Isn't denying the existence of sqrt of 2 on the grounds that it isn't a computable number — sime

Didn't read back to find the source of the quote, but sqrt(2) is certainly computable. For example you can use a standard iterative procedure.

The arrow may be momentarily stationary, but it has momentum. — jgill

Can you explain this to @Metaphysician Undercover and @Ryan whose handle doesn't show up when you use the @ button?

But actually it's a good question. Suppose there were such a thing as an instant of time, modeled by a real number on the number line. Dimensionless and with zero length. So the arrow is there at a particular instant, frozen in time, motionless. Where does its momentum live? How does it know where to go next?

Does it have, say, "metadata," a data structure attached to it that says, "Go due east at 5mph?" You can see that this is problematic.

Yes. I've made your argument many times. Usually I am ineffective in getting the point across. It comes up a lot in discussions about the multiverse. — T Clark

The value of rationality is greatly overrated in human discourse.

Sure, the object is described as moving, it must have a velocity. But it cannot have a velocity at an instant, if no time passes at an instant, just like a point has no spatial extension. That's why points and lines are incompatible, and a line is not composed of points, but points mark off line segments.

So the solution to the issue with velocity, is not to say that it has no velocity, it is to say that there is no such thing as the instant. Time is not composed of instants. So the arrow, or car always has velocity, all the time that it is moving, but that time has no instants. The instant is just an arbitrary point which we insert for the purpose of making a measurement. — Metaphysician Undercover

Ok. I can live with that. Whether it's a moving arrow or a current driving the speedometer, it's a change occurring over a short interval of time. But my original point was that we don't need calculus to determine the velocity. Actual velocities are not subject to the ancient philosophical mysteries of calculus.

Still, would you at least grant me that velocity over a short but nonzero distance exists?
— fishfry

Sure, but the whole point I am arguing in this the thread is that the inclination to reduce the nonzero distance to zero, or even define it as somehow related to zero, produces theoretical absurdities. And this is well demonstrated by these Zeno type paradoxes which speak of time as consisting of instants. — Metaphysician Undercover

Ok. Maybe. Let me put to you a hypothetical. An object moves with constant velocity. Does it have a velocity at a given instant?

Likewise does the speed of light have velocity 'c' at a given instant?

I'm kind of done with this topic, the point I'm making isn't worth all this ink. You don't need calculus to do analog measurements. And yes physical measurements depend on time, even if those intervals are tiny. There aren't any actually physical instants as far as we know. Or as far as we don't know. The matter is not answered by current science.

And as you drive your car continually accelerating and decelerating, the spring behind the needle is continually playing 'catch-up' and thus reporting some sort of average. In fact, it is most meaningful to say that it is always reporting an average. — Ryan O'Connor

I'll accept this point. It still has nothing to do with what I originally said, which is that you don't need calculus to determine the instantaneous velocity of a moving object. And I'll concede that by instantaneous I only mean "occurring over a really short time interval."

I have to say I'm not nearly as invested in this point as the number of words written so far, I should probably stop.

One of my university professors said once in a class: The world could have not existed, and the chances of it not existing were infinitely greater than the chances of it existing. — Amalac

The posterior probability that the world exists is 1. Whether that's a satisfactory response to the conundrum you raise, I can't say.

Consider. Flip a trillion fair coins. What are the odds of all heads? They're $\frac{1}{2^{10^{12}}}$. Pretty unlikely.

But what is the probability of any other particular result? They're exactly the same! People only think all heads is unlikely because it stands out. The probability of any particular exact sequence of heads and tails is exactly the same as any other: one out of two to the trillion. Yet some result must occur. And after that result occurs, in retrospect it is a perfect miracle. You just don't notice it because it happened with posterior probability 1.

This is the lottery paradox. It's not rational to buy a lottery ticket because you almost certainly won't win. But somebody has to win. So you might as well buy a ticket.

By the way your professor was being vague and imprecise when (s)he spoke of "infinitely more likely." I don't know what that means and neither did they. That's why I like the example of a trillion coins. That's an experiment that's physically realizable. We don't need to appeal to infinity to see the essential mystery. Any particular sequence of coins is extremely unlikely, but some outcome must occur.

