Epistemological Relativism

The purpose of Science is not the establish the most accurate depiction of reality possible. Its purpose is to enable the mind to most easily assign value to various assertions. An assertion supported by scientific evidence is not more true than an assertion void of evidence, it is simply a more valuable idea to utilize when making decisions.

The factual universe is outside the realm of the subjective experience. The subjective experience is capable only of behaving in whichever way it can find to be most advantageous. Science enables the organism to discover the most statistically advantageous model to base decisions upon, not the most accurate depiction of reality in general.

A friend of mine disagrees with me in this particular regard. He believes that the most accurate assertion of reality is not necessarily the most functional. He cites organized religion to argue that irrational ideas are often more capable of functioning and propagating than rational ideas. Benefit is therefore not related to Truth. I disagree, I believe the only means we have to find the most accurate depiction of reality is to observe the most successful behavior. Or rather that it is impossible for the subjective mind to ascertain something which is more true than something else, and therefore the goal of the organism is to find success, not truth. Discovering the most accurate depiction of reality possible is only beneficial so far as it serves the function of the observer. The Scientific Method increases an organisms chances of success by providing a more stable foundation to influence their behavior than Dogmatic Tradition. Ideas such as belief, right, wrong, true and false are antiquated in my mindset. I am interested in the practices the organism utilizes in order to prosper.

For example we know ethics is typically considered relative unless it is conflated with piety. I consider ethics to be an intuitive development of Game Theory, and research on Game Theory shows that the most advantageous behavior includes compassion, fairness and other ethical ideals. In other words ethics are the tactics which are most advantageous when considering the complexity of life and the length of time it takes for certain processes to reach fruition. Ethics are the tactics for those wishing to with-hold instant gratification and seek out success on a larger scale than their own personal gain, or more precisely in search of a sustainable and more advantageous gain than what is delivered through opportunism, such as a more stable and prosperous society.

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Originally Posted by Omnis Dei

A friend of mine disagrees with me in this particular regard. He believes that the most accurate assertion of reality is not necessarily the most functional. He cites organized religion to argue that irrational ideas are often more capable of functioning and propagating than rational ideas. Benefit is therefore not related to Truth.

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Am I just drunk or is your friend not very on point here?

How do the propensities of rational and irrational ideas for spreading pertain to which of them is a more accurate description of reality? Why does the most accurate idea have to be the one that best propagates? And what is even meant by an accurate model of reality?

One thing I can tell you is that your response to my posts displays a very inaccurate reflection of my opinion.

My friend used plate tectonics as an example for his claim. There's this theory that the poles are shifting, the earth is expanding, its hollow, whatever you want. These theories are all blatantly opposed to scientific evidence. To uphold these claims in the face of all scientific evidence to the contrary is, in my friend's opinion, more wrong than to agree with the conclusions implied by the evidence.

In my opinion, there's no way to judge a subjective opinion or experience as a less accurate depiction of reality than another. That means that someone's opinion that Hamsters created the universe is no less objectively accurate than the current consensus made by astrophysicists. When it comes to someone's subjective model of reality, accuracy in relationship to actual reality is simply an invalid concept. A more valid comparison between differing opinions is the value they serve the individual. This means that if someone believes eagles shat out the universe in order to cool themselves, and that opinion serves them or society in regard to widescale evolution, then its more valuable than an opinion which was not as productive, whether or not the latter opinion had more scientific evidence supporting it.

I look forward to seeing you miss the point and misconstrue my argument again.

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Originally Posted by PhilosopherStoned

Am I just drunk or is your friend not very on point here?

How do the propensities of rational and irrational ideas for spreading pertain to which of them is a more accurate description of reality? Why does the most accurate idea have to be the one that best propagates? And what is even meant by an accurate model of reality?

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You're not drunk, but maybe you are in our subjective world according to Omnis. Yes, yes I think you are drunk and the idea that you have not ingested mass quantities of alcohol which effect your body does not invalidate my perception that you are drunk.

Theories blatantly opposed to scientific evidence in the natural world are what psychologists like to call "delusions." The premise that the world was created by hamsters has no grounding in factual evidence of the natural world. And I don't know where you get the idea that science is a value assigning discipline. Science isn't normative. There are no values in it.

I never said there were. My claim is simply that true and false are not determinable from a subjective standpoint. There is not subjective opinion which is more in line with the objective reality than another. The only way in which one subjective viewpoint can be better than another is by the value it serves the individual's decision making process.

Example: There is no guarantee the sun will rise tomorrow, but I hold the premise that the sun will rise tomorrow as a more valuable basis for my decision making than the premise that it will not. Evidence such as inferring the sun will rise based on what it has done previously and the evidence of a revolving earth gives that premise a greater statistical advantage than the premise that the sun will not rise.

Because industrial London led to lichen free trees, dark peppered moths are more statistically advantageous than light peppered moths. And they most likely will continue to be for some time to come, but that doesn't make the light colored mutation less valid than the dark one, simply less valuable based on the environment it is situated in. Simply because dark peppered moths currently hold the advantage, that doesn't mean the mutation should just go away forever. In fact one day the lichen may grow back and the advantage will switch back.

Whatever the case, the example is meant to show you the difference between the absolutist right/wrong worldview and the relativist advantageous/disadvantageous worldview. Rational, logical thinking doesn't imply what is right, it only reveals a more statistically advantageous basis for decisions which is inherently subjective and relative. One can still choose to experiment, and in fact many of the views we accept today started as explorations of ideas outside the traditional worldview. These ideas were tested for evidence but that didn't make them true, in the relativist view, it merely gained them more statistical advantage.

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Originally Posted by Omnis Dei

I never said there were. My claim is simply that true and false are not determinable from a subjective standpoint. There is not subjective opinion which is more in line with the objective reality than another. The only way in which one subjective viewpoint can be better than another is by the value it serves the individual's decision making process.

Example: There is no guarantee the sun will rise tomorrow, but I hold the premise that the sun will rise tomorrow as a more valuable basis for my decision making than the premise that it will not. Evidence such as inferring the sun will rise based on what it has done previously and the evidence of a revolving earth gives that premise a greater statistical advantage than the premise that the sun will not rise.

Because industrial London led to lichen free trees, dark peppered moths are more statistically advantageous than light peppered moths. And they most likely will continue to be for some time to come, but that doesn't make the light colored mutation less valid than the dark one, simply less valuable based on the environment it is situated in. Simply because dark peppered moths currently hold the advantage, that doesn't mean the mutation should just go away forever. In fact one day the lichen may grow back and the advantage will switch back.

