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Old 01-30-2015, 07:23 PM   #6401
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Quote:
Originally Posted by gonzaw
Yes, I am a skeptic at heart so I can't really say 100% that absolute reality exists in a way that our structures of logic are somehow metaphisically "linked" to our reasoning. But this is the next best thing.

I'm an anti-skeptic. Your skepticism is responsible for your craving for theories.



I'm just gonna focus on the paradox because I'm not arsed making a big reply and I think this might get to the heart of the matter anyway.

The point is that we cannot possibly know for certain that "plus" refers to "+" and not "quus". Let me formulate it myself, where '+' is addition and 'φ' is quus.

___________


So let's imagine you've never added numbers greater than 10 before. Then someone asks you to perform "10 plus 15" and you give the answer as "25".

Now, there's nothing about your past usage of the word "plus" that justifies you in performing the '+' function. Because you could have all the while been performing 'φ' whenever you were met with the command to 'plus'.


'+' = x + y

'φ' = x + y if x and y are less than 10, otherwise the answer is 5


You are in no way justified in believing that 'plus' refers to '+' and not 'φ'. Nobody is. You can't offer any more rules for interpreting because they would also be subject to the paradox.



EDIT: So for example:

Quote:
Originally Posted by gonzaw
To be able to do that, you actually have to know wtf "plus" is.

You can't "actually know". What are you appealing to here?


Quote:
Originally Posted by gonzaw
If you can't be sure whether "plus" is actually the plus we all know about, or is one of those infinite "quus" the wiki page mentions, then no, you can't really use the mathematical theory to do ANYTHING AT ALL with it, even less calculate '68 + 57'. Those might as well be random hieroglyphs to you.

Exactly. That's the paradox.

Last edited by WhiskeyFace : 01-30-2015 at 07:31 PM.
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Old 01-31-2015, 10:33 AM   #6402
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Quote:
Originally Posted by WhiskeyFace
I'm an anti-skeptic. Your skepticism is responsible for your craving for theories.


But, but theories are so yummy

Quote:
The point is that we cannot possibly know for certain that "plus" refers to "+" and not "quus". Let me formulate it myself, where '+' is addition and 'φ' is quus.


I think we can. First you need to understand wtf "plus" and "quus" is (if not, how do you even distinguish the two?)
Then you need to understand the underlying theory behind '+' (is it algebra? is it arithmetic? is it some weird abstract categorical algebra thing? Is it some other random unimportant one?).
Then you need to understand how the underlying logic system works. This last one you don't always NEED to do it, because it comes to you naturally (why? Because you use reasoning and logic tries to model reasoning, and does and actually pretty good job).
Then, and only then, you need to figure out if this maps to your understanding of "plus". Take a look at the definition of '+' (whatever that is). It surely has a definition, and is accompanied by some theorems, rules of construction, and whatever. Learn those, understand those, and check to see if your understanding of "plus" is consistent with those.

With this, you can be sure if "+" refers to "plus" or "quus". But yes, those intermediate steps are not trivial, and you need to do a little thinking and shit.

I understand the reasoning behind this "paradox", in the sense that I believe they think that last step (being sure "plus" maps to "+") is the one we should be skeptic of. And that is true, that step is actually the one that makes this thing fun, trying to figure out what these symbols and theorems represent in real life.
That is indeed informal and intuitive, but it's as informal and intuitive as anything you can do regarding philosophy. If you believe that to be true, then you believe it to be true, just as you may believe that an absolute reality may exist, or may believe determinism exists, or may believe there is no absolute morality, or whatever.

Quote:
So let's imagine you've never added numbers greater than 10 before. Then someone asks you to perform "10 plus 15" and you give the answer as "25".

Now, there's nothing about your past usage of the word "plus" that justifies you in performing the '+' function. Because you could have all the while been performing 'φ' whenever you were met with the command to 'plus'.


'+' = x + y

'φ' = x + y if x and y are less than 10, otherwise the answer is 5


You are in no way justified in believing that 'plus' refers to '+' and not 'φ'. Nobody is. You can't offer any more rules for interpreting because they would also be subject to the paradox.