In fact you can do this experiment at home by flipping a coin only 100 times in a row. $2^{100}$ is a pretty huge number. It's larger than 1 followed by 30 zeros. Whatever sequence you flipped, the odds were 1 out of 2 to the 100th power that you would have flipped exactly that sequence. Yet you did.

You seem to be missing the point fishfry. — Metaphysician Undercover

Not for the first time I'm sure.

Velocity is a measurement of motion, and motion only occurs when time is passing. At an instant zero time passes. Therefore there is no motion at an instant, and no velocity at an instant. — Metaphysician Undercover

Yeah yeah. One of Zeno's complaints. If you look at the arrow at a particular instant it's not moving. How does it know what to do next in terms of direction and speed? Not a bad question actually, one that I won't be able to answer here.

A measurement of velocity requires a determined distance over a determined duration of time. It requires two instants, to determine a duration of time, one to mark the beginning of the period of time, the other to mark the end of the period of time, just like it requires two points to determine a distance. One instant (point in time) is insufficient for a determination of velocity, just like one point is insufficient for a determination of distance. — Metaphysician Undercover

Yes you already said that. I take the point. If you show me a photo (taken over a sufficiently short time interval, since even a photograph takes time) the arrow appears stationary and you can't determine its velocity.

Yet, it still HAS a velocity, wouldn't you agree? And what does a speedometer measure? A current. And as @Ryan pointed out, even that's a flow of electrons. Since current is a flow, does it exist at an instant? Well I'm sure that a modern physicist would point out that the electromagnetic field exists at every moment. But if you have a magnet in a coil, you have to move the magnet to create a current. I'm really not enough of a physicist or a philosopher to know these things. Good questions though.

Still, would you at least grant me that velocity over a short but nonzero distance exists? And likewise a current flow? Then a moving car has a velocity that can be determined without recourse to formal symbolic manipulations, which was my original point.

Moderator note: When I hit the @ button to search for @Ryan O'Conner his handle doesn't come up, any ideas why?

Your original claim was that my rejection of instantaneous velocity is falsified, which I think is false. If you now claim that the speedometer must necessarily be reporting some average or approximate velocity then I have no problem with that. — Ryan O'Connor

What do you think speedometers measure?

I take your point about instantaneous motion, it's related to one of Zeno's paradoxes. If the arrow is not moving at a given instant, how does it know it's moving, or something like that. I don't think I have to resolve that ancient mystery to read my speedometer and know that it's telling my my instantaneous velocity. Even if it's only actually reading a current from an induction motor.

Bonus question. What is the speed of light at any given instant?

This notation was suggested by a Japanese mathematician. I was starting to use something else, but switched to his. — jgill

A cursory search shows that I can't find it used anywhere. "Today I learned!"

Oh -- L and R. Nice. I thought iterated functions were getting a lot of attention these days. Fractals and such.

L2k=1gk(z)=g2∘g1(z)=g2(g1(z)) — jgill

Iterated composition. Hadn't seen that notation before. Thanks.

That's what happens when multiplying a+bi by i. — jgill

Right, that's the answer to "does the square root of -1 exist?" Just as the number 5 can be interpreted as stretching a line segment by five units; and multiplying by -1 preserves the length and reverse the direction of a line segment; multiplying by i rotates the segment a quarter turn counterclockwise. And if you do it twice in a row, you get the same effect as multiplying by -1. This in my opinion is what they should be explaining to every high school student. But they don't. And apparently they don't explain it to physicists either!

I play in the complex plane all the time, and I have always visualized figures and imagery and motion. Even created what might be considered art in the process. — jgill

So what does the L mean in your equation earlier? Not familiar to me.