Whatever the case, the example is meant to show you the difference between the absolutist right/wrong worldview and the relativist advantageous/disadvantageous worldview. Rational, logical thinking doesn't imply what is right, it only reveals a more statistically advantageous basis for decisions which is inherently subjective and relative. One can still choose to experiment, and in fact many of the views we accept today started as explorations of ideas outside the traditional worldview. These ideas were tested for evidence but that didn't make them true, in the relativist view, it merely gained them more statistical advantage.

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You are conflating science with subjectivity. If you were to be saying "You can't prove my favorite ice cream flavor is true or false" then I (and I think Stoned) would not really have a problem with what you are saying. Preferences such as this are subjective and it is based on aesthetics, not logic.

However you are saying scientific knowledge of the natural world is based upon relative observations, but it isn't. If we were to stand in the same spot, all things being equal, we would we the same distance from the sun or would have the same measurements of its size. Science is agent-neutral meaning it that its truth isn't dependent upon the individual on hand.

The nice thing about measuring is that it provides good statistical advantage to base decisions upon. But you're conflating the measurements made by the subjective observer with the measurements existing in objective reality. The epistemological relativist point of view is that if 500 people were to measure something and 499 get one measurement and 1 person gets a different measurement, the 1 person's measurement is not objectively wrong, their assessment simply isn't advantageous compared to the 99.5% majority and decisions made related to the measurement are preferable if based upon the result of the 499 rather than the one.

Or, when using science to negate dogmatism, if 499 people were to make a claim without proof and 1 person made a claim backed up by a mountain of evidence, the value would go to the one. This is not objectively true, it's simply my advice based on my relativist perspective. I would assign more value to evidence than no evidence. But I would not assign truth to evidence.

The core principle here is that objective truth is an impossible idea, and that functionality is a preferable goal. The goal is not to find out what objectively is, but would would best serve you.

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Originally Posted by Omnis Dei

The nice thing about measuring is that it provides good statistical advantage to base decisions upon. But you're conflating the measurements made by the subjective observer with the measurements existing in objective reality. The epistemological relativist point of view is that if 500 people were to measure something and 499 get one measurement and 1 person gets a different measurement, the 1 person's measurement is not objectively wrong, their assessment simply isn't advantageous compared to the 99.5% majority and decisions made related to the measurement are preferable if based upon the result of the 499 rather than the one.

Or, when using science to negate dogmatism, if 499 people were to make a claim without proof and 1 person made a claim backed up by a mountain of evidence, the value would go to the one. This is not objectively true, it's simply my advice based on my relativist perspective. I would assign more value to evidence than no evidence. But I would not assign truth to evidence.

The core principle here is that objective truth is an impossible idea, and that functionality is a preferable goal. The goal is not to find out what objectively is, but would would best serve you.

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Because there is no subjective reality toward measurements. A foot is 12 inches...everywhere. It's a priori. If 500 people were to measure something and one gets it wrong, then that is called variation. This is because of user error in engaging in the measurement. That is why I said, all other things being equal.

Your core principle that "objective truth is an impossible idea" is a performative contradiction because the fact that there is no objective truth is itself an objective truth about the world. Congratulations.

Honestly, save yourself some time. Just get over this relativity phase.

Being condescending isn't going to make you any better at arguing your viewpoint, in fact it makes you appear dismissive which strikes me as though you don't have much confidence in your own viewpoint because you're unwilling to argue it.

A foot being 12 inches is abstract, and abstraction can be absolute in the frame that it's devised in. But abstract truth is limited to circular logic. Something becomes true because we deemed it as such for the sake of being able to communicate effectively, not because it's true in any real sense. When someone claims a foot is not 12 inches (or 2+2=5, or any other abstract ideas) that also doesn't make them objectively wrong, it simply makes them a bad communicator, unwilling to play by the agreed upon rules. These things still have nothing to do with objective reality.

The idea that objective truth is an impossible is, in fact, contradictory with epistomological relativism, and I knew that when I said it. Epistomogological relativism would hold that an absolutist is no more wrong than a relativist. This in itself is a paradox in the philosophy, for a relativist to argue their viewpoint they must also argue that absolutism is as equal as their own viewpoint. I broke those rules in my attempt to communicate with you that it's impossible to discover objective truth as the subjective observer. I believe that explanation should be more clear.

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Originally Posted by Omnis Dei

One thing I can tell you is that your response to my posts displays a very inaccurate reflection of my opinion.
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I look forward to seeing you miss the point and misconstrue my argument again.

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Ditto. I was giving you an argument to use against your friend's perspective since you apparently were unable to spot the fallacy. Your friend apparently doesn't know how rationality works anymore than you do since his argument is about on par with what I would expect from you. Did you find a problem (that you have failed to explicate) with my rebuttal of your friend's position or was assuming that I was opposed to your opinion just a knee-jerk reaction on your part?

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Originally Posted by Laughing Man

And I don't know where you get the idea that science is a value assigning discipline. Science isn't normative. There are no values in it.

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Science is absolutely a normative, value assigning discipline. It's primary normative tools are predictive power and falsifiability. The values it assigns are related to the explanatory power of the hypothesis under consideration. This is why creationists get laughed at if they manage to slither into a biology department.

Good thing too. A disipline that can't do these things isn't much of a discipline, is it?

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Originally Posted by Laughing Man

However you are saying scientific knowledge of the natural world is based upon relative observations, but it isn't. If we were to stand in the same spot, all things being equal, we would we the same distance from the sun or would have the same measurements of its size.

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The idea that objective observation is even possible is one of those assumptions which lay at the heart of the rational materialist model. It is only in our experience that such measurements do not depend on who carries them out. It makes the universe much cleaner to think about and is a very useful assumption but this does not make it objectively true.

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Originally Posted by Omnis Dei

Being condescending isn't going to make you any better at arguing your viewpoint, in fact it makes you appear dismissive which strikes me as though you don't have much confidence in your own viewpoint because you're unwilling to argue it.

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I just don't have much tolerance for nihilism because so many who find out what it is waste their intellectual power trying to promote it because its groovy or something like that.

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Originally Posted by Omnis Dei

A foot being 12 inches is abstract, and abstraction can be absolute in the frame that it's devised in. But abstract truth is limited to circular logic. Something becomes true because we deemed it as such for the sake of being able to communicate effectively, not because it's true in any real sense. When someone claims a foot is not 12 inches (or 2+2=5, or any other abstract ideas) that also doesn't make them objectively wrong, it simply makes them a bad communicator, unwilling to play by the agreed upon rules. These things still have nothing to do with objective reality.

