a magic penny
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if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #61
the number 5 independently resides in lots of minds but does it reside anywhere outside of individual minds? I think the answer can only be no.
Well of course it's a "no", to the extent that the phrase "reside anywhere" implies that there is a "where".

But that doesn't imply that it has no mind-independent existence.  (Triple negative alert.)

Tell me, do you think that the "5" represented in my mind is the same thing as the "5" represented in yours?

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #62
Do I think there is anything other than the representation? No.
Love is like a magic penny
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if you give it away you'll have so many
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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #63
And I can't imagine any way to argue the contrary so I'm very interested in how you would.
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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #64
It doesn't even make sense to call it a representation unless it is a representation of something.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #65
No response to this?
I made no reference to the operation producing the same result every time.  In your narrative, it's not even true that the operation produces the same result every time.  Since you're taking the operation to be nothing but a mental process, the fact is that the mental process of "doing" a mathematical operation can give variable results.  There won't be much variation in 2+3, of course, but there can be a lot of variation when the questions get harder.

It's easy to account for such things in my narrative:  There's a right answer (2+3=5), but sometimes people make errors (2+3=6).  Since you're denying the existence of a mind-independent underlying mathematical truth, I don't see how you can refer to "errors" in your narrative, unless you do something weird like trying to make mathematical truths democratic (e.g. "usually when people contemplate 2+3 they get 5, so we'll take that to be 'right'").  Of course the word "usually" will itself depend on some sort of mathematical understanding as well, so the democracy-as-truth model would probably break down under its own weight.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #66
It doesn't even make sense to call it a representation unless it is a representation of something.
an abstraction is an abstraction. what do you propose it represents?
Love is like a magic penny
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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #67
Not all abstractions are representations.

But I would say that my mental representation of the number 5 represents the number 5.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #68
No response to this?
I made no reference to the operation producing the same result every time.  In your narrative, it's not even true that the operation produces the same result every time.  Since you're taking the operation to be nothing but a mental process, the fact is that the mental process of "doing" a mathematical operation can give variable results.  There won't be much variation in 2+3, of course, but there can be a lot of variation when the questions get harder.

It's easy to account for such things in my narrative:  There's a right answer (2+3=5), but sometimes people make errors (2+3=6).  Since you're denying the existence of a mind-independent underlying mathematical truth, I don't see how you can refer to "errors" in your narrative, unless you do something weird like trying to make mathematical truths democratic (e.g. "usually when people contemplate 2+3 they get 5, so we'll take that to be 'right'").  Of course the word "usually" will itself depend on some sort of mathematical understanding as well, so the democracy-as-truth model would probably break down under its own weight.
Time constraints. But logic is logic. If the rules say how something must behave, following those rules faithfully produces the same results with errors happening through failure to apply the rules correctly (arithmetic errors) or ambiguity in the rules. Computers do not make errors in computation generally. But each time a computer needs to know the sum of 3 and 2 it needs to perform the operation. Just because the rules only permit one answer does not make that answer anything other than the product of the operation.
Love is like a magic penny
 if you hold it tight you won't have any
if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #69
Not all abstractions are representations.

But I would say that my mental representation of the number 5 represents the number 5.
which is an abstraction. QED?
Love is like a magic penny
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if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #70
But logic is logic.
and math is math.
Quote from: Testy
If the rules say how something must behave, following those rules faithfully produces the same results with errors happening through failure to apply the rules correctly (arithmetic errors) or ambiguity in the rules.
Again, it's hard to see how the word "error" is even meaningful within your narrative.  You are portraying mathematical operations as being nothing but mental processes.  With any mental process, you get what you get.  There is no such thing as "error" if there isn't some sort of mind-independent standard with which to compare your results.

Unless you see mathematical errors as analogous to moral errors?  But moral matters are famously squishy.

Gotta run.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #71
which is an abstraction.
ok
Quote from: Testy
QED?
nope.

Really gotta run.

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #72
But logic is logic.
and math is math.
Quote from: Testy
If the rules say how something must behave, following those rules faithfully produces the same results with errors happening through failure to apply the rules correctly (arithmetic errors) or ambiguity in the rules.
Again, it's hard to see how the word "error" is even meaningful within your narrative.  You are portraying mathematical operations as being nothing but mental processes.  With any mental process, you get what you get.  There is no such thing as "error" if there isn't some sort of mind-independent standard with which to compare your results.

Unless you see mathematical errors as analogous to moral errors?  But moral matters are famously squishy.

Gotta run.
I see them as mental processes, yes, based on an agreed set of rules which are to some small extent arbitrary and a result of our particular ways of interacting with our environment (euclidean geometry and base 10 for example). In order for 2+3 to = 5, the rules need to be established first.

But I don't see how a procedural error given a set of rules is analogous to a moral error.
Love is like a magic penny
 if you hold it tight you won't have any
if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #73
Love is like a magic penny
 if you hold it tight you won't have any
if you give it away you'll have so many
they'll be rolling all over the floor

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Re: infinities and the mind-dependence of maths (split from Newton etc.)
Reply #74
As I understand what he's saying, Testy is basically advocating a radical form of constructivism itt. That actually isn't so ridiculous from the platonist perspective Bro D is leaning toward since it's difficult to pinpoint the ontological status of highly non-constructive objects. More specifically, suppose that P(x) is a predicate in the language of some suitably-chosen mathematical theory T. If there is a non-constructive proof of the statement "there exists A such that P(A)" but demonstrably no constructive proof, then we're forced to admit the existence of objects A such that P(A) while nevertheless holding that there are no examples of such objects (for an example would yield a constructive proof!). This is an awkward position to be in as a platonist because there must be an objective matter of fact about whether such an A "exists" for a pretty naively common-sense notion of what it means to "exist." As far as I can see, the only way a platonist has around this difficulty is by claiming that the theory T doesn't actually adequately capture everything there is to know about the subject matter of T, and that there is indeed an objective matter-of-fact about that subject matter that we'll never know. That seems pretty mystical when we're talking about abstract objects.

ETA: The view that mathematical objects are the "results" of constructions (though maybe not in the temporal sense Testy is suggesting) is a pretty intuitive conclusion to reach from these considerations, and a lot of well-informed mathematicians and philosophers of mathematicians have held similar views (e.g., the late Wittgenstein seemed to believe something like this. See here for example, which provides a fascinating read regarding the intersection of constructability and infinities in general).
  • Last Edit: September 08, 2016, 02:39:30 PM by Quizalufagus