What truly amazes me is how nature has a logic all its own.
Last night I watched a documentary on the Science Channel called Mutant Planet. It’s a series that probes the relationship between biological mutation, adaptation and the survival [or lack thereof] of particular species in particular environments.
The focus in the first episode was marsupials in Australia. There was one segment in which this tiny speck of a creature had detached itself from its mother’s umbilical cord in the womb and had to crawl up her belly and into the her pouch. Somehow this is hard-wired into it genetically. It “knows what to do” on automatic pilot but how can something like that be programmed into it? Why doesn’t it just let go and fall to the ground? Why doesn’t it crawl up the mother’s back onto her head instead?
The logic used to “crack” the paradoxes may be intellectual contraptions but that does not make the antinomies themselves go away. It just means we may be a long, long way from fathoming them. Or, perhaps, our brains are simply not hard-wired to fathom them. There may actually be intelligent life forms out there who could stumble upon posts like this and marvel at just how primitive we are.
“Existence” is still basically a profound mystery to us.
No, no, no. Every paradox is theoretically solvable, in one of the three basic ways that they always have been. Maybe four. I may be forgetting one. But they are due to a flaw in logic, which is not surprising - logic has been developing for centuries, although propositional logic can be said to be rather mature. Or they are due to a misunderstanding of language, which makes them vulnerable to something like Russell’s “logical analysis”, which is not the application of logical proofs per se but a careful analysis of the internal structure of statements themselves. Or they are “dissolved” by attacking the underlying assumptions of the premises themselves. These techniques are not mutually exclusive. But to suggest that superhuman brainpower is required to solve problems in a very human language is wrong-headed. Even paradoxical.
Logical paradoxes have nothing whatever to do with “existence”.
Is there a particular one that troubles you? No matter how difficult you find it to be, existential angst is not called for.
What? I’m just saying that if you quote who you’re replying to, it’s a lot clearer for all concerned. I’m not trying to control who says what to whom, just understand what it is you’re responding to. Although you seem to have trouble working it out even with quotes provided.
“Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong.”
“That logic (that you’re using there) when applied badly is flawed.”
“What do paradoxes suggest about human logic?”
“(They suggest) that logic when applied badly is flawed.”
There is a difference in what you are perceived as saying, using exactly the same words, depending on who you reply to. This forum lark is dependent on people understanding each other’s meanings, which they gather from what they say in context.
You really are quite patronising, yes obviously I’m a retard.
This forum it seems is dependant on not actually being able to understand anything unless its spealt out to them a million times IMO. But there you go.
Yeah, but that affects the possibility of “completeness” within those systems. A very simple way of stating this is that such systems can never prove their axioms. This was known to logicians, particularly to Tarski. Godel formalised this idea and allowed for it to be universalized to all “arithmetic” logical systems. But a given logical argument is a ways “down the line” from this metatheory. All arguments are, at bottom, circular.
What Godel did, in a way, was to make it safe to call some values “undefinable”. Which Tarski had also done. A lot of folks don’t like to see paradoxes “solved” this way, which is why those paradoxes persist. In fact, i think that if many people who continue to “explore” the Liar’s Paradox were more familiar with Russell, Tarski and/or Godel (which is to say "if they studied a little logic) they would find the Liar’s Paradox less interesting.
Yes, theoretically, lots and lots of things “philosophical” can be reduced down to concepts defining and defending other concepts. The words say what you make them say. Then someone makes them say something else and you squabble over them. Nothing ever gets resolved however because the words invariably point only to each other for back up. In other words [pun intended?], there are almost never any empirical “things” to make reference to.
Indeed, in my view, John Jones post are epic examples of how this unfolds in here. Has anyone finally established definitively how big infinity is…or whether time is a silly idea?
They do in the sense that, more often than not, the same folks who claim their own logic has solved them make the same claims regarding the “logic” of their “objective” moral and political claims.