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Actually it makes them objectively wrong because it is beyond logic to show that 2.0000+2.00000 equals anything but 5. Math is based on logic, logic is universal and inescapable. There is no such thing as an illogical mind because we wouldn't be able to perceive it, understand it or interact with it.

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Originally Posted by Omnis Dei

The idea that objective truth is an impossible is, in fact, contradictory with epistomological relativism, and I knew that when I said it. Epistomogological relativism would hold that an absolutist is no more wrong than a relativist. This in itself is a paradox in the philosophy, for a relativist to argue their viewpoint they must also argue that absolutism is as equal as their own viewpoint. I broke those rules in my attempt to communicate with you that it's impossible to discover objective truth as the subjective observer. I believe that explanation should be more clear.

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So now you are saying that objective truth being impossible is contrary to epistomological relativism? It Sounds like you need to hash out what you really believe before this conversation continues.

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Originally Posted by PhilosopherStoned

Science is absolutely a normative, value assigning discipline. It's primary normative tools are predictive power and falsifiability. The values it assigns are related to the explanatory power of the hypothesis under consideration. This is why creationists get laughed at if they manage to slither into a biology department.

Good thing too. A disipline that can't do these things isn't much of a discipline, is it?

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Actually it is not. Humans can place value upon scientific studies but science itself does not place value on itself or its study. Science can show you what happens when you put two hydrogens and an oxygen together but it does not say why you should put it together nor if it is good to do so etc.

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Originally Posted by PhilosopherStoned

The idea that objective observation is even possible is one of those assumptions which lay at the heart of the rational materialist model. It is only in our experience that such measurements do not depend on who carries them out. It makes the universe much cleaner to think about and is a very useful assumption but this does not make it objectively true.

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What other experience would there be that would not be dependent upon humans?

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Originally Posted by Laughing Man

Actually it makes them objectively wrong because it is beyond logic to show that 2.0000+2.00000 equals anything but 5.

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First off, is it 2.000 as a real number or 2 as an integer?

2 + 2 = 1 is a true statement. Taken modulo 3.

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Originally Posted by Laughing Man

Math is based on logic

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You should check out logicism. Essentially you are making a religious claim.

tl;dr: math has not been logically reduced to logic.

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Originally Posted by Laughing Man

logic is universal and inescapable.

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More of the rational materialist religion. It's a good religion and good, useful assumptions but that doesn't make them anything more than that.

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Originally Posted by Laughing Man

There is no such thing as an illogical mind because we wouldn't be able to perceive it, understand it or interact with it.

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There is no such thing as a logical mind either.

More on point though, your assertion that it doesn't exist (i.e. "no such thing") is itself based on the assumption that the only way for something to exist is if we can percieve it, understand it, or interact with it. This assumption isn't even necessary for rational materialism to function as one of the most distinguished of a number of possible models of reality. However, there's no way to have it be The One True Way though without this assumption.

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Originally Posted by Laughing Man

Actually it is not. Humans can place value upon scientific studies but science itself does not place value on itself or its study. Science can show you what happens when you put two hydrogens and an oxygen together but it does not say why you should put it together nor if it is good to do so etc.

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Science places value on specific scientific statements. It doesn't say why one should do something or if it's good. It says if the statement is correct or not. This is a valuation. With statistical inference it can say how likely it is for the statement to be correct. Statements of biblical creationism are rejected by the normative process of science and valued far less than statements that take place within the scope of evolutionary biology. Some of those will even be "de-valued" over time.

Try to apply a little imagination.

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Originally Posted by Laughing Man

What other experience would there be that would not be dependent upon humans?

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Any of the other number of sentient beings that exist. Aside from that (purposeful?) misunderstanding though, I was referring even to measurements made by two distinct humans. It is a matter of faith (assumption) that if they both make the same measurement correctly then they will get the same result. Like I said, it's a useful assumption but it is still an assumption.

If you make up math rules that don't make any sense any doesn't come out correctly mathematically, then yea you are wrong. You are always wrong. You are absolutely, 100% objectively wrong. We can easily prove you are wrong. Just because you try to act philosophical doesn't mean you are any less wrong.

Who's making up math rules that don't make sense?

Why the strong reaction? Is having the sacred script of one of your choice religions questioned bothering you? Check the logicism wiki link. There is no serious way to claim that mathematics has been reduced to logic.

Mathematical statements are also meaningless unless you specify in which context they are meant. 2 + 2 = 4 taken mod 5 or higher and in all fields which contain the integers. It comes to 0, 1 and 0 when taken mod 2, 3 and 4 respectively.

So even in mathematics, context can change everything.

That isn't a different context, that is a different equation. Context doesn't really matter, leaving stuff out obviously does matters. You might as well say, 2+2=5 if you add one more. Though 2+2+1 is a totally different equation, than 2+2.

Leaving something out and then adding it back in later doesn't prove math is flexible and changing, it only shows you made an error in the original problem.

Doesn't matter if you believe in logicism or not, that doesn't change that math is logical.

Alric, you're having a hard time here. It helps to have a clue what you're talking about. There were no equations in the post to which you are responding. There were (as I said) various mathematical statements concerning the relation between objects and operators on said objects. The truth or falsity of those statements were dependent upon the context in which they were taken.

Take it over Z or Z/nZ for n > 5 and 2 + 2 = 4. In Z/2Z and Z/4Z, 2 + 2 = 0. In Z/3Z, 2 + 2 = 1

So 2 + 2 = 1 is false in Z but true in Z/3Z.

You think that's weird?

The ring Z/nZ has much more in common with Z than Z does with the rationals. Z/nZ will have (for n not prime) a non-trivial ideal structure whereas Q has no nontrivial ideals. So why is moving from Z to Q no big deal (as laughing man did by switching to 2.000 + 2.000 instead of 2 + 2) while a simple move to finite rings is?

Why don't you accuse laughing man of making up weird mathematical rules? He's the one that's actually doing it.

But you want an equation. Here's one.

x² + 1 = 0

This equation has no solutions with x in the reals but has precisely two (i and -i) solutions in the complex numbers. It's the same equation (it lives in Z[X]. Ok actually the function x |-> x² + 1 lives there but a little conflation is fine in this setting) but taken in two distinct contexts yields two distinct sets of solutions.

So again, context matters even mathematics.


Also, please note that the question of if logicism has achieved its goal or not is not a matter of "belief" any more than the correct proof of a theorem is. If it was done, then it would be done and everybody that knows enough to deserve an opinion would know it. It hasn't been done and hence nobody that knows enough to deserve an opinion would think of stating that mathematics has been reduced to logic.

But you know better? Without knowing what an equation is?

If you say two things are equal to one another that is an equation. So yea, there was equations in the previous posts on this thread.

