kriminal99

Thats a hard one. To begin with, it seems like a little clarification is needed to determine what is "different". Is a match of the same cards at different locations different? Also is it ok to assume that the first deck of n cards contains the same cards in it as the second deck of n cards?

DOH I put my thread like this in the philosophy forum. I didn't realize there was an education forum. Thread in philosophy forum

There are more receptors in the brain, but the heart still has some and sure enough you feel things located in your heart sometimes... What is meta claiming beyond this exactly?

Any time you see infinity in a math equation just replace it as limit x-> infinity with the x where the infinity was. The subconsious meaning of infinity is "always growing". Therefore writing like 1/infinity is equivalent to saying 1 divided by a value which constantly grows, so really all you can do is take a limit. Where a limit is just to say as x gets closer and closer to a certain value and you have some function of x, then the function will approach some value z until a point where you can no longer distinguish between f(x) and z given a set amount of precision (decimal places you can monitor).

Well, to get my argument just ask yourself how a behaviorist comes up with a factor he is going to test to see if it is correlated with a certain behavior. At first you might just say intuition, or random guessing, or whatever else, but as the factors which are correlated to certain behaviors become less and less obviously correlated to the responses you need more and more complicated reasoning to come up with theories to test. Ultimately you would have to have a complete theory of mind to know what factors to examine.

We are not yet ready for that... We need to finish philosophy in our current state first before we progress to that type of thing.

If someone said that to me I would just calmly ask them how they came to that brilliant conclusion. Especially considering that it isn't really known completely what composes intelligence or "smartness"...

But then you are doing something dishonest. You are depending on errors in the way people think and the weaknesses of induction to cause people to have faith in your "non reality founded" belief set. Anotherwords on day 1 of math class you tell them 1 +1 = 2. They see this is true in their every day life. Then you tell them a bunch of other stuff they can see in their life. Then you come up with all these random terms and ways of thinking that are not optimized for practicality or based on reality. But because of the way people think they are reluctant to challenge your claims... Even though the stuff you told them that was helpful could have been part of many mathematical belief sets. It also might have been MADE by someone who would follow another belief set because that person believed it was somehow better, and you may just be using it in your belief set to decieve people into thinking you are an authority so they won't doubt you. (You isn't pointing to any one person exactly) Even as you say we are not claiming any connection to reality, you are relying on people to respect you as a mathematician, which is dependent on people's belief that what you have to say is the not only useful, but the best way of thinking about it. If you are constantly searching for ways to optimize and revise the mathematical belief set, then you are doing the best you can and there can be nothing wrong with that. Even if every mathematician does not do so but some sort of specialize in it, and then the rest just remain open to these ideas and consider their worth then there can be nothing wrong with the situation. However if you, for selfish emotional reasons, reject all alternative ideas, and fail to investigate new ways of thinking, then what you are doing is basically brainwashing. The issue I have with religious groups is their methods of persuasion. If youve attended any religious sermon before you probably know that the majority of their arguments are metaphors of one form or another, and they make no argument to connect the two situations being related in the metaphor. Anotherwords, they are circumventing each person's faculty of reason in order to get them to submit to their views. In this sense mathematicians are behaving in the same way. Of course if one day people become more aware of their weaknesses and how to get around them this will become less of an issue. The only ideas which will ever gain any social signifigance are those which are perfectly logical. I am working towards this myself, but I have no way of knowing if I or anyone else will ever be succesful in this. The cases where -1 "has" a square root is no doubt a result of an earlier lack of connection between mathematics and reality. Anotherwords for example if you try to model something in real life space where logicaly there can be no reason why the height of a location from an imaginary axis can not have a square root despite the fact it is behind wherever you put the imaginary x-axis. So if you want to keep thinking the way you have been of course you have to make up ideas like sqrt(-1) (which may in some way contradict themselves) in order for your belief set to be able to accoplish something in reality. EDIT: When I was talking about contradictory statements, as I said before the belief set may be coherent. (Meaning if you think about it a certain way, the statements are not contradictory) However when you fail to make a complete connection to reality, but you still want to accomplish certain things in reality using your belief set, you end up having to make silly statements as I mentioned before, or at best end up having to redefine common terms to suit your needs. Also if you begin changing things in a belief set to suit any need other than consistency, then you are going to end up with contradictions even within your belief set. If the math belief set was perfectly grounded in reality, then the need to accoplish things in the real world and the need for consistency would be one and the same.

