You mean like postponing judgement until you've "inhabited" the other side of the argument?

Not something I'm familiar with... :wink:

OK, then I'm not sure how feigning agreement would relate to procrastination...but maybe I misunderstood your meaning...

It was a good old puzzler. Had me stumped.

See how delta-t becomes zero? So your average is a division by zero. — Banno

What? Delta-t doesn't become zero. It "approaches zero". Can you not understand the significant difference between approaching something and becoming it? If delta-t was actually zero, it would render the whole formula as nonsensical.

But that's not right; mathematicians, even those in primary school, do apprehend infinity in their considerations. — Banno

Sure, we apprehend infinity, but not necessarily in that way. That way is inconsistent with constructivism, as I explained.

And i think that is an end to this discussion. — Banno

Yes, it seems to be approaching zero. But your capacity to argue a point is already at zero it seems.

What? Delta-t doesn't become zero. It "approaches zero". — Metaphysician Undercover

Correct. Most people understand that.

Right, so the question that follows is: what happened so that we generally rejected constructivism? — frank

I'd answer that with simplicity sake.

And what are the philosophical costs of having done so? — frank

I'd answer that with significant misunderstanding, as demonstrated by Banno.

Have I got this wrong? — Baden

Banno appears to be a lost soul.

Correct. Most people understand that. — frank

SO do you agree with Meta that there is no such thing as instantaneous velocity?

SO do you agree with Meta that there is no such thing as instantaneous velocity? — Banno

For all practical purposes yes, we calculate instantaneous velocity. Actually instantaneous? Of course not. Most people can plainly see that that wouldn't make any sense.

So be it.

What is "instantaneous velocity"? Does it mean anything other than 'velocity at some instant'?

How's your maths?

It's just how fast something is going at some particular time. It's a basic bit of physics.

So, no.

Yes, I am familiar with that definition as "velocity at some instant". I thought it should be obvious that I was implicitly inquiring if you or Metaphysician Undercover had some other definition in mind such that it might be reasonable to agree that there is no "instantaneous velocity" per that other definition.

Oh, ok. Well, instantaneous velocity is such a commonplace in physics that it is usually just called the velocity.

Wittgenstein talks of a picture having one enthralled; unable to see something in a different way. Hence the duck-rabbit and such. This is perhaps a case in point.

So a physicist using classical mechanics would say that an object has only one location at an instant, but that it can have both a velocity and an acceleration.

Meta has an idea - Aristotelian, perhaps, that since an object can't go anywhere in an instant, it can't have a velocity.

Meta has an idea - Aristotelian, perhaps, that since an object can't go anywhere in an instant, it can't have a velocity. — Banno

That just sounds like a bit of Zeno-ian silliness!

That just sounds like a bit of Zeno-ian silliness! — Janus

Yeah, it is.

It leads to the confused reply he gave to my OP:

As I argued in that thread, "infinite extension", which is what conventional set theory allows, is incoherent, based in contradiction. An object, as a unity, being unbounded, is fundamentally contradictory. — Metaphysician Undercover

There's a certain coherence in what he is saying; and it is said with such conviction. It also seems to me to be a very similar to the misapprehension he had in @Sam26's discussion of rules.

"From a conceptual point of view, instantaneous velocity is a limit: if you compute the average velocity (Δx/Δt) for every smaller values of Δt, you will see that it nicely converges to a value: this is the instantaneous velocity. From an experimental point of view, this is unreachable."

Physics stackexchange

Yep.

Yes, I am familiar with that definition as "velocity at some instant". I thought it should be obvious that I was implicitly inquiring if you or Metaphysician Undercover had some other definition in mind such that it might be reasonable to agree that there is no "instantaneous velocity" per that other definition. — Janus

What is not reasonable is to call any sort of velocity "instantaneous velocity" because any velocity requires a period of time, and "instant" implies a point in time. So that phrase is really self-contradicting, oxymoronic. Because physicists use that saying, it gives people like Banno the impression that they can actually figure out what the velocity of something is, at a point in time, when they really can't. So it's a misleading (deceptive) use of words.

So a physicist using classical mechanics would say that an object has only one location at an instant, but that it can have both a velocity and an acceleration. — Banno

I would say that this is obviously contradictory. Movement is change of location. Velocity is an attribute of movement. Therefore it is impossible that an object could have one location, and also velocity.

Meta has an idea - Aristotelian, perhaps, that since an object can't go anywhere in an instant, it can't have a velocity. — Banno

Yes, that is my idea, it's known as conformance with the law of non-contradiction. You might call it an Aristotelian principle, I would prefer to call it common sense. We normally reject contradiction out of common sense.