Secondly I never said math is reduced to logic, I said math is logical. Which it is. The rules flow from logic and all make sense, it isn't random and chaotic or arbitrary in nature.

If you are converting to another system of counting, the math still works perfectly fine just how it is. You just need to covert it. The reason you say all that other stuff, is because you have to, in order to tell people what you are doing, otherwise it become wrong.

Even in your examples, the math is still working logically. Even imaginary numbers tell you something about what is going on in a given problem.

Philosopher Stoned:

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Why does the most accurate idea have to be the one that best propagates?

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This gave me the knee-jerk reaction that you misunderstood the post because I was arguing that in my view right and wrong are useless and in my view we are incapable of judging absolute reality in a truthful way (or rather that an illogical conclusion is just as correct and incorrect as a logical conclusion), we are only capable of perceiving reality to guide our decision making process. My friend argued against the idea that the most accurate idea is the one that best propagates, he claimed absolutists do far better than logicians at propagating. I argued that the most prosperous result is the most feasible way of creating the most accurate model to follow. Neither of us argued that the most feasible result or idea with best propagates is the most accurate perception of objective reality.

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Originally Posted by Laughing Man

I just don't have much tolerance for nihilism because so many who find out what it is waste their intellectual power trying to promote it because its groovy or something like that.

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Then you should learn the difference between epistomological relativism and nihilism. See the above message I sent PhilosopherStoned. Nothing about my argument relates to nihilism because my perception leads me to determine comparative value, I simply don't believe there's any such thing as objective value nor objective right and wrong, nor objective truth to begin with. A nihilist would be someone who see's no value in anything period, possibly because life is an infinite but ultimately purposeless theater. If you want to rant about your disgust of this perception, there's a thread for that. This thread is intended to discuss the concept that logic stands upon its own circular logic, in that logic becomes truth because its logical, but not because it's true. It makes an assumption it has no right to make and the entire concept of logic is based upon a false postulate. Logic is a tool because it implies certain agreements one can use as a means of navigation.

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Actually it makes them objectively wrong because it is beyond logic to show that 2.0000+2.00000 equals anything but 5. Math is based on logic, logic is universal and inescapable. There is no such thing as an illogical mind because we wouldn't be able to perceive it, understand it or interact with it.

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Again, you're leaning upon the postulate that logic is truth without justifying why it's truth. You are containing the entire universe and reality and etc. within one, solitary toolset at your disposal.

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So now you are saying that objective truth being impossible is contrary to epistomological relativism? It Sounds like you need to hash out what you really believe before this conversation continues.

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Or you could stop using strawmen. Perhaps you should reread my post.

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it's impossible to discover objective truth as the subjective observer

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IE

Logical conclusions based on perception =/= reality

PS covered the rest. Props to PS

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Originally Posted by PhilosopherStoned

Z than Z does with the rationals. Z/nZ will have (for n not prime) a non-trivial ideal structure whereas Q has no nontrivial ideals. So why is moving from Z to Q no big deal (as laughing man did by switching to 2.000 + 2.000 instead of 2 + 2) while a simple move to finite rings is?

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protip: The ring Q[X] has much more in common with Z than any of the Z/nZ do. Z/nZ will always have a finite ideal structure whereas Z and Q[X] (or R[X] or C[X]) have infinite ideal structures. Or rather, for any n, one can cook up a strictly monotonic nesting of ideals n deep. Also, they both have an infinite amount of maximal (and hence, being Noetherian, prime) ideals. finally, I would just call Z/nZ Z_n but that involves subscripts. LaTeX makes this stuff so much easier. To get subscripts one has to type tags or use the mouse. In LaTeX it's just _{n}. So much nicer. It should be an easy extension...

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This equation has no solutions with x in the reals but has precisely two (i and -i) solutions in the complex numbers. It's the same equation (it lives in Z[X]. Ok actually the function x |-> x² + 1 lives there but a little conflation is fine in this setting) but taken in two distinct contexts yields two distinct sets of solutions.

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I'm being sloppier than I meant. The function x |-> x² + 1 lives in R[x] not R[X]. It will be different depending on what solutions are allowed. x will belong to Z, Q or R when the equation has no solution and it will belong to C when it does. All four are different functions. I meant that we're solving the equation derived from the formal polynomial X² + 1 which is what actually lives in Z[X] (The ring of formal polynomials over Z). This induces a function A -> A on any algebra, A, over Z. Setting that function equal to 0 makes an equation. So it's the same equation. They're different problems (if you're into taking tests) but it's the same equation. This is even more the case because all homomorphisms in sight have a trivial kernal and can be regarded as inclusion mappings; it's the same 0 (the one that's in Z) that's being solved for.

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But you know better? Without knowing what an equation is?

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I'm being a bit of a hypocrite here giving my view towards psychology (it's getting better) but I'm dead on with economics. Did you know that somebody got the Nobel Prize in economics for an incorrect result? Mathematically correct to be sure (to such an extent as such a thing exists in economics) but it didn't mirror reality. :cackle:

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Originally Posted by Alric

If you say two things are equal to one another that is an equation.

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No, that's a statement. An equation involves an unkown to be solved for.

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So yea, there was equations in the previous posts on this thread.

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No there weren't.

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Secondly I never said math is reduced to logic, I said math is logical.

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To say that 'math is logical' is very informal and hence, in the strict interpretation of the word, illogical. I assumed that you meant that formally, (i.e. in a logical sense) mathematics is logical, i.e. a subset of logic. It's not. Math uses logic (I love a good contrapositive proof myself, can't remember what the logicians call them (arguing the somethingorother I think)) but that doesn't make it logical any more than physics is mathematical. Of course if your primary interest is taking tests (and jumping through other people's hoops) then I suppose physics is mathematical (as long as you can cut basic calc) and math is logical. But whatevs. Math is no more made of logic than a car is made of socket wrenches.

The rest of your post is addressed by pointing out that you don't know what math and logic are and are hence in no position to demand that your post is addressed without educating yourself or asking direct questions. I guess I'm a hypocrite concerning psychology. Hi DuB.


Omnis, I'm fairly drunk right now and in no shape to properly respond to your post) However I disagree with a few of your points (probably just semantics but nonetheless important) and will respond later. Peace.

No, you are totally wrong. Notice the first part of the word, equation. It comes from the word equal. If there is an equal sign and the statement is comparing two values then it is an equation. There doesn't have to be an unknown, and you don't have to solve it. You are totally wrong on this.

Secondly, why are you assuming weird things? I said math is logical as in the rules of math are based in logic. As in the rules act in a predictable way, that are obtained through reason. Everything is orderly connected and thought out. If you prove anything in math, you can go through it step by step and see how it follows in a logical order.