When you are adding numbers, do you think in your head "Oh, if these numbers are less than 10, surely I must be following this rule. But if the numbers are greater than 10 then the answer is obviously always 5". Is that really your conception of "plus"? Do you actively think that when adding numbers? If not, then you can't say it can ever refer to "quus".

Like, this goes more into how you conceive of this "function". Do you conceive it as something a little bit general? First you added 0 and 1, then 1 and 2, then 0 and 2, etc and got some numbers. When you finally realized "Yes! I understand addition!", how did you conceive it? Did you just memorize the output for all possible inputs and nothing else? Or did you abstract it into a general rule you can follow for any number, even if you only applied that to numbers below 10?
If it's the 1st one, then yes, nobody can say whether you actually refer to "plus" or "quus"
But if it's the 2nd one, then you can confidently say you are not talking about "quus". If someone where to describe "quus" to you, you'd tell them that's not actually the function you have in mind.

Quote:
You can't "actually know". What are you appealing to here?


I mean the above. The concept of "plus" doesn't magically appear in your head. You have to understand it somehow. How do you understand it? That's a pretty big deal, and it's the difference between you understanding what "plus" is, or actually understanding what another completely different thing is, which you just call "plus" (like if I said "Oh, 2 + 3 = Orange, I understand plus!")

Quote:
Exactly. That's the paradox.


I understand what it says, but I fail to see it as a paradox. To me it's like saying "Oh, how can you be certain determinism is true or justify believing it, huh? You can't, therefore paradox".
Like, this is the reason we are sentient beings and came up with philosophy: to figure this shit out. This "paradox" seems like an extreme skeptical copout, which you can do with almost anything.
Like I said, at heart I agree, but not when trying to keep it in a practical level. Covering your ears saying "lalalal you can't be sure of anything at all anywhere, it's a paradox, you are stupid lalalal" won't achieve much.


P.S:
Quote:
You are in no way justified in believing that 'plus' refers to '+' and not 'φ'. Nobody is. You can't offer any more rules for interpreting because they would also be subject to the paradox.


Also, when saying things like "justified in believing" I keep thinking that we are going down to semantics again. Or we are using some overloaded terms when we should figure out exactly what they are. For instance in this example, why do you load the term "justified in believing" in such a way that makes this example a paradox? With all the stuff I said, I think someone thinking "plus" is represented by the "+" function is entirely justified in believing it so. Are we going to go into a semantic war about what "justify" means?
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Old 01-31-2015, 10:38 AM   #6403
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Like, if your understanding of "plus" is different from the common understanding of plus/addition, then this is not a problem of addition or a paradox or anything, it's a problem with your understanding of the world. Like, this can happen with anything, not just mathematical concepts and rules.
How can you be certain your understanding of "tree" is what we all understand a tree to be? What makes it impossible for you to see a brown bear and say "that's a tree!"?. In this case you weren't actually talking about trees, but rather about "beatrees", like so:
Tree = Tree
Beatree = Tree or Bear

So when you talk about trees you can't possibly justify it being the 1st concept, and not the 2nd. You can apply this reasoning to anything ever, be it number addition, trees, soy milk, democracy, pink unicorns, etc. What is so special about this line of reasoning?
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Old 01-31-2015, 02:02 PM   #6404
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Quote:
Originally Posted by gonzaw
I think we can. First you need to understand wtf "plus" and "quus" is (if not, how do you even distinguish the two?)

YOU CAN'T

THAT'S THE PARADOX

There's nothing you've ever done, from your past usage of "plus", that should lead you to believe that '+' even exists and hasn't actually been 'φ' the whole time.

You can't talk about the "common understanding" because this applies to everybody. How do you know the "common understanding" is right?
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Old 01-31-2015, 02:05 PM   #6405
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Originally Posted by gonzaw
Like, if your understanding of "plus" is different from the common understanding of plus/addition, then this is not a problem of addition or a paradox or anything, it's a problem with your understanding of the world. Like, this can happen with anything, not just mathematical concepts and rules.
How can you be certain your understanding of "tree" is what we all understand a tree to be? What makes it impossible for you to see a brown bear and say "that's a tree!"?. In this case you weren't actually talking about trees, but rather about "beatrees", like so:
Tree = Tree
Beatree = Tree or Bear

So when you talk about trees you can't possibly justify it being the 1st concept, and not the 2nd. You can apply this reasoning to anything ever, be it number addition, trees, soy milk, democracy, pink unicorns, etc. What is so special about this line of reasoning?

