logic and paradox

What do paradoxes suggest about human logic?

What they suggest to me is the limitation of human language [philosophical or otherwise] in establishing with any degree of precision the truth about certain relationships.

There are a number of paradoxes [antinomies] philosophers have been debating for centuries—infinite time and space, free will, solipsism, dualism, cause and effect. And we are no closer to resolving them now then ever before.

There may be places logic can’t go. You can’t make the assumption the human brain is fully capable of grasping everything. There may be “realities” it is simply not hard-wired to grasp.

But some of these paradoxes are really just “relationships” invented in the human mind out of the whole cloth that language can be.

Take, for instance, the “arrow paradox” from Aristotle:

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.

This is, for all pratical purposes, absurd. That is not the way motion unfolds out in the world. It is the way it is made to unfold in Aristotle’s mind.

Or a variation of this is the speculation that between the arrow and its target is a distance. And there is always a precise half way point between them. But when the arrow reaches that point, there is yet another half way point to be reached. And this goes on indefinately. Therefore the arrow never reaches the target.

Purely an intellectual contraption.

We could do the same thing with time. Between now and the day a man is to be executed in prison there is a precise half-way point. And when that point is reached there is another one. And this goes on and on and on. And, therefore, the man is never executed.

What is this but a sleight of mind? The syllogistic logic of going around and around in circles.

Nice post. But… do we therefore abandon logic? How do we know when to trust intuition and/or common sense as opposed to logic? What is the place of logic in our lives?

They do indeed outline problems with our interpretation of the world, in an absolute sense. However, it is generally thought that paradoxes highlight problems that aren’t really there. A lot of the antiquated paradoxes individuals have had a crack at and demonstrated a separate way in which to interpret the problem, a way which means it can be solved. I don’t know too much abut physics (unfortunately) but I’m pretty sure Zeno’s race paradox (the distance one) was solved when the laws of motion came about.

Paradoxes fascinate me. They are like the best kind of riddles.

There are no paradoxes.

If we abandoned logic how in the world would technology like this exist? So, for me, it’s really a question of probing what the limits of logic might be in any particular human context.

Maybe some day we will “solve” the perennial pardoxes/antinomies that run the entire route of philosophical inquiry to date. Maybe [re Sam Harris] science will “solve” all of the moral conflicts that rend us.

I don’t know.

Can I know? I don’t know.

For me logic should revolve around those things we are convinced logic can revolve around: the either/or relationships.

But it should steer clear of the mine fields that are the is/ought relationships.

As for metaphysics, sure, probe away. But the farther out on the limb you go the more it seems that logic embraces all sides of every question.

Is there anything you don’t know? ; o )

Whenever you think that you are facing a contradiction, check your premises. You will find that one of them is wrong.

That logic when applied badly is flawed.

Anything applied badly is flawed.

So how can it be a paradox if its just a result of flawed reasoning?

Paradoxes don’t really exist, there is no end of the universe in time or space, I always lie.

I took your post to be a reply to the one above it, but I could read it as answering the opening question of the OP, which changes its meaning significantly. Could you use the quote function? It’s not too hard, even I can manage it.

Paradoxes are a problem if you apply logic well to them, not badly. Applying bad logic to a paradox is an easy way to solve it, just incorrectly.

Logic is a system of constraints. Since language is highly flexible, we can apply those constraints against themselves if we want to; it’s an artificial act, like using language is. Paradoxes just highlight where the constraints of logic lie, they don’t do any work.

It was a reply to you hence no quote.

I was referring to this post:
viewtopic.php?f=1&t=173890&sid=15e5fd00c7da26a44f2522e1c80a9356#p2188460

being readable as either a reply to
posting.php?mode=quote&f=1&p=2188488#pr2188447
or the first sentence of
viewtopic.php?f=1&t=173890#p2188277

I own all the templates, and all the drawings.

It’s interesting to see that physicists finally caught up with Aristotles paradox with Heisenberg, who formulated that a quantum of energy (a vector or an arrow) can not be both known as possessing a velocity and as occupying a space… the more we know of speed and direction, the less we know of location, to the point that when there is an absolutely known velocity, no location is occupied.

This points in to a point which I feel is good to make about logic once in a while: it is subservient to the ground form whence it came, which is observation of pysical stuff. Whenever a paradox like this arises, you know logic has been uprooted from reality, because the terms used to compute are imperfectly calibrated, either to each other or to the world.

a place not made of logic?

-hth
God bless

They suggest to me that logic is not the only rule by which we think.

It should be noted that the great majority of antinomies are a result, not of how logic can lead us to them, but that we can start from false premises. Take the debate over free will and determinism. The most trivially simple solution is just to drop the assumption that free will exists and to denounce it as a mere epiphenomenon or illusion of sorts. If you don’t assume free will exists, then there is not antinomy.

I agree that these paradoxes are a purely intellectual contraption, but that should be obvious to anyone (like yourself as you demonstrated) who knows how the real world works (it’s those who insist that the artifacts of their purely abstract contemplations on these matters is the ultimate truth - that they somehow trump reality - whom we have to worry about). What’s more interesting to me is the question of whether these paradoxes and antinomies can be resolved from within the abstract realm of the intellect. The fact that we’ve been failing to do so over the passed two and a half millennia is no indication to me that the answer is ‘no’ - it all depends on how subtle, deep, and insightful we are required to be in our attempts (as an example, the enigmas of quantum mechanics and relativity theory likewise took almost two and a half millennia to become known to us - is it because we were merely that unlucky in our attempts to unravel the truths of the universe until the twentieth century, or did it just take that long for our intellectual skills to become sufficiently refined and adept at uncovering them?)

Yes, this is a rather useful axiom in the world of science and mathematics. But Ayn Rand rather foolishly attempted to apply it to human moral and political conflicts in turn.

To wit:

From The Ayn Rand Lexicon:

Ethics is an objective, metaphysical necessity of man’s survival. . .

See the paradox? Each man and woman is an individual. But in order that their “choices” be objectively and necessarily rational they must be in full accordance with what is ever objectively and necessarily true. And that was always and without exception what Ayn Rand believed to be true.

In other words, the oxymoronic absurdity of the objective individual!

From Bryan Magee’s Confessions of a Philosopher:

[b][Philosophy] is a medium for carrying on the public aspects of an activity whose proper focus is always reality, or some aspect of reality…

This is a point over which Schopenhauer took Kant to task, and in my view justifiably. Kant had characterized philosophy as the disciplined examination [Wissenschaft, which is usually translated as “science”] of concepts, to which Schopenhauer replied that although philosophical activity could be conducted only in concepts, and although it was only in concepts that any conclusions it might reach could be expressed, it was a science in concepts, not a [or the] science of concepts. Concepts were its medium, not its subject matter. Its subject matter was reality, and its aim was to deepen our understanding of the nature of reality.[/b]

[emphasis the author’s]

When logic probes the major paradoxes/antinomies of philosophy it almost always becomes entangled in the concepts of its own making. The logic thus becomes internal, predicated by and large on the assumptions made regarding what the words mean.

iambiguous -

Of course.

Every deduction claims that to say the premises is to say the conclusion.

Put another way, the conclusion of a deduction is always only a restatement of its premises. It is never anything more.