It also seems to me to be a very similar to the misapprehension he had in Sam26's discussion of rules. — Banno

If you are going to argue that language use is a matter of following rules, then it makes sense that you would actually follow the well known fundamental rules, in your argumentation. Otherwise it's hypocrisy which actually shows the falsity of what you re saying. So if we cannot adhere to the fundamental rules, the law of identity, the law of non-contradiction in our discussions of mathematical axioms, what's the point in saying that language use is a matter of following rules when actual usage demonstrates otherwise?

There's a certain coherence in what he is saying; and it is said with such conviction. — Banno

Contradiction and equivocation are abundant in mathematical systems. It's very clear that rigorous philosophical discipline has not been adhered to by those who have dreamed up the axioms. It appears like the axioms are designed to hide the problems which we have in understanding the nature of physical existence (such as Zeno paradoxes), rather than to expose these problems so that we can work on resolving them. The hiding of the problems creates the illusion that they have been resolved, which many people seem to believe as reality. But issues like the uncertainty principle demonstrate very clearly that the problems have not been resolved.

A secondary type of problem has now emerged. This is an even worse condition than the original problem, which is our inability to understand these aspects of physical reality. Since many people believe that these artists, the mathemagicians who have dreamed up the axioms that are capable of covering up the problems, have actually solved the problems, they falsely conclude that there are aspects of physical reality demonstrated by QM, which are incomprehensible. Instead of accepting the fact that the mathematical axioms which are employed are stacked with logical flaws, and this is why certain aspects of physical reality appear incomprehensible, they will defend the mathematical axioms to no end, and argue that this is just the way nature is, certain aspects of physical reality are fundamentally incomprehensible. For example, there is a commonly expressed attitude that the uncertainty of the uncertainty principle is a fundamental feature of physical reality, rather than a deprivation of the mathematical principles employed. Do you see how wrong this attitude is?

1 is a beautiful number that multiplies and divides, the most prestigious command.

It does refer to 1. 1 = 1 but it's not how it's written, it's how it's concieved.

Take two hypothetical scenarios for something, in one it's still, in another it's moving.
Physics can differentiate the two at time t by different motion vectors, speed and direction; by momentum too for that matter.
If you can't, then you're missing something.
Simple school physics could plot out the different speeds at different times throughout the scenarios, and see acceleration/deceleration (change in speed) over time; the former scenario would be a bit boring.
If you can't, then you're still missing something.
Gravity expressed as acceleration (the equivalence principle): at time t, Earth gravity is a downward acceleration that we're subject to.
Without differential (and integral) calculus, physics would be impoverished, it's proven in action, so our philosophical musings best account for this, or we'd be missing something.

So the universe is not quite as you thought it was. You'd better rearrange your beliefs, then. Because you certainly can't rearrange the universe. — Asimov (1941, 1990)

The conflict that appears in this thread regarding velocity comes down to semantics and turns on this fact about instantaneous velocity:

From an experimental point of view, this is unreachable.

I thought everyone agreed that velocity inherently meant change of distance while an instant of time is refering to certain properties that is true, so unchanged. Would seem obvious that it would be contradictory. Remember, All observations can be measured ultimately with Distance(m), time(s), and mass(g).

Sure. But that fact that someone can add one to any number does. — Banno

No, that just implies you can add one - a finite value - to any number - another finite value. So where does one get the notion of infinity from when you are starting somewhere in using numbers to count and then simply adding one to where you started.

The notion of infinity comes when contemplating things not just with no ending, but no beginning as well - like a circle or the visual feedback loop that you observe when looking in mirrors positioned in opposite sides of the room.

You keep confusing potential infinity with actual infinity.

Wait, I not well veresed with potential and actual in infinity, is pi a potential or actual infinity.

Numbers represent potentials, not actuals. Why does dividing things by three, into thirds, create an "infinite" number of threes after the decimal point, as if we can never get to an actual third of something?

(y)

What is not reasonable is to call any sort of velocity "instantaneous velocity" because any velocity requires a period of time, and "instant" implies a point in time. So that phrase is really self-contradicting, oxymoronic — Metaphysician Undercover

When you glance at your speedometer and it reads 60 mph, indeed that is based on an approximation made over a small interval of time. So you do have a point, although a rather insignificant one. "Instantaneous" velocity or speed is a shorthand for a limit process. What single word would you suggest be used in this context, rather than instantaneous?

Why does dividing things by three, into thirds, create an "infinite" number of threes after the decimal point, as if we can never get to an actual third of something? — Harry Hindu

6/3=2

Again, a major problem in philosophical discussions is exhibited. :sad:

6/3=2

Again, a major problem in philosophical discussions is exhibited. — jgill

Yes, but you seem to be ignoring what I said. If what you and I both said is true, then how do we reconcile our opposing, but true, viewpoints? I was hoping for something like this but while pointing out the problem you failed in trying to solve it.

So basically, if you have 6 apples and three people, then the number of apples divides equally, but try dividing one apple evenly among three people.