Thread: Epistemological Relativism

Originally Posted by Alric

I was speaking in general that people can't just make up math rules, and it was in response to Omnis saying people can make up their own rules and that saying a foot isn't 12 inches isn't objectively wrong. Yet a foot is a unit of measurement and saying a foot is say 42 inches would be 100% incorrect.

It's not objectively wrong that a foot is forty two inches, it's a matter of convention that it's twelve.

Originally Posted by Alric

As for distorting what you said, no I didn't. I defined logical multiple times as following reason. There are multiple ways to define logic and I was quiet specific in saying when I said logical I was using it in the general sense of saying math uses reason and has structure.

That's entirely besides the point of epistemological relativism. Why even bring it up? Laughing man was trying to say that the universe is mathematical and logical and that these things can't be escaped. As I'm about to elucidate for him, he's totally wrong to assert this as a fact and not a hypothesis.

Originally Posted by Alric

For the challenge, I was just asking for something that doesn't follow the rules of math, and can't be explained is a reasonable fashion.

Banach-tarki doesn't fit that. It may not seem intuitive at first glance but a person can explain why it happens without any weird unexplained things happening. It is entirely reasonable.

No, it's entirely formal. It's not at all reasonable. What's reasonable again? If you can't even define it, how do you know it describes reality? What you mean by rational is intuitive. And it's not intuitive at any glance.

In no way what so ever does it mirror reality.

It's also a great example of context in mathematics. I'll explain to LaughingMan too.

Originally Posted by Laughing Man

That isn't just 2+2. You are adding to the equation.

No, I'm interpreting in a different context. Here's a more striking example.

x²+ 1 = 0

By the definition we've agreed to so far in this thread, that's an equation. It has an equal sign in it. This will be solved by any x for which x² = -1. In the real line, there is no such x. In the complex plane, we have i and -i as solutions.

Banach-Tarski is an excellent example as well. It can only be proven with assumptions that go beyond the standard, most basic model of mathematics (Franko-Zermelo set theory), the most common of which to use is the Axiom of Choice. There are other axioms with which one can extend FZ to get it though.

So in some contexts (models of mathematics) Banach-Tarski is true. In others, it's false. Context matters.

Originally Posted by LaughingMan

Everything is based off logic so you saying that math has not been reduced to logic is erroneous. Whether you are a Kantian or a Thomistic you either impose logic upon the reality around you or receive it from the reality around you. In either case logic is at work in your surrounding environment.

Please explain how everything is based off of logic. You've only said that it's either imposed or learned, neither of which make everything based on logic. It certainly isn't known to the satisfaction of either the mathematicians or the logicians that this is the case or logicism wouldn't even be an issue. Or is there some specific misunderstanding of the article that I've made?

In this reality, the only things that do exist are those that can be perceived, understood or interacted with. It does not necessarily have to be all three at the same time. You can perceive something and not understand it etc.

That seems to be either an implicit definition of existence or a simple reassertion of the fact that I asked you to support.

Addressing it as an implicit definition, I'll point out that there are others. For example, there are Deists who believe that God exists but satisfy none of those criteria. So it's not the only definition of existence. Also, it's not a particularly good one. I can perceive and interact with things that don't exist in any meaningful sense of the word.

Addressing it as a reassertion, I'll point out that I understood it but will ask how you know it it to be true.

Originally Posted by Laughing Man

Truth isn't an evaluation. Whether something is true or false does not assign good or bad perceptions about it. You are assigning value to the fact that science establishes that biblical creationism is false.

We're using value in two different ways. My way is more general than and includes yours. You're just fixed on a valuation being a map from some set into a spectrum of good/bad. I'm allowing it to be into a set of true/false, accurate/misleading, dark-red/light-red, or any other dualistic pair or spectrum.

So I am assigning good/bad value to the fact that science attaches an accurate/misleading value (that I happen to agree with) to biblical creationism.

That doesn't change the fact that science, logic and mathematics all specialize precisely in using valuations (accurate/misleading, valid/invalid, true/false respectively) to winnow down the universe of potential statements to something manageable and useful.

They wouldn't be useful if they didn't do that.

Originally Posted by LaughingMan

IF both individuals make the same measurement correctly of the same item at the same time (all things being equal) then it is not a matter of faith that it will come to the same result if we are talking about the world of natural sciences.

No of course not. That's assumed within the world of natural sciences. We're talking about the world of actual reality though. Regardless of what a good approximation of reality science may construct, It will always be a matter of faith that the world of natural sciences is anything more than an approximation (sometimes very crude, sometimes very sharp) to the world that we actually live in.

Originally Posted by PhilosopherStoned

Please explain how everything is based off of logic. You've only said that it's either imposed or learned, neither of which make everything based on logic. It certainly isn't known to the satisfaction of either the mathematicians or the logicians that this is the case or logicism wouldn't even be an issue. Or is there some specific misunderstanding of the article that I've made?

Because their is a rationalization for events that transpire in this reality (a reason). The discovery and understanding of this reasoning is the basis of logic.

Originally Posted by PhilosopherStoned

That seems to be either an implicit definition of existence or a simple reassertion of the fact that I asked you to support.

Addressing it as an implicit definition, I'll point out that there are others. For example, there are Deists who believe that God exists but satisfy none of those criteria. So it's not the only definition of existence. Also, it's not a particularly good one. I can perceive and interact with things that don't exist in any meaningful sense of the word.

Addressing it as a reassertion, I'll point out that I understood it but will ask how you know it it to be true.