I never said math is a subset of logic, I said math is orderly and makes sense and is based entirely in reason, ie its logical.

It makes me wonder if English is a secondary language for you. Since you don't know what an equation is, and use words in uncommon ways.

Alric, you're probably a moron. I've never seen you say anything intelligent that someone else hasn't already told you. You probably never will. Your mind is far too riddled with assumptions and you think you know way to much to even contemplate doing any such thing. Just letting you know. And it's ok. The vast majority of people are so stupid that we would be living in huts and using fire for warmth if there weren't (very!) occasionally intelligent people to actually figure things out. After that, the stupid people can do stuff. Don't take credit above your class and know your place.

I'll moderately concede that you're right about equations. (although see later where wikipedia asserts that many mathematicians back me up) So include 2 + 2 = 4 as an equation, you can squeeze it into the definition.

Here's wikipedia backing me up: "Many mathematicians[2] reserve the term equation exclusively for the second type, to signify an equality which is not an identity. The distinction between the two concepts can be subtle;" Equation - Wikipedia, the free encyclopedia under the headings "identities".

Here, the second type refers to statements that aren't always true and are only true for certain values of the unknowns. This implies in particular that there are unknowns (i.e. variables, i.e. independant variables) in one of the expressions or they would be constant functions and hence the relation would be true for all values.

That's the way I was educated at least.

Second, I'm not assuming weird things. I'm assuming mundane things that you don't have a clue about but that are at the core of your beliefs. How are you so sure of them if you don't even know. I'm only talking undergraduate (or maybe first year graduate) stuff here.

You were asserting that math is logical. Formally it's not and that's what matters in math. You're stupid. I don't have to respond to you. You're beneath me and I'm better than you, you subhuman monkey. :okbyenow:

P.S. It doesn't matter if english is a second language for me because the second you wanted to start talking about math we stopped talking in english (where it's impossible to talk about math other than in the most masturbatory of ways) and started talking in mathematical enlish. This is where precision lays, this is where the power of the rational materialist model lays and this is where you substitute religion for clear thought and hard work.

I hate people that think common sense is a good thing. They're almost as bad a creationists! Common sense is a prison in which small minds rot till the body that manufactures them dies.

Yea I am stupid, yet you need to look up 'equation' on Wikipedia in order to understand what it is? Then even though Wikipedia proved that you are an idiot and were wrong you tried to twist the wording to some how say you are right. Yet you are still wrong because your are taking the quote out of context.

If you think 2+2=4 is an identity and most math people would call it an identity rather than an equation, then I think you are just hopeless. You are obviously just pulling things out of your ass.

What they are talking about on Wikipedia is that something like A*0=0. That is an identity. As opposed to an equation which is A+0=0, which is an equation. BOTH are equations, but if you want to be more specific, one is an identity(true for all numbers), and one isn't an identity(true for one one set of numbers).

You can insult me and call me stupid all you want, but even a 5th grader knows what an equation is, which apparently you do not.

I'm not twisting words or anything. I'm not taking it out of context. Learn to read.

There are just two different definitions in current use. I was raised with one of them.

Subhuman is harsh but I stand by the rest.

And that is how I can tell you are just a poser, and don't actually know squat. You read it incorrectly, and if you knew the topic you wouldn't have done so. You weren't taught that basic arithmetic equations are called identities.

Identities are basically rules that work for all numbers, no one would ever call 2+2=4 an identity, because it isn't one. You just saw a loophole, a way out of looking like an idiot for saying it wasn't an equation and tried to use it. However you totally failed because it doesn't work the way you think it does.

You can try to twist things all you want, but no one is going to believe that you were taught that arithmetic problems are called identities. I would of just chalked it up to you making a simple mistake with words, since everyone makes mistakes, but then you kept arguing with me that it wasn't an equation but an identity. So obviously it isn't a mistake, you are just clueless.

Actually, asshole, 4 is a "constant function". That's how it is because it's usual to regard anything as a function so that an equation would be f(x) = g(x) and that would be an identity if f(x) = g(x) for all x. So 2 + 2 would be the constant function 2 added to itself and we have something like f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4.

Look up constant functions. And accept that you don't even know basic math or everything I've said would be comprehensible. You've just learned some algorithms. A computer could do anything you could...

And what about swearing that math is logical while refusing to acknowledge that it's not, formally, logical. So you have to go beyond math and logic to talk about them but then try to act like you talk with the authority of them both.

Who's weaseling?

Moron.

I still don't regard identities as equations (and 2 + 2 = 4 is most definitely an identity) and wikipedia supports me in claiming that many mathematicians don't.

You are either trying to be obnoxious, or you are really are totally clueless. I know what functions are, and I know everything you have been talking about on this thread. That is how I know you are totally wrong, and what you are saying doesn't make any sense.

You could write the problem as f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4, but that doesn't help your argument at all. Even written like that is still not an identity. Like I said identities are more like general rules, not specific equations, and that problem right there is a very specific equation.

And stop saying wiki backs you up, because it doesn't. We already know you suck at math, but you are proving that you suck at reading too. So let me educate you on reading.

Here is what wiki says, "Many mathematicians reserve the term equation exclusively for the second type, to signify an equality which is not an identity."

Okay you read that, but here is your problem. You didn't read what it was referring to when it said the "second type" of equation. So lets read what the second type of equation was.

"However, equations can also be correct for only certain values of the variables. In this case, they can be solved to find the values that satisfy the equality."

So here is your problem once again, f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4.

What?! Your equation is only correct for certain values of the variables? When f(x)=2 and when g(x)=4. I know you are a little slow, so read the post over five or six more times if you need to. Wikipedia actually says you are wrong, and that the problem is an equation, not an identity.

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Originally Posted by Alric

You could write the problem as f(x) + f(x) = g(x) where f(x) = 2 and g(x) = 4, but that doesn't help your argument at all. Even written like that is still not an identity. Like I said identities are more like general rules, not specific equations, and that problem right there is a very specific equation.

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LMAO. So cos²(x) + sin²(x) = 1 isn't an identity? Better inform all the trig teachers. It seems pretty specific to me. Or it at least removes the assertion that 2 + 2 = 4 can't be an identity because it's "a specific equation". Not that I think it's an equation but it is by your definition.

Pressed for time right now. For fun, I'll come back and correct the rest of the post later.

But will you at least admit that the statement that math is logical is neither a mathematical statement nor a logical one? You seem to be ignoring that and that's the primary point.

That is a trig identity because it works for all numbers. It isn't specific, but extremely general. If x is 5 it works. If x is 7 it works, if its 320, 76, 2, 5.4, 1/2, pi, 1,000, a million, it doesn't matter. That all work. I told you like five times, if something works for all numbers then it is an identity.