With you being a crankologist, I'd really benefit from your criticisms and I think you'd enjoy learning my view as I believe I am coming at infinity from a unique angle. As such, I think you'd need a different strategy to take down my ideas (assuming I'm wrong). But your time is short and crankery is infinite so whether you find time or not, it's all good. — Ryan O'Connor

On the contrary, I have too much time on my hands. I've been over active on this forum lately and I'm feeling the need for a break. I think my reacting negatively to @Wayfarer's helpful link to a Sabine Hossenfelder video was a clue. I'm just crabby lately for the sake of being crabby and when I find myself doing that it's time for a forum break. Sorry @Wayfarer, I apologize.

You're definition of the instantaneous velocity of a car rests upon a dynamic quantity: the flow of electrons through a wire (i.e. current). So you've only shifted the problem from instantaneous velocity to instantaneous current. Consider this example. — Ryan O'Connor

Yes but this is true of any physical quantity. How do I measure the mass of a bowling ball? Well I can put it on a scale, but that only measures weight and not mass. The weight would be different on the moon.

So to measure mass, we must observe the bowling ball's acceleration response to force, as described in this fascinating thread.

https://physics.stackexchange.com/questions/179269/how-do-we-measure-mass

How can we do that? We can suspend it from a spring with a known spring constant using the formula for a harmonic oscillator. But then you (and @Metaphysician Undercover) will object that all I'm doing is measuring the springiness of the spring.

Or I can measure the centripetal force on a centrifuge, or use a small angle pendulum. But in each case aren't we just measuring something about the apparatus and not the mass itself?

In short, your objection is valid, but overly general. We can't measure any physical quantity at all by your logic. What if I want to measure the wavelength of a beam of light? Well I use a spectrometer, but all that really measures is the prism or the glass or however spectrometers work.

What if I want to measure the temperature of air? I use a thermometer, but that's only measuring the response of mercury or the coil of a metal spring or however thermometers work these days.

So what you and @Meta are saying is that we can't measure ANY physical attributes at all. This is hardly an objection to my point about velocity being directly measurable without recourse to formal calculus. It's a philosophical objection to the idea that we can do any measurements whatsoever, or to the idea that objects even have physical attributes before we measure them by proxy. But that doesn't actually address the different point that I'm making: That moving objects have a velocity, which we can measure directly (by proxy with an induction motor coupled to the driveshaft), without needing formal symbolic methods of calculus.

After all, bowling balls fall to earth with an acceleration of -32 feet/sec^2, and this was true even before Galileo discovered it and Newton modeled it with his law of gravity. You and @Meta can not deny that bowling balls fall down and that they do so with a measurable velocity at any instant of time; without denying the whole of physical science. You don't need calculus to know that falling bowling balls have a velocity. You're both confusing the mathematical model with nature itself. And the fact that all measurements require some intervening apparatus is a red herring.

ArcTan(z)=L∞k=12z1+1+14kz2‾‾‾‾‾‾‾‾√, Lnk=1gk(z)=gn∘gn−1∘⋯∘g1(z), π=4ArcTan(1) — jgill

Arctan(1) is the proof of the Leibniz formula. What's the meaning of $L$?

What would you say the meaning is? Just curious. — jgill

A quarter counterclockwise turn in the plane. That's the simple meaning. I was probably too harsh with my criticism of her video though, it's an excellent summary of the use of complex numbers in physical science. Just missed the mathematical essence IMO.

Oh come on fishfry, you're smarter than this. The current you refer to is just measuring revolutions of the driveshaft. Then the speedometer of the car is scaled to how many revolutions are required to cover a specific distance. It is not measuring the instantaneous velocity of your car. What happens when you use the wrong size tires? — Metaphysician Undercover

Jeez man it's an analog computer. It gives a direct measurement of a physical quantity. You're saying there's no such thing as velocity. Your scientific nihilism is spreading from math to physics.

No problem at all. I appreciate the message! Although I don't expect a response, — Ryan O'Connor

I'll take a run at your graphs when I get a chance. You went to some trouble to draw them, you deserve a response.

I do want to say a couple of things. I obviously know how to plot a polynomial in the traditional sense (and I also know how to use plotting programs). If you don't see a polynomial in my graphs it's because you don't understand my view (I'm not blaming you, this may be entirely my fault). — Ryan O'Connor

I agree that I don't understand your viewpoint. I have no trouble with adjoining points at plus/minus infinity to the real line, that's just the two point compactification of the real line. But the rest of it I couldn't follow.

