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.

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?

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

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.

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

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.

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

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