logic and paradox

Philosophy Forums Philosophy
41

Maybe I’m shifting philosophy in a whole new direction. It seems to me if someone argues persuasively that time is infinite and another argues persuasively that it is not that’s two arguments. They are contradictory but there is no way in which to point to the one that is actually right or actually wrong.

Consider, for example, this excerpt from the “Big Bang Theory” at the All About Science website:

According to the standard theory, our universe sprang into existence as a “singularity” around 13.7 billion years ago. What is a “singularity” and where does it come from? Well, to be honest, we don’t know for sure. Singularities are zones which defy our current understanding of physics.

Technically, you might be right. But it is certainly a paradox to me. One rational argument is made demonstrating infinite time and another rational argument is made demonstrating time to be but a manifestation of that infamous “singularity event” we know as the Big Bang.

No, I suspect he hasn’t. And if you actually imagine you yourself have fugured out what time and space are I wouldn’t put much stock in your philosophical credentials either. Of course: No one knows with a high degree of certainty what they are, how or why they came into existence or what their ultimate fate shall be.

Or, teleologically, what it all has to do with us.

But if you actually think you do I have another question for you: What happens after we die?

Magee:

Again, I can imagine an astrophysicist explaining the Big Bang to a child. And then when the child asks, “but how did it all just pop into existence out of nothing?”, what does the scientist say? What do you say? Personally, I find it rather peculiar when someone speaks of these things as though they actually know what they are talking about. Instead, right at the center of this profound conundrum it’s still just a WAG.

But, sure, go ahead, tell us precisely what time and space are.

iambiguous wrote:

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.

I’ll look them up when you actually respond to the point I am making. At no time does an actual arrow remain motionless until it reaches its target. So why create this paradox in which we are supposed to believe it does? Or, worse, the one in which it is suggested an arrow shot always has to reach a half way mark in distance. Then when it reaches that point there is another half way point. Then another and another. Therefore, according to the paradox, the arrow never reaches the target!!

Yeah, right. These paradoxes exist soley in a world of words. But Magee’s paradoxes are much more profound because we are talking about space and time that we interact in and experience day in and day out.

iambiguous wrote:

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?

Ah, the tree falling in the forest that doesn’t fall at all unless someone is around to see it and to hear it?

Suppose we fall asleep and the numbers on the clock say 11:00 PM. We wake up and the numbers on the clock say 8:00 AM. Are we to believe that throughout the night the numbers on the clock weren’t really advancing because no one saw them advance? Or, per George Berkley, that God alone is the mediator?

Now that’s an antinomy that goes way, way back…in time?

iambiguous wrote:

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?

Stuff.

But how could the stuff in the Big Bang [some 14 billion years ago] become the stuff we know today if no sentient being was around for 99.99999999999999% of the time that this evolution elapsed?

Now, I’ll be the first to admit that talking about things like this makes your head start spinning. But that’s my point: We don’t really have a clue as to how this all “works” in reality. Let alone why it works how it works.

Not yet anyway.

Well, I make a distinction between the narratives embedded in science and the narratives embedded in moral and political philosophy. The former in my view revolve far more around either/or relationships. But the paradox is this: if you do go far enough out on that metaphysical limb you fall into the intellectual equivalent of a black hole. Reason might go in but no one really knows for sure what comes out.

42

I guess it’s this “infinity” thing that has got you confused. But it’s like saying that “length” is infinite. That doesn’t mean that it goes on forever. It means that the idea of a limit doesn’t apply to the idea of length. The idea of “red” doesn’t apply to length, either.

Well, we’re here looking for empirical answers to empirical questions. These are not the only such questions that we haven’t found yet, and i really don’t see their relevance to the question of time as we understand the concept or to paradox.

Again, he presents no arguments either way, but only what things seemed to be like to him when he was twelve.

I’m not questioning his credentials. I’m not eve arguing against his claims. His claims are again, what he thought when he was twelve. I wouldn’t argue with a twelve year old about cosmology. In fact, a great many people know what time and space are - you are just one of the few who do not. Sometimes i think that everyone who doesn’t know what time is comes to this site, eventually.

That’s your real problem. Those who think that time has something do do with us, teleologically will regularly deny the very simple explanation that I have given you. You can look for the answer to your question, or you can look for God. You won’t find both.

That’s unrelated to someone like me. For those who seek God, or Never-Never Land, I suppose it’s related.

Look, iam - we could go on forever with this. I knew at the start that you were making either a political or a religious point. I now know which it is. But I come here to converse with philosophers. Best of luck.

