DS, ticking clocks meet dying stars and death of cosmos as useful concentrations of energy die out.

There are oscillating universe models which are consistent with an infinite past, as I stated. Replace each tick with a big bang/crunch cycle.

And that an actually transfinite number of ticks can in principle occur is the precise thing to be shown.

No. I am saying that Spitzer assumes that an infinite number of ticks *cannot* in principle occur as part of his argument. The burden is on him to prove that.

A down to 2, 1, 0. Where A = 1/m, m –> 0 i.e. is infinitesimal. KF

There are no infinitesimals in sight in your statement above. All the numbers are real and finite.

Now that we’ve clarified the ticking vs. counting issue, do you still have mathematical (not physical) objections to the eternal ticking clock example? If so, I challenge you to take some time and write them out precisely (avoiding such concepts as “of order aleph-null” and abuse of the hyperreals). Maybe even post it as an OP.>>

To this I responded:

KF, 112:>>Permit me to amplify, that first the oscillating universe models have fallen to entropy rise challenges.

Further, the observational data on the only actually observed cosmos points away from re-collapse to expansion, and as was discussed earlier with you, is fine tuned, on some calcs to 2 parts in 10^24 on density at 1 ns post singularity, with hints of yet finer tuning at earlier points.

Beyond, Spitzer summarised arguments that the transfinite cannot be traversed in separate finite steps. He did not merely assume.

Above, the exchange we have had is about precisely that.

You have admitted that you are unable to show such a traverse, and are now adverting to oscillating models that have failed.

I have taken time step by step to put the challenge in terms of completing the arrival at the present; in the face of many objections on your part.

You have spoken of how at any specific point, already an infinite number of steps is complete. I have set about constructing a distinct whole number A at transfinite distance in steps from an origin, by (in the end) using *some m –> 0, an infinitesimal such that 1/m = A, a transfinite whole number where A = W.F is such that F = 0, the fractional part vanishes*. The focal task then becomes traversing onward from A to 0, envisioned for the moment as the singularity, from which onward we go to now, n. Where as you objected to negatives [though how that was used was explained] I use asterisks to show the finite up-count since the singularity. Of course the lead ellipsis indicates that *A is not the beginning of the steps we may identify and list as a succession, it is preceded by an arbitrarily and per your suggestion for argument even possibly transfinitely large and unending set of previous values*:

. . . A, . . . 2, 1, 0, 1*, 2*, . . . n*

Such, of course was already outlined by way of making the way clear after successive objections.

The start point for a count is arbitrary, so* let us put the start at A and put it into correspondence with the naturals, i.e. this is in principle countable . . . as is implicit in stepwise succession as would happen with clock ticks*, one providing the basis for the next as energy is gated from a source and as positive, precisely lagged feedback is applied:

A, (A less1), . . .

0, 1, . . .

*Given that the traverse from A to 0 is transfinite, the task here is comparable to counting up from 0 to a transfinite in finite successive steps*, which is a supertask that is unattainable. (And I have taken the step of identifying A as a specific number a reciprocal of a number close to 0 [as the hyper reals approach takes to identify what an infinitesimal is, only in reverse], to avoid all sorts of issues on what does subtraction mean with a transfinite. Such will of course be of at least the order — scale if you will — of aleph-null from the origin at 0. I take it that we can accept the reasonableness of infinitesimals close to but not quite attaining to zero; such being foundational to a way to understand the Calculus.)

For, *once we count 0, 1, . . . n, we may always go on to n +1, etc in further steps, always being finite*.

The evidence is that *traversing an infinite succession of finite discrete steps is a unattainable supertask*, precisely as Spitzer sums up.

The worldviews significance is this, that a contingent succession of beings, with each being b_i subject to on/off enabling causal factors it must have in place for it to begin or continue to exist, must be a part of a chain of successive and in context finite discrete causes. This can be in principle enumerated and compared to the step-wise succession, e.g. of clock ticks on a clock.

