Fer chrissakes, Timothy, enrol in a Phil 100 course.

"If its any help, the "number" of points inside a cube is the same as found on one of its defining edges (lines)."

Can you develop that a bit further? Points in any continuum are infinitely many.

"If there were a finite number of things on 3 axises, could that same information be represented in a single line?"

Yes indeed. You might read up on Georg Cantor, who did a lot of work in this area.

"It wasn't until they shifted their perspective of mathematics from "truthbearer" to "useful tool" (roughly) that negative numbers started to become accepted. And for good reason, they clearly work and make mathematics more pleasant to work with."

I think this answers your own question, Jerry. What is the square root of -1? We haven't a bloody clue, so we call it "i" to disguise our ignorance. Funny thing is, engineers use "i" all the time to build suspension bridges and skyscrapers which safely carry thousands of us every day. It's just our way of recognising that the universe is cleverer than we are. We are relatively stupid beings, but (paradoxically) we are intelligent enough to discover interesting things we can't understand.

"Being able to reason in exactly the right way may be useful for some people, but not all."

Tobias, can you even hear the words which are coming out of your mouth? In what way could "wrong reasoning" possibly be useful to any human being?

I'm sorry, but isn't this supposed to be a mathematical philosophy page?

Ok,,, I am familiar with expressions like btw and imho and fyi, but I would never have guessed that "grok" means "get the picture"...!

But Sam26: it is always a tactical mistake to ask members to watch a video. Much better to summarise the argument of the video in 100-200 words, and include a link to it in your post, for those who want to pursue it in more detail. Nobody is going to invest 1.5 hours in watching a video which may or may not be relevant to their philosophical interests.

Can I take this opportunity to remind contributors that this is a mathematical page, and we are discussing polarity in the purely mathematical sense?

To return to mathematics for a moment, polarity first becomes significant when we develop the relational number line out of the natural number line. The relational number line, the line of the negative and positive numbers, is sometimes (confusingly) referred to as the "integer" line; I prefer the term "relational", because it more accurately captures what is important and interesting about this particular number line.

Whereas a natural number is the name of a set, by adding a polarity to the number, we transform it into a quantitive relation. In the context of the "relational" number line, the relation is obviously to 0; -2 points to the value which is 2 less than 0. In any other arithmetical operation, the relation -2 points to the number which is 2 less than the preceding number; so, 0 - 2 = -2, but 5 - 2 = 3.

I remember that Winifred Atwell was a wonderful piano player... or am I thinking of a different Atwell?

If you have been bitten by a dog on your only encounter with a dog, then of course you are wise to treat all dog encounters with caution in the future. The fallacy in your reasoning is to suppose that your response to a single encounter can have any connection whatever with inductive reasoning.

"If all the numbers in your calculations are such that they cancel out and leave you with a nice whole number answer, you're (almost) guaranteed to have solved the problem correctly."

I would be curious to know what argument from mathematical philosophy supports this assertion? I can see a sense in which one could argue that set theory revolves around "nice whole numbers", but I am not sure how one might apply it to quantum mechanics or relativity theory.

I think this is a very wise analysis.

What are the 6th and 7th Dedekind/Peano axioms?

"grok" is a philosophical term I haven't come across before...

Assuming this is a current post...

Please try to explain your thesis in natural-language terms, in the way that Bertrand Russell did in his Introduction to Mathematical Philosophy, for example. There are many competent mathematical philosophers reading the forum who aren't necessarily proficient in a system of logical symbolism.

I do not have the expertise to address your post, Newberry, but you will find that, like me, there is nobody reading this forum who is actually competent in mathematical philosophy.

Philosophically we have much to learn from the bamboo. The bamboo bends before the breeze, but survives the typhoon.

Why do you say it's obvious? I suppose "I think, therefore something exists", could be considered as self-evident. But that isn't what you mean, because you speak of OBJECTIVE truth (ie something which would continue to be true, even if I personally didn't exist.)

"Reality must have non-caused events" - if you sincerely believe this, any textbook of introductory theology will satisfy your needs. If you are commited to the pursuit of truth, however uncomfortable the consequences, enrol in a philosophy 100 course.

You need to express more clearly which "properties" you are referring to, I think. The simple arithmetical operator <> already expressess a non-equivalence of the property of numerability. On the other hand, if we wish to distinguish the property of "oddness", <> will not distinguish between 3 and 5.

I'm sorry, jancanc, but I am not sure what question you are asking here? Everything in your post is correct, I think. What exactly are you asking?

"Studies suggest that we are gradually becoming less intelligent."

I think the average philosophy forum thread would certainly support the contention. Not this thread, especially, but certainly the average.

How about an elephant hanging over a cliff with its tail tied to a daisy?

How about the question: does God love a thing because it is good, or is it good because God loves it? Presumably one can be ruled out - but which?