Well whatever they have a meaningful existence is dependent upon your evaluations. The fact that they do exist is the point you are missing. You seem to have a problem with value assigning especially with science.

Originally Posted by PhilosopherStoned

We're using value in two different ways. My way is more general than and includes yours. You're just fixed on a valuation being a map from some set into a spectrum of good/bad. I'm allowing it to be into a set of true/false, accurate/misleading, dark-red/light-red, or any other dualistic pair or spectrum.

So I am assigning good/bad value to the fact that science attaches an accurate/misleading value (that I happen to agree with) to biblical creationism.

That doesn't change the fact that science, logic and mathematics all specialize precisely in using valuations (accurate/misleading, valid/invalid, true/false respectively) to winnow down the universe of potential statements to something manageable and useful.

They wouldn't be useful if they didn't do that.

No you are using value improperly. You are already assuming that there is value in truth or that it is more valuable then falsity. You are already assigning your own values to the science. Again, whether science proves something is true or false is irrelevant until the observers values are taken into consideration. Therefore science does not have values, just the observer.

Originally Posted by PhilosopherStoned

No of course not. That's assumed within the world of natural sciences. We're talking about the world of actual reality though. Regardless of what a good approximation of reality science may construct, It will always be a matter of faith that the world of natural sciences is anything more than an approximation (sometimes very crude, sometimes very sharp) to the world that we actually live in.

The world of actual reality is what the natural sciences are trying to elucidate. Are you trying to make the argument that unless we can measure say the mass of the sun to the last digit then it is not objective truth?

It is intuitive, just not at first glance. If you compare it to say an infinitely long line, then cut that line in half, you get the same result. Two identical lines. Most people would accept that without any major problems, and it sounds entirely reasonable. You are doing a similar thing with Banach-tarki and its a little more complicated, but if you understand the line thing then it all makes sense, for why it is possible.

Everything in math has a reason for why it is there, and it is all linked together in a coherent and organized manner. Which is why I say it is logical.

Originally Posted by Laughing Man

Because their is a rationalization for events that transpire in this reality (a reason). The discovery and understanding of this reasoning is the basis of logic.

How do you know that there is a rationalization for events that transpire and not that some just happen?

Originally Posted by LaughingMan

Well whatever they have a meaningful existence is dependent upon your evaluations. The fact that they do exist is the point you are missing. You seem to have a problem with value assigning especially with science.

I tried to decipher this but couldn't. To whats existence are you referring here. You're asserting that they exist but I don't know what they are. What value am I not assigning here?

Originally Posted by LaughingMan

No you are using value improperly. You are already assuming that there is value in truth or that it is more valuable then falsity.

You're using value to mean (again) good or bad. A value is just a value. fifteen is a value as is "fifteen" but they are not the same value.

Originally Posted by LaughingMan

You are already assigning your own values to the science.

No I'm not. You're the one that talks about science discovering true and false. I reserve that for mathematics and that's because only within the context of mathematics can I even define true and false.

I didn't say that it's good or bad that science focuses on accurate or inaccurate. I just said that it is.

Originally Posted by LaughingMan

Again, whether science proves something is true or false is irrelevant until the observers values are taken into consideration. Therefore science does not have values, just the observer.

I'm not talking about family values here. I'm talking about the value of a variable. A valuation would then be something which takes a statement or event and assigns a value to it. So mathematics is a valuation on the set of possible statements that could be made on certain subjects into the set {true, false}.

Can you handle homonyms? I was initially confused because I read the word in the sense which I usually take it but I have explained this several times. You're still being hung up on valuations into {good, bad}.

The world of actual reality is what the natural sciences are trying to elucidate. Are you trying to make the argument that unless we can measure say the mass of the sun to the last digit then it is not objective truth?

No, that's a sophomoric argument. I'm saying that there is no a priori reason to expect that the sun has a mass, only one mass, finite amount of masses, or infinite amount of masses at any given time.

There are purely empirical reasons for believing that it has a mass and that that mass is well defined. But it's purely assumption that empirical reasoning is a good way to go if you're after truth. You can not prove that you get to truth through empirical reasoning without using empirical reasoning. It's circular.

Originally Posted by Alric

It is intuitive, just not at first glance. If you compare it to say an infinitely long line, then cut that line in half, you get the same result.

Totally different. The infinitely long line has an infinite amount of 2-volume. A sphere does not have an infinite amount of 3-volume.

Also, a line extending infinitely in both directions is different (i.e. not congruent) to a line extending in one direction.

So you've just shown that infinity divided by two is still infinity. Banach-Tarski is much closer to 1 = 2. Granted, they take 1 apart so it's not 1 any more and then put it together cleverly so that it's 2 instead. But that's what's going one.

Two identical lines. Most people would accept that without any major problems, and it sounds entirely reasonable. You are doing a similar thing with Banach-tarki and its a little more complicated, but if you understand the line thing then it all makes sense, for why it is possible.

Do you enjoy just making things up to sound like you know what you're talking about?

Everything in math has a reason for why it is there, and it is all linked together in a coherent and organized manner. Which is why I say it is logical.

Congratulations. It's entirely besides the point.

To back up PS in my own laymen format.

Math is just a form of communication. Paradox can be found virtually everywhere in math as well as other logical system making logic an inaccurate model of reality. When trying to apply math to reality, one runs into all sorts of dilemma such as the problem of infinity (.999 = 1) or even the problem of 1/0. These are not problems that can be resolved with logic, and reality itself cannot be resolved with logic, either. Logic is merely one tool, better applied to decision making than to determine what objectively exists.