We then see that *the traversal of an infinite succession of such beings is to be doubted, on grounds of needing to arrive at the singularity then onward up to us*. From the singularity (for reference to current cosmology, actually any reasonable zero point would do equally) to us is explicable on a succession, but the problem is to arrive at 0.

This may then be multiplied by the challenge that non-being, the genuine nothing, can have no causal powers. There is not space, time-point, energy, mass, arrangement, mind etc “there.” So were there ever utter nothing, such would forever obtain.

We face then, the need for a necessary root of being to account for a world that now is.

Necessary, so connected to the framework of a world that no world can be absent such. As an instance, 2 must exist in a world W where distinct identity, say A, exists: W = {A|~A}.

A world now is, so something always was.

Following, frankly, the line in the classic work, Rom 1:19 ff (which I find to be enormously suggestive of a frame for a reasonable faith worldview), this world is a world in which we find ourselves as self aware, responsibly free and rational individuals; contingent beings subject to moral government and intuitively sensing the need to respond appropriately to evident truth about ourselves and our circumstances in a going concern world.

It is appropriate in such a context to ask, what sort of serious candidates — flying spaghetti monsters etc are patently contingent imaginary parodies that do not meet the criteria for necessary being and need not apply — can we see in making a worldview level choice?

After centuries of debate, there is one serious candidate, by utter contrast with non-serious parodies, and by contrast with the challenge of traversing the transfinite etc.

The bill to be filled looks extraordinarily like:

an inherently good creator God, a necessary and maximally great being worthy of loyalty and the responsible, reasonable service of doing the good in accord with our nature.

This is Candidate A.

Candidate B is: ___________ ?>>

It seems to me, that this is the underlying worldview level issue, and that as usual, the question pivots on just what is it that can be seen in comparing difficulties of start points, first plausibles. And of course as every tub must stand on its own bottom, DS is just as duty-bound to show why he thinks an infinite successive finite step traverse is impossible as he thinks Spitzer is to justify his assertion that such is not possible. And in the bargain, I think I have stipulated that m is infinitesimal and have taken reciprocal 1/m = A as a transfinite, specific whole number in reverse of the general approach used in defining hyper reals and using the concept that properties of reals extend in the argument to the hypers. **END**

There are oscillating universe models which are consistent with an infinite past, as I stated. Replace each tick with a big bang/crunch cycle.

No. I am saying that Spitzer assumes that an infinite number of ticks

cannotin principle occur as part of his argument. The burden is on him to prove that.There are no infinitesimals in sight in your statement above. All the numbers are real and finite.

Now that we’ve clarified the ticking vs. counting issue, do you still have mathematical (not physical) objections to the eternal ticking clock example? If so, I challenge you to take some time and write them out precisely (avoiding such concepts as “of order aleph-null” and abuse of the hyperreals). Maybe even post it as an OP.>>

To this I responded:

KF, 112:>>Permit me to amplify, that first the oscillating universe models have fallen to entropy rise challenges.

Further, the observational data on the only actually observed cosmos points away from re-collapse to expansion, and as was discussed earlier with you, is fine tuned, on some calcs to 2 parts in 10^24 on density at 1 ns post singularity, with hints of yet finer tuning at earlier points.

Beyond, Spitzer summarised arguments that the transfinite cannot be traversed in separate finite steps. He did not merely assume.

Above, the exchange we have had is about precisely that.

You have admitted that you are unable to show such a traverse, and are now adverting to oscillating models that have failed.

I have taken time step by step to put the challenge in terms of completing the arrival at the present; in the face of many objections on your part.