Exactly. So how do you know you're using words and mathematical functions correctly?
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Old 01-31-2015, 03:09 PM   #6406
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Originally Posted by WhiskeyFace
YOU CAN'T

THAT'S THE PARADOX

There's nothing you've ever done, from your past usage of "plus", that should lead you to believe that '+' even exists and hasn't actually been 'φ' the whole time.

You can't talk about the "common understanding" because this applies to everybody. How do you know the "common understanding" is right?


You (and the author) keep pushing this idea that "plus" is somehow defined by how many times you used it, with phrases like "... from your past usage of 'plus' ...."
What does "past usage" have to do with anything, specially with something as the understanding of an abstract concept like addition? Is it because you are tying up the concept of "plus", with the pedagogical tools we use to teach it? As in, we usually teach people to add numbers by using examples of adding "1" and "2", etc, and do so by using big numbers in an incremental way.
So is this actually a discussion about how we initially form the conception of addition via these methods (which would include us adding numbers below 10 at first, and then below 100, and so and so)?
But isn't this discussion about the actual "full" conception one has of addition, after one has understood it?

I still don't really understand this.

Quote:
You can't talk about the "common understanding" because this applies to everybody. How do you know the "common understanding" is right?


The "common understanding" is that "plus" represents addition of numbers. So 1 plus 2 is 3, 50 plus 10 is 60.
But anybody in the world could have hit their head and conceived of addition as the process of scrapping mud off the back of a whale for all I know. So when we talk about "plus" we do not talk about any personal conception which could actually be anything arbitrary at all, but we talk about a defined concept we have accepted to be and understand. If we don't have this very assumption, then we can't have any argument about this at all (except for the skepticism argument about that assumption, which is not the case, and that would be very boring).

Quote:
Originally Posted by WhiskeyFace
Exactly. So how do you know you're using words and mathematical functions correctly?


Because the words correspond to a concept I understand, and the mathematical function corresponds to an operator from a certain theory (arithmetic) I understand, and I accept the "link" between the two of them. I.e I accept that said model and theory represents the concept we actually use in real life to do shit and stuff.

Why do I accept that model and theory then? Because I check out the construction of such a function "+", and the theorems about it, and they correspond neatly to my own understanding of "plus", AND my understanding of all the other things related to it (numbers, application of rules, etc). I also accept that the logic system underlying this theory models the way I reason about "plus" and "numbers", so using this logic system to construct "10" out of "4 + 6" is neatly isomorphic to my own mental process of applying what I know to be "plus" to what I know to be "4" and "6".

There is no way I can confuse "plus" with "quus" in this context. I have a specific conception of "plus" and a specific conception of "quus", and I believe I'm smart enough to figure out which one is actually mapped to the mathematical model and theory, based on all of the above.

Sorry, but trying to argue anything else seems futile to me. It would be as futile as arguing about solipsism and that shit. Sure, you can be skeptical about the foundations of everything, about reality, about knowledge, about reasoning, understanding and how you form new concepts and work with them. But that's just food for thought, not anything you'd actually believe in real life. Seems this is just trying to be skeptic for the sake of it

P.S: Also, what exactly is the paradox?

Last edited by gonzaw : 01-31-2015 at 03:15 PM.
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Old 01-31-2015, 03:15 PM   #6407
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Also, I'm not sure if you actually believe this, or you are just being devil's advocate and arguing in the author's place (seems to happen an awful lot around here lol >_> )
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Old 01-31-2015, 04:00 PM   #6408
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Quote:
Originally Posted by gonzaw
The "common understanding" is that "plus" represents addition of numbers. So 1 plus 2 is 3, 50 plus 10 is 60.

"Wtf are you talking about? Addition means you add numbers except when it's 50 and 10. When it's 50 and 10 you multiply them and then divide by 20 so that the answer is 25. Have you been going your whole life thinking 50 + 10 is 60? It's 25 you maniac!"

How do you respond?