Had I chosen to also plot y=0 then you would have seen the points corresponding to the roots. — Ryan O'Connor

I'll take a more detailed look at what you wrote and try to frame some specific questions.

Your speedometer is measuring the average velocity but one measured over quite a short time interval. — Ryan O'Connor

Not so, please see my response to @Metaphysician Undercover here. Briefly, your speedometer is driven by an induction motor coupled to your driveshaft. It gives a direct analog measurement of instantaneous velocity without any intervening computation.

And I enjoy the quips, even that's all I hear from you. — Ryan O'Connor

Often that's all I can manage. And I find many subjects in philosophy are best responded to with an old pop tune or a line from a film.

Velocity is always an average over a duration of time. So-called "instantaneous velocity" is just a derivative from an average. Since velocity is a measure of change, and change without a duration of time is impossible, then also true "instantaneous velocity" is also impossible. — Metaphysician Undercover

Funny you should mention that, since it's so easily disproven.

Consider the speedometer in your car. How do you suppose it works? Is there a tiny little freshman calculus student in there, frantically calculating the limit of the difference quotient moment by moment?

No, actually not. Not even a computer program doing the same. Rather, there is a little induction motor attached to the driveshaft. The faster you travel, the faster the drive shaft spins, the faster the induction motor turns, the more current it outputs. And that current directly drives the needle of your speedometer.

Your speedometer is not a mathematically derived average. It is in fact a direct analog measurement of the instantaneous velocity of your car; subject of course to slight mechanical error common to any physical instrument. The velocity is an actual, physical quantity that can be directly measured -- that IS directly measured -- without recourse to any formal mathematical procedure.

You are confusing the velocity of an object, with the procedure we teach calculus sufferers students to find the velocity of points moving in the plane or in space.

It's just a term of convenience, to be able to say that at x point in time, the velocity was such and such. — Metaphysician Undercover

No, as I have just explained, velocity is a directly measurable physical quantity, like the mass or volume of an object, or the wavelength or luminous intensity of a beam of light.

What is really taken is an average over a duration, — Metaphysician Undercover

No, as I've just explained.

and from that we can say that the velocity at any particular point in time within that duration was such and such. — Metaphysician Undercover

You're confusing freshman calculus with the actual, directly measurable instantaneous velocity of a moving body.

But you can see from the applicable formula, that "instantaneous velocity" is really just another average. — Metaphysician Undercover

No, because the calculus formalism is not the velocity, it's merely the way we determine velocity given the position function. But we don't need to do that if we have a direct way of measuring the velocity.

But even your remark about the formalism is wrong, because although the value of the difference quotient at any point is not the true velocity, but rather the slope of the secant line; the limit of the difference quotient is exactly the velocity. It is not an approximation.

And it's quite obvious that the idea that something has velocity at a point in time, when there is no duration, is nonsensical. — Metaphysician Undercover

Yet another instance of the phenomenon whereby something false appears "quite obvious" to you solely by virtue of your lack of knowledge. You wield your ignorance like a weapon. A comic book character, Ignorance Man, whose slogan is "Believe the science!" while knowing none of it. Come to think of it there's rather a lot of that about these days, wouldn't you agree?

Unfortunately, there are “woman’s” who are far too selfish and negative, who become mothers and leave deep traces, sometimes unforgivable in the innocent soul of the child. — 4ever1friend

Uh oh you are in trouble with the woke police now. Suggest you turn yourself in for cancellation.

ah OK - a hit, and a miss! — Wayfarer

Just my opinion, I didn't want to give you a hard time for posting it, she's always worth watching. That particular video annoyed me but as you know I'm easily annoyed! It's good that you posted it and people should watch it. She does talk about the use of complex numbers in physics and that's definitely worth watching.