heheh Uh I think I didn't get my point across really well... Its kind of hard to put into words but my point is that the subconsious definition of time is "difference between observable events" We have an internal clock so if we don't see anything going on outside of us (and I mean absolutely nothing changing) we can still gauge time by this. But the point is time would have no meaning if nothing was changing anyways.

Thought experiment: You stare at a clock, and nothing else is moving, nothing changing, no internal clocks either (or imagine all you have is your internal clock). The clock ticks once, and then again but the second time a longer amount of time passes before it ticks. Would you have any way to tell that the second tick took longer before it happened? How could you? Whats the point? The subconsious definition of time is something like the difference between events. The smallest possible unit of time is the smallest amount of time in between two events. The smallest possible unit of time recognizable by a human depends on the physical nature of the mind (refresh rate? frequency?)

I figure what the greeks probably couldn't fathom (and with good reason) is how the rational numbers could be dense and yet not contain all possible numerical values. That is a logical contradiction. Of course irrational "numbers" aren't really numbers at all they are just non-mathematical infinite algorithms for creating numbers, motivated by the need to measure lengths in directions they already shrunk into infinitely small points in their primitive coordinate system (or similar needs)... Even if there was no alternative to this system, there would be no need to call them numbers since practically they are only ever treated as rationals - the result of said algorithm after following it to a certain point where the decimal of the precision you want no longer changes... What I am arguing here is that mathematicians, to have to get around their contradictions, end up having to make statements like "a number isn't really a number its kinda like a number but has this that and the other attributes instead" and other such gibberish. In whatever warped world this eventually puts you in, it might even be said that their belief set is coherent, but they are still contradicting common terms and getting farther and farther away from being able to claim that math is in any way motivated by reality. (Which eventually would make mathematicians religious fanatics as opposed to bastions of reason) I can't have pi apples because theres no such thing (in the real world) as a perfect circle, perhaps because theres no such thing as an infinitely small length... and therefore no such thing as a ratio of a circle's circumference to its diameter... @ Matt IMO The numbers that actually exist are the natural numbers alone. We have no reason to believe that anything exists in infinitely small quantities. Without those, any fraction is really a discreet natural number system on a different scale. But then we might use rational numbers to avoid scales where we have like 2000000000 molecules of water for a subjectively small amount of water. IMO Irrational numbers are not numbers, but rather as described above. Once defined to a certain precision they reach the point of discreet units (and decimal places of the irrational number past that point become irrelevant), and if we knew how far they could be broken down on the original scale then they could just be considered rational in that scale. If a logical calculus is effectively created (I know what types of problems have been run into trying this and why) then "irrational numbers" might eventually be considered objects of this system rather than numbers, and numbers will be left as simple quantities.

If you are talking about imaginary numbers other than to say that they have no relevance and do not exist then one can assume you believe they have some relevance. So it seems we can get a question from his original statement after all... And to answer this question I think it is a contradiction. I realize I misread your original post though, grime... @ zap's post- This is exactly what I meant by mathematicians often trying to redefine logic... You can't give something a definition that contradicts the definitions of the composing ideas.

Thats called human nature perhaps we should instead be questioning why we think we should care about everyone else to begin with.

Psychology is for the most part an ill-concieved misapplication of the ideas that allowed people to succesfully investigate the classical sciences... The difference for the most part being the lack of ability to directly test the outcome of every question they might want to answer. The truth is there is plenty of information contained in common experience to answer any (non-physical) question about the human mind... but you have to know what to do with it.