I think this thread may be re-inventing a 140-year-old wheel; if you google "the eternal recurrence", or "Henri Poincare", you should find some informative links.

(and unfortunately, few mathematicians are really familiar with any of them). — alan1000


"Is this opinion or fact? Please state your references if the latter. "

My apologies! I was too facetious.

Thanks for your help! My reading so far has been fairly haphazard. This should allow me to put some system into it.

I'd appreciate it, I'd like to read up more on this topic area.

Thanks for your detailed and considerate reply, TonesInDeepFreeze. I need some time to digest it, as I'm a newcomer to this area of philosophy!

Marigold23, your question is expressed in such general terms that it is impossible to answer in less than 5000 words. The answer depends upon the nature and circumstances of your hypothetical state.

What is the average standard of education? Population density? Natural resources? How big an area does it cover? Does it exist in a 'cockpit' area, like Belgium or Palestine? What are its relations with its neighbours? What are its previous traditions of government? Are there internal ethnic tensions?

Is there a way to resolve Russell's Paradox without resort to Type Theory? Can it be resolved by argument from the axioms of set theory?

I think you should just go with the flow for the next year or two at least, Daniel. Let's face it, your intellectual life is currently a dog's vomit and your philosophical consciousness is a toilet. One thing that even the cat at home knows is that you won't find any magic answers in Athens or anywhere else, because enlightenment comes from within, if indeed it ever comes.

Other than the subjective experience of feeling powerfully attracted to some object or person, can you suggest any additional properties of 'love'?

Human 'love' can be rationalised in terms of the need to perpetuate the species; this explains why most humans fall out of love once they pass reproducing age (or even earlier).

"One molecule of H2O is not water."

I'm sorry, but you are wrong, H2O is precisely the definition of water. A single molecule of water can, in fact, achieve the states of molecular excitation which typically result in freezing, crystallisation, or boiling.

If only one molecule of water is present, then obviously crystallisation can't take place. But that doesn't stop it from being a molecule of water. If it isn't water, what else is it?

This has nothing to do with circular arguments in the traditional sense. What you are asserting here is 'Sartrean' consciousness - the [self]-awareness of consciousness - as opposed to the simple, reactive consciousness of, eg, Behavioural Psychology,

Euclid's Elements epitomise an enormously important insight of Greek philosophy: firstly, you must agree on the definitions of the key terms you are going to discuss, otherwise, your discussion will just go around in circles. Secondly, you must agree on the logical principles which bind those definitions together [the axioms], otherwise, again, your discussion will go around in circles.

Once you have agreed the definitions of the key terms, and the logical rules by which they can be manipulated, you can go on to elaborate theorems (ie knowledge).

This is true for ALL branches of science and mathematics, and just as much today as it was two and a half millennia ago.

With regard to mathematics, there are three axiom sets you need to be familiar with (and unfortunately, few mathematicians are really familiar with any of them).

1. The Peano/Dedekind axioms of arithmetic.

2. The axioms of mathematical logic.

3. The axioms of set theory.

By the way, Euclid's Elements orginally included no diagrams. Its arguments were entirely based on logic.

Hi Lif3r,

I think your post is perceptive and thought-provoking, but why on earth do you think blockchain is the answer? There is nothing LESS transparent and accountable. The two most common criticisms levelled against BitCoin, for example, are that it is a playground for wealthy speculators and god's gift to the criminal community.

Not really sure.

Love is the irrational faith that selflessness properly produces selfishness, and that reciprocally, selflessness properly produces selfishness. Love is simply faith in this reciprocity. Self-love is selflessness out of this faith, while love of others is also selflessness out of this faith.

Unless of course one is motivated entirely from selfishness.

"there a moral obligation to contribute to organizations working to alleviate poverty until doing so involves sacrificing something of comparable moral significance."

Owain, this is essentially the Principle of Utility; the greatest happiness of the greatest number. Faced with a moral choice, you have to decide: what should I do, to guarantee the best possible outcome for the greatest number of people? Which outcome is the least of all evils?

Unfortunately, this principle cannot give you concrete answers to the specific moral difficulties which arise in your life, because only you can evaluate the outcomes of your actions. Don't waste your time phoning a talkback line; only YOU can evaluate the options.

There was a guy from Nazareth, a homeless Palestinian fundamentalist, who preached "Do as you would be done by". If you follow this guy and his teaching to its logical conclusion, you must treat familes from the other end of the planet the same way you would treat your own.

With regard to this question, if you run a search on the noted works of "Gongniu Fenbian", I think you will find some interesting results.

Nagel, the general drift of your question is clear, but you cover a thousand kilometres of philosophy in every paragraph. I seriously recommend you undertake a formal college course in basic philosophy, or read through a few "Introduction to Philsophy" textbooks, to clarify your thoughts on the problems which interest you.