What is so hard to understand about this concept? If it is a general rule and you can plug anything into it and it remains true its an identity. If it only remains true with only a very specific variable then it is an equation.

Hence the trig identity which has an infinite amount of possible x's is an identity, when the formula you gave before that only had a single possible x, is an equation.

To answer that other question no. Obviously saying math is logical isn't a math statement, but I never claimed it was, because it has no math in it. It is however logical. You have not put forth anything to suggest that math isn't logical, and only stated it as your opinion. However, since you apparently don't know much about math, and your arguments are extremely chaotic, random and nonsensical, I don't really think your in a position to offer opinions on logic or math.

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Originally Posted by Alric

That is a trig identity because it works for all numbers. It isn't specific, but extremely general. If x is 5 it works. If x is 7 it works, if its 320, 76, 2, 5.4, 1/2, pi, 1,000, a million, it doesn't matter. That all work. I told you like five times, if something works for all numbers then it is an identity.

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We're not disagreeing that if something works for all inputs then it's an identity. That's basically the definition of an identity: it's true across it's entire range of input values, i.e. across its whole domain.

Now disregard constant functions and consider 2 + 2 = 4. Where are the independent variables? There are none. Hence its domain is the empty set and there is no value in it's domain for which it's false. Hence it's an identity. Remember the negation of "is true across it's domain" is "there exists one element in its domain for which it's false". There are no elements in its domain so there is no way in which there can be an element over which it's false.

To phrase this in terms of constant functions (which you already agreed to using) if f(x) = 2 and g(x) = 4 then regardless of the domain (i.e. the elements from which we choose x) then f(x) + f(x) = 2 + 2 = 4 = g(x). Hence any which way we choose x, the statement is true and we see that it's an identity.

So either by the definition of a constant function or by vacuous truth, 2 + 2 = 4 is an identity.

For elucidation, let's consider 1 = 0. The same considerations as above show that this is an equation by the definition supported by 'many mathematicians' as explained in the 'identities' heading of the 'equation' wiki article. In particular, by either vacuous truth or with constant functions, there is no way in which we can choose some dependent variable to make that true.

So you don't know what you're talking about.

You stepping beyond your intellectual means here is of little interest to me here (though I may use this later as an example of how the majority of people have no capacity for logical or original thought). If I am a poser then Xei (at least) would freely point it out and not rise above his station in doing so.

For the sake of amusement, could you prove that if A is a ring then choosing an element c of A and making the substitution X -> c induces a homomorphism A[X] -> A? Here A[X] is the ring of formal polynomials over A. If you understand everything I've said then surely you understand that. Unless you're the poser here. That's too trivial of a problem to be assigned in books. However it's a fact that needs to be referenced and hence stated. Therefore it's often stated in books but not proved. The author would simply assume that the student is reading the book with a pen and paper in hand and is hence ready to prove any such trivial statements if such cannot be done purely in mind. A simple sketch of the proof will suffice to show that you know what you're talking about. There's no need for the sort of formality that I usually prefer.

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Originally Posted by Alric

To answer that other question no. Obviously saying math is logical isn't a math statement, but I never claimed it was, because it has no math in it. It is however logical. You have not put forth anything to suggest that math isn't logical, and only stated it as your opinion. However, since you apparently don't know much about math, and your arguments are extremely chaotic, random and nonsensical, I don't really think your in a position to offer opinions on logic or math.

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Hmmm. I referenced the fact that logicism has, to the present date, failed. Can you support the fact that mathematics is logical or is that just your opinion as well? If the statement that mathematics is logical is just an opinion, then it certainly doesn't carry the weight of mathematics or logic behind it, does it? It's basically just the preconceived notions of someone that doesn't know much about math (at least not enough to solve the trivial posed problem) or logic, right?

For the sake of completeness, it's not quite true that 2 + 2 = 4 is false over Z/2Z, Z/3Z or Z/4Z for the simple fact that 4=0, 4=1 and 4=0 respectively over those rings. It is true that 2+2 = 1 and 0 over the specified rings however. You could have pointed out this discrepancy easily if you really know everything that I've been referencing.

punk

Sorry.

Plebeian punk.

Using your logic, all equations(that actually exist as valid equations) are identities and clearly that is incorrect. In fact, that is exactly what you defined an equation as, since no equation would have a number within it's domain that is false. The definition of a domain, is all possible numbers that can be inputed into an equation. If some number is false, it can't be plugged into the equation and thus doesn't exist within it's domain.

In fact, 1=0 could be labeled an identity, because it has no domain and thus no varible within it's domain is false. So once again I proved by your own logic, your an idiot and totally wrong.

You seem to be missing the entire point of what identities are, and why they are seperated out as a subgroup. Which strongly suggests you are just arguing based on definitions you read some where, and not on actual knowledge of the subject.

The point of identities is that they are used as rules. There are identities that don't exist for all real numbers, and many have specific exceptions within them. However they are patterns that help people undersand and solve the different rules within math.

No person would think 2+2=4 is a special rule for solving math, and thus no person would ever call it an identity. For the sake of arguement, even if you did want to call it an identity, you would have known what I meant when I said equation, and you didn't seem to be aware of it at all.

For someone who claims to be very specific and precise you are using a lot of words in the wrong way, without having a solid grasp of what they mean. A person who needs to look up the words equation, and still doesn't grasp the concept is in no position to be trying to put others down.

We are just going in circles though. You keep making stupid arguments and then insult me, hoping that the insults will some how make your nonsense appear more valid, but then I point out the huge obvious flaws in what you are saying, and we go around and around.

My main point is that math follows set rules, and thus is logical and orderly, and that math doesn't arbitrarily changed based on peoples perspective. You can do that by actually following the rules and seeing that they do work.

So what does it mean for a number to be false? Or for a variable to be false? Would you care to clarify?

We are precisely going in circles because you have no idea what you're talking about.

What about the problem? I'll give you a few more posts and then solve it for you. Would you care to issue a challenge in algebra which is what we're talking about?

That it doesn't exist. There are no numbers within a domain that don't exist, because being within the domain implies that it does exist.

Also, the rule 2 + 2 = 4 is useful precisely when one has an expression including 2 + 2 that one would like to simplify. Don't let the point that it's trivial fool you.

One could say the same thing about cos²(x) + sin²(x) = 1. The point is to allow one to simplify expressions containing the left hand side of the identity down to 1 or to introduce the left hand side into an expression involving 1 in hopes that something will cancel.

You're seriously lost aren't you?