Sabine Hossenfelder has a current blog post on Do Complex Numbers Exist? Might be relevant, I'm not qualified to judge. — Wayfarer

I love her videos and articles but felt that she entirely missed the meaning of complex numbers in that video. When physicists talk about math it's always a disaster. But she's always worth watching.

What argument have I lost? — Metaphysician Undercover

@Ryan claims that we should poll everyone in the world; I claim we should poll the professional mathematicians; and you claim we should poll the philosophers specializing in metaphysics. Doesn't seem like there's any qualitative difference between your position and the others.

"Existence" is a word which is being used here as a predicate. — Metaphysician Undercover

Don't start that! I'm sure you know the trouble one gets into using existence as a predicate. Existence is not a predicate.

So we need criteria to decide which referents have existence in order justify any proposed predication. Naturally we ought to turn to the field of study which considers the nature of existence, to derive this criteria, and this is metaphysics. — Metaphysician Undercover

This is a mistake on your part. Doctors know more than the average person about doctoring; and baseball players know more about baseball. But metaphysicians don't know any more about existence than the rest of us. All they know is what other thinkers have said about the problem. Being a philosopher confers no special knowledge at all about what's true. That's one of the fundamental problems with philosophy. If I study math in school, I'll learn about math. If I study philosophy, I'll learn about what the great thinkers have said about philosophical problems; but I won't learn the truth about anything. So you have no credential whatsoever.

Mathematics does not study the nature of existence, so mathematicians have no authority in this decision as to whether something exists or not, — Metaphysician Undercover

Agreed. But mathematicians have total authority in terms of what has mathematical existence.

regardless of whether it is a common opinion in the society of mathematicians. — Metaphysician Undercover

That's the main criterion. And yes it's historically contingent, and yes it's somewhat unsatisfactory if one wants to believe in some kind of ultimate existence, but that's the position I'm taking.

If you are arguing otherwise, then show me where mathematics provides criteria for "existence" rather than starting with an axiom which stipulates existence. — Metaphysician Undercover

The entire history of mathematics is filled with examples, starting from the discovery of irrational numbers right through to the present day. Now you may well respond that if I'm admitting this was a discovery and not an invention, then irrational numbers were already "out there" waiting to be discovered. I have no good answer for this objection but neither does anyone else.

I like your quote and I see where you're coming from, especially given that I'm talking so informally. — Ryan O'Connor

It was wrong of me to poke fun at you without responding to your last two lengthy posts to me. Fact is I wouldn't know where to start so it's better for me to leave it alone. If you can't graph a simple polynomial then there's no conversation to be had. Note that the poly I gave you has a real root at 2 which none of your pictures show. And your claim that there's no such thing as instantaneous velocity is falsified by your car's speedometer. I'm sure you have some interesting ideas but I probably won't engage much going forward, and I'll refrain from indirect remarks even if they are from great movies.

Of course I realize that. I'm trying to show Ryan the difficulties with his approach. — norm

I haven't been able to understand Ryan's approach. As in Apocalypse Now, when Kurtz asks, "Are my methods unsound?" And Willard responds: "I don't see any method at all, Sir."

Why do believe in a single pi in the first place? — norm

Pi only encodes a finite amount of information. $\displaystyle \pi = 4 \sum_{k = 0}^\infty \frac{(-1)^k}{2k + 1}$. That's 16 characters if I counted right.

I don't see why this discussion is hung up on such an obvious point. Pi is no more mysterious than 1/3 = ...3333, another number that happens to have an infinite decimal representation. Decimal representation is handy for some applications and not for others. Decimal representation is broken. Some real numbers have infinite representations and others have two distinct representations. You should never confuse a number with any of its representations, so all of the other expressions for pi are just as valid.

https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

If you're a cisgender straight guy and you prefer not to date a male-to-female transgender, you're a transphobe. That's the word from the SJW playbook these days.

https://www.advocate.com/commentary/2019/12/14/refusing-date-trans-people-transphobic

https://www.huffingtonpost.ca/entry/transgender-dating_ca_5de12effe4b0d50f32a106a4

https://www.bbc.com/news/blogs-trending-42652947

https://www.vice.com/en/article/3kgvab/transgender-sex-chasers-cisgender-men

https://www.reddit.com/r/AskFeminists/comments/9ulig6/is_it_bad_to_be_a_straight_guy_whod_only_date_cis/

The only thing we have access to is qualitative sensory data. That's all. — Dharmi

Berkeley's subjective idealism.