Existential angst by its very nature is a manifestation of dasein. It is rooted in the embodied mind of each of us who see ourselves and the world around us in profoundly different ways. What might not trigger angst in you will in others.
Well, not exactly, because paradox doesn’t exist at the level of “word”, but in the relations between words in a statement or argument. You can’t make the relations anything you want just to solve a paradox. in fact, just making them anything you want is the origin of some paradoxes.
Of course not. It’s logic. It’s about the relations. Even if there are “empirical things” to make reference to, logic is not about those things.
I have never understood why people “accuse” logic of doing what it is designed to do, and of not doing what it was not designed to do.
Is that what you’re upset about? Those aren’t paradoxes. There is nothing paradoxical about infinity.
Hmmm. That’s just mixing up very different sense of the same word. But you’re beef isn’t with logic, but with people.
Well, something triggers murder, rape and pillage. That doesn’t mean it’s appropriate behavior.
The relationship between words used in premises that rely soley on the manner in which each individual defines the meaning of the words still results in conclusions that are largely circular. At least regarding the discussions and the debates that often swirl around most paradoxes.
If you look up logic in a dictionary of philosophy you get this:
Branch of philosophy concerned with the distinction between correct and incorrect reasoning. It commonly comprises both deductive and inductive arguments.
But reasoning with respect to what?
Again, Aristotle’s “arrow paradox”:
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
It’s just a thought experiment. It treats the relationship between space, motion and an arrow in motion through space only “intellectually”. Aristotle does not actually go out and demonstrate an arrow “at rest” at a particular time in a particular space on a particular flight of a particular arrow.
So, his reasoning has absolutely nothing to do with actual space and actual motion when an actual arrow is heading for a an actual target. Is he then assigning logic to a task it was never capable of addressing?
It seems profoundly paradoxical to many. Again, Bryan Magee on the paradox of infinite time and space:
[b]Time:
For a period of two to three years between the ages of nine and twelve I was in thrall to puzzlement about time. I would lie awake in bed at night in the dark thinking something along the following lines. I know there was a day before yesterday, and a day before that and a day before that and so on…Before everyday there must have been a day before. So it must be possible to go back like that for ever and ever and ever…Yet is it? The idea of going back for ever and ever was something I could not get hold of: it seemed impossible. So perhaps, after all, there must have been a beginning somewhere. But if there was a beginning, what had been going on before that? Well, obviously, nothing—nothing at all—otherwise it could not be the beginning. But if there was nothing, how could anything have got started? What could it have come from? Time wouldn’t just pop into existence—bingo!–out of nothing, and start going, all by itself. Nothing is nothing, not anything. So the idea of a beginning was unimaginable, which somehow made it seem impossible too. The upshot was that it seemed to be impossible for time to have had a beginning and impossible not for it to have had a beginning.
I must be missing something here, I came to think. There are only these two alternatives so one of them must be right. They can’t both be impossible. So I would switch my concentration from one to the other, and then when it had exhausted itself, back again, trying to figure out where I had gone wrong; but I never discovered.
Space
I realized a similar problem existed with regard to space. I remember myself as a London evacuee in Market Harborough—I must have been ten or eleven at the time—lying on my back in the grass in a park and tryhing to penetrate a cloudless blue sky with my eyes and thinking something like this" "If I went straight up into the sky, and kept on going in a straight line, why wouldn’t I be able to just keep on going for ever and ever and ever? But that’s impossible. Why isn’t it possible? Surely, eventually, I’d have to come to some sort of end. But why? If I bumped up against something eventually, wouldn’t that have to be something in space? And if it was in space wouldn’t there have to be something on the other side of it if only more space? On the other hand, if there was no limit, endless space couldn’t just be, anymore than endless time could.[/b]
That’s not paradoxical to you?
iambiguous wrote:
…more often than not, the same folks who claim their own logic has solved them make the same claims regarding the “logic” of their “objective” moral and political claims.
My “beef” is with people who imagine that, in using logic, you can derive the most rational and ethical human behaviors—behaviors that, out in the world we live and interact in, come into conflict over and over and over again.