You have spoken of how at any specific point, already an infinite number of steps is complete. I have set about constructing a distinct whole number A at transfinite distance in steps from an origin, by (in the end) using

some m –> 0, an infinitesimal such that 1/m = A, a transfinite whole number where A = W.F is such that F = 0, the fractional part vanishes. The focal task then becomes traversing onward from A to 0, envisioned for the moment as the singularity, from which onward we go to now, n. Where as you objected to negatives [though how that was used was explained] I use asterisks to show the finite up-count since the singularity. Of course the lead ellipsis indicates thatA is not the beginning of the steps we may identify and list as a succession, it is preceded by an arbitrarily and per your suggestion for argument even possibly transfinitely large and unending set of previous values:. . . A, . . . 2, 1, 0, 1*, 2*, . . . n*

Such, of course was already outlined by way of making the way clear after successive objections.

The start point for a count is arbitrary, so

let us put the start at A and put it into correspondence with the naturals, i.e. this is in principle countable . . . as is implicit in stepwise succession as would happen with clock ticks, one providing the basis for the next as energy is gated from a source and as positive, precisely lagged feedback is applied:A, (A less1), . . .

0, 1, . . .

Given that the traverse from A to 0 is transfinite, the task here is comparable to counting up from 0 to a transfinite in finite successive steps, which is a supertask that is unattainable. (And I have taken the step of identifying A as a specific number a reciprocal of a number close to 0 [as the hyper reals approach takes to identify what an infinitesimal is, only in reverse], to avoid all sorts of issues on what does subtraction mean with a transfinite. Such will of course be of at least the order — scale if you will — of aleph-null from the origin at 0. I take it that we can accept the reasonableness of infinitesimals close to but not quite attaining to zero; such being foundational to a way to understand the Calculus.)For,

once we count 0, 1, . . . n, we may always go on to n +1, etc in further steps, always being finite.The evidence is that

traversing an infinite succession of finite discrete steps is a unattainable supertask, precisely as Spitzer sums up.The worldviews significance is this, that a contingent succession of beings, with each being b_i subject to on/off enabling causal factors it must have in place for it to begin or continue to exist, must be a part of a chain of successive and in context finite discrete causes. This can be in principle enumerated and compared to the step-wise succession, e.g. of clock ticks on a clock.

We then see that

the traversal of an infinite succession of such beings is to be doubted, on grounds of needing to arrive at the singularity then onward up to us. From the singularity (for reference to current cosmology, actually any reasonable zero point would do equally) to us is explicable on a succession, but the problem is to arrive at 0.This may then be multiplied by the challenge that non-being, the genuine nothing, can have no causal powers. There is not space, time-point, energy, mass, arrangement, mind etc “there.” So were there ever utter nothing, such would forever obtain.

We face then, the need for a necessary root of being to account for a world that now is.

Necessary, so connected to the framework of a world that no world can be absent such. As an instance, 2 must exist in a world W where distinct identity, say A, exists: W = {A|~A}.

A world now is, so something always was.

Following, frankly, the line in the classic work, Rom 1:19 ff (which I find to be enormously suggestive of a frame for a reasonable faith worldview), this world is a world in which we find ourselves as self aware, responsibly free and rational individuals; contingent beings subject to moral government and intuitively sensing the need to respond appropriately to evident truth about ourselves and our circumstances in a going concern world.

It is appropriate in such a context to ask, what sort of serious candidates — flying spaghetti monsters etc are patently contingent imaginary parodies that do not meet the criteria for necessary being and need not apply — can we see in making a worldview level choice?

After centuries of debate, there is one serious candidate, by utter contrast with non-serious parodies, and by contrast with the challenge of traversing the transfinite etc.

The bill to be filled looks extraordinarily like:

This is Candidate A.

Candidate B is: ___________ ?>>

It seems to me, that this is the underlying worldview level issue, and that as usual, the question pivots on just what is it that can be seen in comparing difficulties of start points, first plausibles. And of course as every tub must stand on its own bottom, DS is just as duty-bound to show why he thinks an infinite successive finite step traverse is impossible as he thinks Spitzer is to justify his assertion that such is not possible. And in the bargain, I think I have stipulated that m is infinitesimal and have taken reciprocal 1/m = A as a transfinite, specific whole number in reverse of the general approach used in defining hyper reals and using the concept that properties of reals extend in the argument to the hypers.

END