Go by math.stackexchange.com and ask if 2 + 2 = 4 is an identity. LMAO

The trig identities are useful as a rule because they help in a lot of situations. With 2+2=4 you would never memorize it as a special rule, you would just do the insanely easy addition.

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Originally Posted by Alric

That it doesn't exist. There are no numbers within a domain that don't exist, because being within the domain implies that it does exist.

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So the domain is empty (not "doesn't exist"). Hence the statement 2 + 2 = 4 is true for all elements of its domain vacuously. Like I said, find an element of its domain (either the empty set or any set that you want to define a constant function from) for which it's false. This is vacuous truth and is one of the more basic issue that beginning math students must grapple with. You're sure gung-ho about the virtues of math and logic for someone that doesn't understand it.

So is the statement that math is logical your opinion or a fact? It doesn't sound like you're using "logical" in a very logical manner. Normally if something is logical one would expect it to be provable using means from some system of logic.

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Originally Posted by Alric

The trig identities are useful as a rule because they help in a lot of situations. With 2+2=4 you would never memorize it as a special rule, you would just do the insanely easy addition.

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So an identity has to be something that you memorize as a special rule? Where does it say that on wikipedia or any other source?

You seem to be missing the point. If you make the claim that an identity is an equation where all the values within its domain exist, then by default all equations are then identities because domains are just numbers that exist for the given equation. That is the claim you made, and it is incorrect.

If you actually read the definitions of identities, and the wiki example is fine, you would see that it is speaking of the variables not the domain. If any number works then it is an identity.

You switched 'any number' with 'any number within the domain'. You can't do that, because they have different meanings. The wiki definition also specifically includes the word variables, which 2+2=4 has no variables. So how can you plug any number into a variable that doesn't exist? You can not. And even if you rewrite the equation, which you tried to do, the variables still did not accept any values except the specific ones you gave.

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Originally Posted by Alric

You seem to be missing the point. If you make the claim that an identity is an equation where all the values within its domain exist, then by default all equations are then identities because domains are just numbers that exist for the given equation. That is the claim you made, and it is incorrect.

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I didn't say that all values within the domain exist, I said that it's a mathematical statement which is true for all values within its domain. That's the claim I made and it's correct.

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If you actually read the definitions of identities, and the wiki example is fine, you would see that it is speaking of the variables not the domain. If any number works then it is an identity.

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A free variable is just an element of the domain. So to say that it's true on a specific domain or an a free variable that takes its values from that domain is the same.

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You switched 'any number' with 'any number within the domain'. You can't do that, because they have different meanings.

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Yes I can because 'any number' is just shorthand for 'any number within the domain'. Or really, any element. There's no need to restrict ourselves to numbers.

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The wiki definition also specifically includes the word variables, which 2+2=4 has no variables. So how can you plug any number into a variable that doesn't exist? You can not. And even if you rewrite the equation, which you tried to do, the variables still did not accept any values except the specific ones you gave.

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Here's the relevant quote:

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Originally Posted by wiki

One use of equations is in mathematical identities, assertions that are true independent of the values of any variables contained within them.

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Note the use of 'any'. So it's true that 2 + 2 = 4 is true regardless of the values of any variables contained in it. This is again the concept of 'vacuous' truth. Again, for it to not be true that 2 + 2 = 4 is true regardless of any variables, one would have to exhibit some variable contained in it and some value which that variable could assume that would make the statement false. But there is no way to do this because there are no variables in sight. Hence it's vacuously true that it's true for all values of all variables contained within it and is hence vacuously an identity.

Do you understand vacuous truth?

What about the problem? Like I said, it's an easy one if, as you claimed, you knew what I was talking about. It should be easy to back up. You're not a poser are you?

What about the important part? The statement that 'math is logical' is just your opinion, right?

To recap I called an equation, an equation. You insulted me and called me stupid for thinking an equation could actually be called an equation. You admit that it was an equation, but insulted me some more and in an attempt to save face for being wrong you made the claim that a lot of people wouldn't call it an equation. I disagreed, you posted a bunch of crap. I even admitted that it could technically be consider an identity but that is so pointless no one would ever call it such, we argued some more and here we are.

I think the real lesson here, is that I shouldn't bother trying to debate you when you are trying to act like a troll, and you were definitely acting like a troll when you personally insulted me for saying something you admitted to being true.

Any way I posted the question on that site, and got pretty much the answer that I expected to get. People said it is technically both, but that it isn't a very interesting example of either. So you can call both, or call it whatever you want, since no one cares. Problem solved.

As for the math logic issue, that is simple. Give an example of a illogical math problem that doesn't follow reason, yet is still correct. You claim math doesn't follow reason or logic, then there should be some reason you believe that and you can give an example.

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Originally Posted by Alric

To recap I called an equation, an equation. You insulted me and called me stupid for thinking an equation could actually be called an equation. You admit that it was an equation, but insulted me some more and in an attempt to save face for being wrong you made the claim that a lot of people wouldn't call it an equation. I disagreed, you posted a bunch of crap. I even admitted that it could technically be consider an identity but that is so pointless no one would ever call it such, we argued some more and here we are.

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That's a bad and biased recap. You called something an equation. I knew it to be an identity. According to the only definition I've actually run across in books (most consider it known) a statement with an equal sign in it is either a definition, an equation, or an identity. But this is already an identity. Hence it can't be an equation. An equation is something one solves.

You were already being insulting by saying that everything I say is 100% wrong. Far from it.

So I pointed out your error with about the same level of insult. Maybe a little more just to punish your insolence. You persisted and I looked it up on wikipedia. I'm not in the habit of learning my math from them (I prefer textbooks) and they gave a stupid definition. We can discuss why an identity shouldn't be an equation later and I intend to post an answer to your question on math.stackexchange.com that argues as much. We'll see what the community decides. I love upvotes and downvotes. I intend to get a few of each.

I admitted not that it was an equation (again, who's distorting truth here) but that it could be considered an equation under an inferior definition. Surely an equation is something to be solved. That's the intuition that the definition should capture. For something to be solved, i.e. for the values on which it's true to be sorted out from the values on which it's false, there should be some non-trivial amount values for which it's not true.

The fact that wikipedia plainly stated that "many" mathematicians consider this to be the defining feature of an equation backs me up. So you tainted your "recap" by asserting that it was me and not wikipedia (with a reference backing it up) making that claim. Again, who's distorting reality here? I guess we both are because that's the way of things but who's actually trying not to?

So I got insulting after you botched understanding a simple statement. Or rather, I got honest. I told you what I really think. I stand by it too. You're an excellent example of how stupid people can stumble upon largely functioning world views by pure cultural osmosis. No rational thought required.