Subjective idealism, or empirical idealism, is the monistic metaphysical doctrine that only minds and mental contents exist. It entails and is generally identified or associated with immaterialism, the doctrine that material things do not exist. Subjective idealism rejects dualism, neutral monism, and materialism; indeed, it is the contrary of eliminative materialism, the doctrine that all or some classes of mental phenomena (such as emotions, beliefs, or desires) do not exist, but are sheer illusions.

https://en.wikipedia.org/wiki/Subjective_idealism

Perhaps your time is better spent telling me why my 'parts-from-whole' view is wrong rather than hearing me informally complain about why I think your 'whole-from-parts' view is wrong... — Ryan O'Connor

I don't understand your idea at all. Suppose the position of a particle at time $t$ is given by $f(t) = t^3 - 5 t^2 + 9t - 6$. Find the acceleration of the particle at t = 47.

How do you do that problem after you've thrown out 350 years of calculus and our understanding of the real numbers? What happens to the whole of physics and physical science? Statistics and economics? Are you prepared to reformulate all of it according to your new principles? And what principles are those, exactly? That there aren't real numbers on the real number line?

that a line is not composed of points, but instead points emerge from lines? — Ryan O'Connor

What does that mean?

ps -- I'm not making a geometric statement. The real number line is composed of real numbers. How can you disagree with that?

If time can be broken down into a collection of instants and if at one instant we're stationary and the next instant we're not — Ryan O'Connor

Second clause does not follow from the first. A mathematical line is composed of points. But there is no "next" point after any given point. You are confused on this ... point.

I think he's touching on something — Ryan O'Connor

You're thinking of Andrew Cuomo.

FWIW, and because no one has mentioned it yet, 'infinite limits' are taught in calculus as usefully specific ways to indicate divergence. — norm

This has been mentioned to @Metaphysician Undercover repeatedly. For years.

Beyond the excellent point you make about these points, I'll invoke the issue of intelligibility. What exactly do we have in mind? I understand representing something like a pure location with a vector, but it's still somewhat vague. — norm

Not sure what you mean. Mathematical points on a line are represented as real numbers; mathematical points in n-space are represented as ordered n-tuples of real numbers. There are other kinds of spaces with other notions of points. For example in function spaces, functions themselves are the points.

None of which has anything to do with physics. Physics uses math to express and model their theories of nature, but the theories are not literally nature itself. Nature is beyond math IMO.

He must know how crankish he sounds — norm

This isn't the time or place to discuss Wildberger's crankitude and I'll leave you to your research. FWIW he's one of two PhD-level math cranks I know, the other being Edgar Escultura. As I mentioned, Wildberger has some very nice historical expositions on Youtube and is a perfectly sane and smart guy, just cranky about the real numbers. Then of course there was the late Alexander Abian, a perfectly respectable mathematician who advocated blowing up the moon.

That's his proper name, probably the one he was born with, and he's publicly called a crank. A little part of me cheers for the underdog — norm

You're right, he's a professor of math and he puts his ideas out there under his own name, and the likes of me throws rocks from behind my anonymous handle. Can't deny it.

obviously you have every right to call Wildberger a crank — norm

I'm not the only one, Google around. And FWIW, I'm a crankologist. I enjoy reading math cranks and am familiar with the work of most of the prominent ones.

Hi ! I'll private-message you about that. — norm

Oh boy they're gonna gossip about the rest of us!

It's true, math is a social activity, but I bet a lot of it exists without a preponderance of mathematicians even being aware of it, much less agreeing it exists. — jgill

In your professional research, did you have the feeling that you were investigating aspects of truths outside yourself that you were trying to find out about? Or that you were merely pushing around symbols in a formal game? I'd wager the former but I'd be interested to know.