43

There is no conflict in saying time is infinite mathematically or philosophically from our perspective it is simply all there is that can be known and it seems unbounded except by the heat death of the Universe. Hence even though it is supposedly finite it is still a valid infinity. Neither maths nor logic have any problems dealing with this any more than they do the fact the Universe is infinite. In fact maths relies on infinities to define what can and can’t happen and what something will approach or converge to. The only paradox is when you say something like:

Newtons formula of gravitational force.

Where r =0 or distance between objects = 0.

Then you get division by 0 which creates a problem like a singularity which cannot be adequately described, and hence, no one really believes the maths suits the subject in general relativity or Newtonian mechanics (as a matter of interest we use a Schwarzchild radius to model high density masses “beyond” normal physics laws). In science a paradox merely tells you you got something wrong. In philosophy it means you probably are approaching the problem with either faulty assumptions or unrealistic expectations.

44

If you are not profoundly confused about time and space you have barely scratched the surface in thinking about them. If time and space don’t “go on forever” where do they start and stop—at any point along the “time/space continuum”?

Or certainly—for each and everyone of us [eventually]—in oblivion.

Your arguments of course are entirely circular. Or, perhaps, elliptical?

All About Science:

Out in the world empirically are you and I. We reside on planet earth resides in the solar system resides in the Milky Way galaxy resides in the Local Group resides in the unviverse resides [perhaps] in an infinite number of parallel universes reside in…what exactly?

Are you suggesting that how “we” understand time and space here is without any possible doubt at all the way time and space actually are?

Which is the manner in which they still “seem” to him. Just as you “seem” convinced your own understanding of time and space is the only way time and space can be understood.

But I know this is not true. Why? Because if it were true that is all anyone in the scientific community would be talking about now. The mystery of time and space [of existence itself?] revealed!!

45

Saying something is finite or infinite “mathematically and philosophically” is not the same thing as demonstrating it one way or the other empirically. We can’t board a space craft and show the world “infinite” time and space; any more than we can reach the point where they began or where they will end.

Instead, we engage in “thought experiments” and we fit time and space into them. There they become words like all the other words we use to speak about the profoundly promlematic “nature” of existence. The words then define and defend other words—but point to nothing subtantive or substantial at all.

46

No it is not exactly demonstrating it empirically demands we actually can see what concepts we are trying to measure.

We engage in though experiments because of our own limitations, but it is better to think about it than to give up I guess.

47

Thought experiments have their place in philosophy. If for no other reason they can be quite fascinating. But sooner or later the words must come into contact with the world. Or a world. Otherwise the “logic” embedded the thoughts is basically internal.

48

iam -

That I don’t know the limits of the Universe doesn’t make me confused - I haven’t seen everything in the world that is blue, but I know what blue is.

If my arguments are circular, at least I am making an argument.

Yeah, perhaps. We don’t have to know everything to know something.

That’s unfortunate.

I am offering an explanation, which, like all science, is provisional. I think it’s better than wetting my pants over what I do not and cannot know.

I haven’t taken a survey, but I am far from alone in this view. And where did “existence itself” come from?

Again, science doesn’t have to possess a Theory of Everything to have theories about some things.

Throe your hand up if you will, but your line of discussion “seems” like scientific nihilism. I cannot see what fruit it could bear.

I mean, just what is your point in all this?

49

That does not conflict with anything I said so yes agreed.

50

If you don’t know the nature of what may well be a limitless universe embedded inside what may well be a limitless number of parallel universes, you can’t help but be confused. Where to even begin in grappling with it?!!

In my view, circular arguments reflect the path of least resistant. And that’s why so many embrace them…religiously?

But what do we really know—what can we really know—about everything there is?

Fine. This is a reasonable point. But you don’t have to wet your pants pointing out to others that what they claim to know is almost certainly but a sliver of all that can be known.

This is certainly true. But science needs to be reminded from time to time that a TOE must somehow accomodate minds that are searching for it. I have always imagined that a TOE would encompass discussions like this. Meaning our autonomy is just an iullusion. After all, how can a TOE be reconciled with free will?

In that case, David Hume was a scientific nihilist too.

No, science is able to propound truths about as close to objectivity as we are ever likely to get. How do we know that? Because what were once just hypotheses in someone’s head are now computers and smart phones and newer technologies that will surely boggle the mind.