Or can't you understand that the definition of equation I learned with is just imposing a partition on the set of statements that you're used to calling equations? It's a simple definitional matter and I conceded it long ago.

We've been arguing about if it's an identity or not.

And that's only because you called me a poser. Poser. Where's the solution to that trivial problem that you'd be able to solve in a heart beat if you actually knew what I was talking about back when you claimed you did? Of course you just called it a bunch of crap so I guess you are a poser.

No matter, I never thought you were intelligent. You're good for explaining basic things to fundamentalists and new-agers that somebody else already explained to you. You get lost when you have to think. That's fine, most people do. I do deeply regret thinking of you as subhuman. We're all good at different things and we're all human (and you're no more of a monkey than I am) and it's okay that you can't think. Really if only one out of a hundred people can think, that's alright as long as the other ninety-nine people know who can think. That's the problem.

Also, where did you admit that technically it was an identity? Could you quote that? I think you're lying though I haven't checked since you made that claim.

Moreover, one doesn't consider x to not be X if x satisfies the definition of X because one doesn't find it interesting that x is X. One just doesn't use the fact. One doesn't say that it isn't. Which you did. Poser.

Who's saving face?

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I think the real lesson here, is that I shouldn't bother trying to debate you when you are trying to act like a troll, and you were definitely acting like a troll when you personally insulted me for saying something you admitted to being true.

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No I insulted you for not admitted that what I said was true. Even after I gave you the link, you still couldn't deal with the fact that there were two definitions. For you to have done that, you would have had to see that it was an identity but you didn't see that till you asked the question like I told you to.

And as I said you already insulted me. Everything I say is 100% wrong. I can't think of a worse insult than that.

The lesson here is that you should mind your p's and q's and stay within your station. Are you an artist? Then you should make art. Are you a plumber? Then you should plumb.

You are most definitely not a thinker and hence you should not attempt to think. Or you should at least take remedial thinking classes. Please don't vote. Unless you agree with me.

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Originally Posted by Alric

Any way I posted the question on that site, and got pretty much the answer that I expected to get. People said it is technically both, but that it isn't a very interesting example of either. So you can call both, or call it whatever you want, since no one cares. Problem solved.

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Hmmm. Both answerers have said it's an identity as I said and you denied. Did you expect to be wrong? I would understand if you did.

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Originally Posted by Alric

As for the math logic issue, that is simple. Give an example of a illogical math problem that doesn't follow reason, yet is still correct. You claim math doesn't follow reason or logic, then there should be some reason you believe that and you can give an example.

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Yes here's the meat of it and again, here you're distorting my statement. I never said math wasn't reasonable, I said that math wasn't logical.

As for responding to your challenge, you'll have to formulate it properly. What is an illogical math problem? I would take an illogical statement to be an inference which violated whatever rules for inference were in place in whatever logical system was being employed.

At any rate, it's not even a valid challenge. Are all things logical until proven otherwise? If that was the case then surely the challenge would be valid and one would have to produce an example of an illogical mathematical theory.

The problem is that people can't even figure out how to phrase mathematics purely in terms of logic. One can surely apply logic to specific statements that occur in the process of engaging in mathematical proof but one can do the same in life. Does that make life logical?

It seems that the default assumption must be that things are not logical until proven otherwise.

Why can you not admit that your statement that math is logical is neither logical (i.e. taking place in a formal system of logic) nor mathematical and is just your opinion? Who's trying to save face? I have no problem admitting that it's a valid opinion but over my dead body will I watch a religious zealot (even one of my preferred religion) tarnish the name of mathematics by attempting to make non mathematical statements with the force of mathematics.

But okay. For the sake of argument, I'll take your challenge in a colloquial manner and just show you this: banach-tarki. This is a well known result and is known to far more people than can understand even the intuition behind its proof.

It is, in the sense which you use the word logical, totally illogical.

It works because of the Axiom of Choice.

Was mathematics logical in the sense that you mean it mathematicians would long ago have considered this to be a proof by contradiction that the Axiom of Choice is false.

But it's not logical in the sense which you seem to mean it.

If you mean it in some other sense, then what is that sense if not that it can be stated entirely within some logical system, i.e. that it can be reduced to logic as I had first assumed you meant?

Oh yeah, that's just a bunch of crap.

Do you like Budweiser too?

I am not going to get into that debate again, anyone can read the thread and come up with their own conclusion on weather or not normal people call that an equation or not.

What I will say, is that I never said you were 100% wrong(at least not about the stuff you said originally). 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. Your context argument doesn't even work here, since you are talking inches and feet which implies a specific context and measurement.

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. 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.

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Originally Posted by PhilosopherStoned

First off, is it 2.000 as a real number or 2 as an integer?

2 + 2 = 1 is a true statement. Taken modulo 3.

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

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Originally Posted by PhilosopherStoned

You should check out logicism. Essentially you are making a religious claim.

tl;dr: math has not been logically reduced to logic.

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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.

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Originally Posted by PhilosopherStoned

There is no such thing as a logical mind either.

More on point though, your assertion that it doesn't exist (i.e. "no such thing") is itself based on the assumption that the only way for something to exist is if we can percieve it, understand it, or interact with it. This assumption isn't even necessary for rational materialism to function as one of the most distinguished of a number of possible models of reality. However, there's no way to have it be The One True Way though without this assumption.

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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.

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Originally Posted by PhilosopherStoned

Science places value on specific scientific statements. It doesn't say why one should do something or if it's good. It says if the statement is correct or not. This is a valuation. With statistical inference it can say how likely it is for the statement to be correct. Statements of biblical creationism are rejected by the normative process of science and valued far less than statements that take place within the scope of evolutionary biology. Some of those will even be "de-valued" over time.

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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.

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Originally Posted by PhilosopherStoned

Any of the other number of sentient beings that exist. Aside from that (purposeful?) misunderstanding though, I was referring even to measurements made by two distinct humans. It is a matter of faith (assumption) that if they both make the same measurement correctly then they will get the same result. Like I said, it's a useful assumption but it is still an assumption.

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It is not a misunderstanding if I am asking a question. I am not making a statement about what you are trying to argue but inside asking you to further explain as to what you are trying to say. 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.

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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.

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

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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.

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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.

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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.

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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.

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Originally Posted by Laughing Man

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

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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.

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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.

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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?

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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.

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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.

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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.

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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.

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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.

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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.

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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?

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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

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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.

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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?

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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.

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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.

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Originally Posted by LaughingMan

You are already assigning your own values to the science.

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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.

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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.

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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}.

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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?

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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.

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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.

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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.

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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.

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

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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.

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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.