No, but these are behaviors that some do rationalize as appropriate for them.
Is there a way then that one can use logic to demonstrate they are necessarily irrational in believing this?
No, and it’s Zeno’s paradox. Reasoning, as we are using the word, can solve the problem. There are at least two ways of solving this paradox that i think are good ones. I didn’t come up with either. The first solution is not strictly of logic - it’s of language. What I mean is that it’s not the relations between words that is at issue. Zeno just employed the wrong word or (since I don’t know the original Greek) concept. That of some sort of static piece of time. In the translation you are using, it’s the word “moment”.
The other solution is less satisfying to me, but surely more satisfying to real logicians. That is the solution that points out that Zeno is using a misplaced quantifier - something that was even more common among his contemporaries than it is now. I’m guessing that this solution wasn’t found until logical symbols were being used, but i don’t really know.
My guess is that you can Google all this up fairly easily.
Logic is up to the task, but Zeno (and Aristotle) knew less logic than is known today.
As for Bryan Magee - he doesn’t mention that time is merely a measurement of motion and that if there was no motion, time would be a meaningless concept. Time is “infinite” in the sense that it’s nonsensical to say “before time” or “after time”.
Like who?
if you could, you would be committing the same sin that you accuse them of.
So, his reasoning has absolutely nothing to do with actual space and actual motion when an actual arrow is heading for a an actual target. Is he then assigning logic to a task it was never capable of addressing?
What problem? The actual arrow is in motion until it hits the target. There is no paradox for the hunter or the animal with with an arrow lodged in it. The paradox [to me] is constructed entirely out of words.
Whatever time actually is, Magee merely points out you can argue reasonably it had a beginning and that it did not. Same with space. Logic works in both directions if you assume the meaning of the words you use in the concepts that comprise your arguments reflect the most rational manner in which to express them.
But either way it still doesn’t get us any closer to grasping definitively what time and space are in relationship to each other.
iambiguous wrote:
My “beef” is with people who imagine that, in using logic, you can derive the most rational and ethical human behaviors—behaviors that, out in the world we live and interact in, come into conflict over and over and over again.
Where to begin! There are veritably hundreds of religious and secular folks out there all claiming that human Virtue begins and ends with either God or Reason. Or, re folks like Kant, both. Think of Ayn Rand and her metaphyical take on ethics. The moral absolutists and authoritarians are everywhere.
What problem? The problem of the apparent paradox. Of course the paradox is constructed entirely out of words! That’s just definitional. Paradoxes are statements or arguments that contradict themselves. They are not hickory shafts with bird feathers on one end and a point on the other. You seem to be complaining that arguments themselves are only words. They are. is this some kind of news to you? It isn’t to anyone else. I hope.
No shit.
Time actually is a measurement. It does matter what it is, just like it matters that an argument is words and not arrows. I can’t give you a date, but time “began” when the first sentient being measured motion. It’s a measurement.
Well, what we, and Einstein, are calling “space”, as in “space/time”, is the first three dimensions, which are also measurements. Space doesn’t literally exist. We used to use a model that included only the first three dimensions, and most physics now includes the fourth - time. We do know the relations between those dimensions, because we invented the mathematical model that they belong to. I’m not sure, from that small excerpt, if Magee knows, but a lot of other people know.
And yeah, Kant. He’s a metaphysicist. Sure. He’s a moron. I’m with you there. Ayn Rand? Not worth bothering over.
Rationalists. And some halfbaked rationalist or other will show up here from time to time. But don;t be angry, brother. I was angry at Kant for years. it took a lot more out of me than it did out of him. Joust join me on these pages to ridicule him and anyone who speaks well of him. Embrace Kant. Love him. He’s easy pickins.
Neither space nor time exist discretely, they are space-time. The fourth dimension is essentially the motion or change or lack there of, of the other 3 usually portrayed by the complex co-ordinate system either i or x,y,z,t=i the imaginary axis is an axis again if you can imagine it parallel to the other 3 axes.