The reason you're not understanding is because you think skepticism can only be solved by appealing to further foundations, or that the rejection of foundations leads to skepticism. It's the opposite.
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Old 02-01-2015, 06:34 PM   #6409
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Originally Posted by WhiskeyFace
"Wtf are you talking about? Addition means you add numbers except when it's 50 and 10. When it's 50 and 10 you multiply them and then divide by 20 so that the answer is 25. Have you been going your whole life thinking 50 + 10 is 60? It's 25 you maniac!"

How do you respond?


How do you want me to respond? First, I'd ask him what "multiply" and "divide" are, and what his understanding of numbers is. Most likely he'll choke up with those and have inconsistencies, in which case I'd tell him "Well, you are wrong about something at least. Try to think a little bit harder and get some consistent definitions".

I believe this is a different argument than the "paradox" one. I.e, this relates to whether there can be any shared knowledge between individuals, and not just different individual understandings of things by different beings, which are inherently independent of each other. E.g, my "plus" is not your "plus". There can be no general "plus"
I can see the points of this argument, and we could have some discussion about it.
But I don't think this has to do with this "paradox". If it has, then it's looking at it the wrong way. If you want to argue for this point, then argue for it, don't come up with this weird situation where you have some "quus" and you bring mathematical theories and "following rules" into it.

Don't bloat it, stick to the core argument.


Quote:
The reason you're not understanding is because you think skepticism can only be solved by appealing to further foundations, or that the rejection of foundations leads to skepticism. It's the opposite.


My point is this:
1)Okay, you are skeptic about everything and reject everything, cool
2)If you keep thinking that way, we won't be able to have any discussion about anything, so this will turn up to be boring quite quickly. So if you want to have some meaningful discussions, assume, for the sake of the argument, that either your skepticism is wrong, or that it is true, but for all intents and purposes the "fake" constructions we are creating are consistent in an unreal way.

I never said these foundations are like the blocks of reality or something. But you can't say they aren't there, and that we can't use them. We can certainly come up with theories, use logic, and deduce results. You can't argue against this, whether these correspond to some absolute entities of reality or not. I find these useful for many situations, and bring a lot of information to light on some concepts we conceive (at the very least if we temporarily accept these logical structures and models).

If you are going to solve a Sudoku puzzle, are you going to say "Oh, there's no way my understanding of Sudoku can be axiomatized into specific rules I can follow. This is futile"? No, you suck it up and use logic to solve that shit. The theory of Sudoku and logic is useful here, and it allows you to come up with some results. Who cares about some paradox or not?


The point I can see could have some arguing against, is my point about how every use of reasoning by humans has a hidden theory behind it, and different logic systems can model it truly, or at the very least can model it truly for a small bounded context. But this is about reasoning alone, not about any other understanding or concept you have (like addition, or trees, or honey badgers), so this paradox doesn't apply to it (at least this specific example of "plus" and "quus")

Last edited by gonzaw : 02-16-2015 at 02:48 PM.
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Old 02-16-2015, 04:58 AM   #6410
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So, I've been wondering about this very important question for quite a while now.....

Why is it called philosophy and not sophophilia?

We don't go around saying stuff like "philonecro" or "philopedo" or "philozoo", do we?
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Old 02-16-2015, 05:29 AM   #6411
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Quote:
Originally Posted by gonzaw
So, I've been wondering about this very important question for quite a while now.....

Why is it called philosophy and not sophophilia?

We don't go around saying stuff like "philonecro" or "philopedo" or "philozoo", do we?

I've just googled it and apparently sophophilia means sexual gratification from learning. So perhaps that's why.
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Old 02-16-2015, 05:36 AM   #6412
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I've just googled it and apparently sophophilia means sexual gratification from learning. So perhaps that's why.


Wait, so the meaning of a word changes when you change the affixes around? Wtf English?

Does that mean that a Philonecrotic is someone that loves dead people, but in a profound emotional way?
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Old 02-16-2015, 05:38 AM   #6413
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Philosophy is a Greek word, isn't it?

Perhaps the order changes the meaning, I'm unsure.
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Old 02-16-2015, 02:00 PM   #6414
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>gonzaw accusing me of bloating things
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