Scientists have defined a "point particle" as a dimensionless element of physical reality. — Proximate1

I do not believe any scientist has proposed the physical existence of such a thing. For one thing, in physics we know that our theories break down at the Planck scale. There might be something "down there" or there might not be; but we have no mathematical tools with which to approach the question.

Newton proved that we can replace a mass with a point mass for purposes of calculation; but that's not the same as anyone thinking there are dimensionless points in reality.

I saw a very interesting video the other day. The Secret Life of Quarks. You know how we're told that protons and neutrons each have three quarks inside them? It's not that simple. The number three comes out of integrating the "quark density function" to show that the difference of the number of quarks minus the number of antiquarks is three. But there might be millions, billions, trillions of quarks. I'm not actually sure how all this works, but I did understand that it's not like three as in one, two, three. You get a different number of total quarks depending on the scale at which you look. It's very mysterious. And this is the limit of theory. Nobody has any idea what's smaller.

I'd be very surprised if reality contains dimensionless mathematical points.

Check this out if you're interested in particle physics, it's quite watchable but a lot deeper than some of the handwavy popularized stuff.

https://www.youtube.com/watch?v=H_PmmMkGyx0

I addressed the issue in my post. There is only a need to conclude infinite acceleration if we assume absolute rest, — Metaphysician Undercover

I addressed this in my post. The position and velocity functions are not differentiable at time zero. So there's no well-defined acceleration. Nor as others pointed out does relativity bail us out. Relative to your own frame of reference, you are at zero velocity at time zero and nonzero velocity a short time afterward. You have to come to terms with that.

I like to think that there exist truths independent of consciousness, whether it's certain axioms of mathematics or the laws of nature. — Ryan O'Connor

Where do they live? And what else lives there? The baby Jesus? The Flying Spaghetti Monster? Pegasus the flying horse? Platonism is untenable. There is no magical nonphysical realm of stuff. And if there is, I'd like to see someone make a coherent case for such a thing.

But I think '5 is prime' is a contingent truth... — Ryan O'Connor

Well this I don't understand. Contingent on what? If there is a Platonic realm after all, surely mathematical truths live there if nothing else.

e.g. Norman Wildberger — Ryan O'Connor

Wildberger is a nut, his math doctorate notwithstanding. He does have some very nice historical videos and some interesting ideas. But his views on the real numbers are pure crankery. You should not use himin support of your ideas, since that can only weaken your argument.

Axioms are not my strength, but could we perhaps reinterpret the Axiom of Infinity to assert the existence of an algorithm for generating an infinite set, without requiring that the infinite set actually exists? — Ryan O'Connor

No. The existence of an inductive set is specifically the content of the axiom of infinity. If all we wanted was a procedure for cranking out infinitely many numbers, Peano would suffice. 0 is a number and if n is a number then so is Sn, the successor of n. That gives us each of 0, 1, 2, 3, 4, ... without end.

The axiom of infinity lets us take all of the numbers given by the Peano axioms and put them in a set. That's the essential content of the axiom.

The Peano axioms gives us 0, 1, 2, 3, ...

The axiom of infinity gives us {0, 1, 2, 3, ...}

The former will not suffice as a substitute for the latter. For example we can form the powerset of {0, 1, 2, 3, ...} to get the theory of the real numbers off the ground. But we can't form the powerset of 0, 1, 2, 3, ... because there's no set.

Also I'm not sure what you intend by writing, "actually exists." We only mean that an infinite set has existence within our theory. There's nothing "actual" about it, of course. Personally I doubt that any sets at all have actual existence. I can see the apple on my desk but I confess I don't see the set containing the apple. Sets are strictly an abstract formal system. Existence is relative to whatever the axioms say. Perhaps you didn't intend for "actually exists" to be different than, "mathematically exists," in which case never mind this paragraph.

I'm not convinced that Diogenes appreciated that profundity of Zeno's paradoxes. — Ryan O'Connor

If I point out to @Metaphysician Undercover that he can get in his car and drive to the store without being crushed before he drives the first inch; am I failing to appreciate the profundity of his beliefs? I think not!