Niels Bohr relied heavily on Kants instrumentalist approaches to formalise Copenhagen.
The best way to envision time is to simply say what do we measure when we measure time, what is time based on? Hours/minute/days what is this a measure of?
What problem? The actual arrow is in motion until it hits the target. There is no paradox for the hunter or the animal with with an arrow lodged in it. The paradox [to me] is constructed entirely out of words.
I don’t see paradoxes/antinomies as contradictory arguments so much as arguments that can be argued rationally from conflicting directions.
And this is how I see most moral and political issues in turn. Arguments contradict each other but neither can be shown to be necessarily irrational.
But there seem to be two types of paradoxes. The first revolves around Magee’s conjectures regarding time and space. Are they infinite? He offers analyses that seem to suggest they both are and are not. But the words can only point to other words by and large because that’s all there are that far out on the metaphysical limb.
But the arrow paradox refers to relationships that clearly do exist out in the physical world. An actual arrow can be shot at an actual animal [target]. And at no time is the arrow motionless until it is sticking out of the animal’s hide.
It seems more than that. Otherwise one could argue that, from the big bang to the point where “the first sentient being measured motion”, time did not exist at all. And what of space? Did it also not exist until the first sentient being became conscious of it? Did Einstein’s “space/time continuum” not exist until he thought it up?
To wit:
Are you saying that until we invented the “mathematical model” these relationships did not exist? Thus if that asteroid had not struck earth 65 million years ago, mammals would not have evolved, we would not exist and therefore neither would time, space and the integral relationship between them?
A paradox is simply a self-contradictory proposition (or argument). When you Google paradoxes, that’s what you get. When you look them up on Wiki or the SEP, that’s what you get. A paradox is not two arguments.
You are clearly not talking about philosophical or logical paradoxes. You are talking about “stuff that makes you go hmmmm”.
There’s no paradox in that passage. he may be bringing up ideas that suggest two different solutions to what he sees as a problem, but that’s not a paradox.
This is okay for a twelve year old. presumably he’s gotten past it. I give him the benefit of the doubt. For a grownup to say this is, well, unfortunate. “Before everyday [sic] there must have been a day before” is not exactly topnotch philosophical arguing. There must have?
Ahh, it seemed impossible. Seemed? Again, this is just fine for an adolescent, but it’s not exactly hardcore empirical evidence, is it.
Again, I don’t know where he’s going with this - it’s just an excerpt, but he seems to be reviewing the thinking of a child. Children can teach us much philosophy, but probably not much cosmology. Time “popped into existence” when someone measured movement or change. I’m not criticising Magee. I’m saying that this is not exactly foundational philosophical text, as far as this excerpt goes.
And so it seemed to a twelve year old.
And so on.
Maybe a better example would be in order. A book report on The Cat in the Hat?
I have alluded to more than one professional analysis of this problem. You haven’t bothered to look them up.
Correct. I am making that very claim - by the definition of time, there was no time until someone measured change. It’s a human concept. Not really a difficult problem. Same with space. Space is defined by the three-dimensional model. I don’t think Einstein was the first to suggest the space/time continuum. He was one of the first to construct a useful model of the known universe using that continuum.
If you lose all depth perception, you can still see objects. You will just see them differently than others do. if you’re blind, you can still know that there’s stuff out there. If we were all blind, would we be so concerned with the question of the speed of light being the ultimate speed? Wouldn’t our models be different?
Stuff exists. Relations do not. Relations are due to our human pattern recognitions. If we perceived the world differently, the relations we talk about and use would be different, but all the stuff would still be there. There’s really only One Big Thing, and how we split the world up into different things is a function of our particular biology. It’s pretty clear that other creatures analyse the world in similar ways, but it’s also clear that the greater the biological similarities are, the greater the similarity between those analyses are.
In the end, stuff just happens. Our science is a narrative - a human narrative.