But: when science goes after the very very big and the very very small it generally recognizes this: the more it comes up with answers the more it spawns even more perplexing questions.

51

I was always taught that paradoxes are apparent contradictions. Paradoxes exist because we don’t see as clearly or in as many degrees as we would like, but real contradictions are impossible. At least it has been useful to be suspicious of contradictions, and hopefully the future continues to be like the past.

52

By not worrying about what it might be and concentrating on what we know of it. WE have scientific descriptions of the parts of the universe we can observe. They are far from perfect, in any sense of that word - but they’re okay. It might be fun to speculate that we are a speck on a mole on a rat that is in turn a speck on a mole of another rat - but you don’t really sound like you’re having fun. It just doesn’t all go to hell - all of the history of science and myth and the discovery of fire and all of human culture - it doesn’t all go to hell because we can’t see that mole.

No - the path of least resistance is to claim that is we don’t know everything then we don’t know anything.

About everything? We can’t know abut everything. Get over yourself. And if you want to know what we really know, then I’ll agree - we really know nothing. But we kinda know a lot.

Look - you want metaphysical certitude that those are really your toes? I can’t help you. And neither can anyone else. But you’re stopping yourself before you even get started. So don;t tighten those lug nuts next time you change a flat. You can’t really know that they’re tight, anyway.

Or, you can philosophise with your blood. As a human, and not as some wannabe god.

I am telling you this as a friend.

I have changed my pants.

Common misconception. He was a closet atheist, too polite and mostly too timid to come right out and say it. He didn’t think there was no causation. He just wanted to remove the idea that causation necessarily obtained. That always leads to an unpalatable infinite regress or worse: God.

As close as we are likely to get may be very far from any meaningful use of the word “objectively”. I am not arguing for absolute knowledge. That phrase doesn’t even make any sense to me, although I know what people mean when they say it.

That’s not unique to science. We can always ask another “why”. Many a philosopher has gotten into trouble because he didn’t know when it was time to shut up and make his garden grow. In a sense, all of metaphysics is the result of an extra “why”. Or two.

53

Fuse - we accept that in real life a dog is not a cat. “Apparent” isn’t out of place when describing paradoxes, but since paradoxes are made only of statements anyway, it doesn’t really matter. They are surely called “apparent” after they are solved. But “I go left when I go right” is an actual contradiction in logic, because, again, logic is concerned only with statements.

54

Faust,

Maybe contradictions can exist in form in logic, but they don’t exist - can never be instantiated - in the world.

55

Yeah, but the philosophical use of the word “paradox” is applied to statements, and not to the real world. The word “contradiction”, in logic, refers only to statements. Never to the real world.

There are no “real” contradictions. Not because they are impossible, but because the word does not apply. It’s just not the same word as we use in logic. In logic, it’s a technical term.

I know it seems a minor point. But it’s all fun and games until someone loses an eye.

All I am saying is this - I apparently have a penis. Also, I actually do have a penis. Neither is wrong to say, and one does not exclude the other.

56

I understand your point, but most people do not speak about paradoxes and contradictions in the strict logical sense.

57

It was the penis thing, wasn’t it.

58

That makes sense until you get out to the very edge of the metaphysical limb.

How can existence have no beginning and no end? After all, everything else does. You, me, this exchange, this computer. Everything around us. Indeed, every single component of this planet had a beginning and will come to an end. The earth and the sun had a beginning; and they too will come to an end.

But somehow existence itself is immune from this?

In fact, there are many scientists who insist that everything that now exist did come into existence out of nothing at all. That time and space and matter and energy literally came from nothing.

The ultimate contradiction?

59

Everything we name comes to an end as the thing we have named. When my dog dies, I can, if I am of a mind to, watch its body decompose. I could measure the gas it emits. If i could measure closely enough (and in tightly controlled conditions, I could), I could account for all of my dog. But when i could no longer account for him (like when I could no longer afford the rent on the lab space) I am not to suppose that the “stuff” of my dog no longer exists, am I?

Stars “live and die”, but it’s only the form that dies. Everything changes. What “ends” is what we say ends. Except for stories. They actually do end. Beginnings and endings have not to do with the universe, but with the narrative.

60

Faust,

EDIT: I have never implied that the way a thing appears excludes it from actually existing as it appears. What I have said is that contradictions are such that they can only appear to be, and cannot actually be. Take mirages, for example. They are always only appearances of things that do not actually exist. The content of contradictions and mirages is always insubstantial, whether apparent or not. And I don’t know why you are on about penises.