I think you want to believe in free will. — turkeyMan
Why would you think that? What have I said that would lead to that conclusion? Or are you just making assumptions? — Banno
That doesn't show that determinism fails, it shows the limits of the predictive method used. — DingoJones
Yet no one could have deduced the resting place of the ball – because of the indeterminateness that you get even in the Newtonian mechanics, arising from the finite accuracy of measurements. From exact figures for positions, velocities, directions, spins and masses you might be able to calculate the result as accurately as you chose. But the minutest inexactitudes will multiply up factor by factor, so that in a short time your information is gone. Assuming a given margin of error in your initial figure, you could assign an associated probability to that ball's falling into each of the pipes. If you want the highest probability you assign to be really high, so that you can take it as practical certainty, it will be a problem to reckon how tiny the permitted margins of inaccuracy must be – analogous to the problem: how small a fraction of a grain of millet must I demand is put on the first square of the chess board, if after doubling up at every square I end up having to pay out only a pound of millet? It would be a figure of such smallness as to have no meaning as a figure for a margin of error.
On review, Anscombe seems to me not to be saying that even if we had perfect information we could not predict the landing place of the ball, but rather that since we do not have perfect information, we cannot do so. — Banno
That is, determinism ceases to be a physical Law so much as a metaphysical desire on the part of certain philosophers — Banno
If nothing else, they ought not be taken as granted. — Banno
So there are 3 things at play, the knowledge of how something is determined to go(which we can do pretty well on pretty simple examples), the actual things that determine the way things go and the range of determinate factors we are actually able (and/or not able to) to track.
It seems to me only the middle one is what determinism is about. The others are so much more generic and tangental as to fall under different purview. — DingoJones
despite it might not be possible to know all the digits of a physical quantity (through mea- surements), it is possible to know an arbitrarily large number of digits.
there exists an actual value of every physical quantity, with its infinite determined digits (in any arbitrary numerical base).
...a finite volume of space can only hold a finite quantity of information. But if a measurement within that volume were made to infinite precision, that measurement would consist in infinite information. Hence, infinite precision is not possible. — Banno
Del Santo's definition, all his own afaik, is that infinite epistemological precision means that the number of of decimal points has no finite lower bound, but may not be infinite. This is equivalent to saying that the error may be arbitrarily small, but not zero, which, to me, says it cannot be arbitrarily small. His infinite precision is that attained by infinite technological progress which always approaches, but never reaches zero uncertainty. It is in itself a reasonable definition, but he is using different language to cast doubt on determinism rather than using argumentation within the same language. — Kenosha Kid
indeed, before you enter into a discussion with Meta, do take a look at the 0.999... = 1 thread. — Banno
Del Santo's definition pertains to a finite number of decimal points, however large. 0.999... has an infinite number of decimal points, and so is identically 1. — Kenosha Kid
However, the principle of infinite precision is inconsistent
with any operational meaning, as already made evident by
Max Born. — https://fqxi.org/data/essay-contest-files/Del_Santo_FQXI_essay_indete.pdf
As we will show in the next section, one can indeed envision
an alternative classical physics that maintains the same general laws (equations of motion) of the standard formalism, but
dismisses the physical relevance of real numbers, thereby assigning a fundamental indeterminacy to the values of physical
quantities, as wished by Born. In fact, “as soon as one realizes that the mathematical real numbers are not really real, i.e.
have no physical significance, then one concludes that classical physics is not deterministic.” [13]. — https://fqxi.org/data/essay-contest-files/Del_Santo_FQXI_essay_indete.pdf
More word games, Banno?The standard philosophical prejudice is that given an accurate enough account of the position of the box and a given ball, a competent physicist will be able to tell us which of the bins across the bottom the ball will land in.
And in this sense the path of the ball is determined.
But of course no one could determine the final resting place of the ball. Even the smallest error in the initial positions will be magnified until it throws out the calculations. — Banno
You actually showed that it doesn't because you used reasons to determine your conclusion.wrote this in a time of only nascent chaos theory, which could only serve to amplify her point.
The notion that the universe is determined fails. — Banno
Many years ago, I visited the Seattle World's Fair, and came across a large display of a Galton Box or Quincunx, [image below]. The adjacent sign says : "when the falling balls are observed one-by-one the path of each is unpredictable, but taken many by many they form an orderly predictable pattern". This is a graphic illustration of order within randomness. The overall bell-shaped pattern at the bottom is predictable, and seems to be predestined by statistical laws of Probability. However, one of the white ping-pong balls was painted red, and it landed in a different location after each randomized ball-drop. That exception to the rule seems to imply that there is Freedom Within Determinism.The standard philosophical prejudice is that given an accurate enough account of the position of the box and a given ball, a competent physicist will be able to tell us which of the bins across the bottom the ball will land in. . . . . The notion that the universe is determined fails. — Banno
we can be quite sure that a third measurement won't be at 0.7T, for instance, unless something other than gravity was acting. — Kenosha Kid
And in this sense the path of the ball is determined.
But of course no one could determine the final resting place of the ball. Even the smallest error in the initial positions will be magnified until it throws out the calculations.
Anscombe wrote this in a time of only nascent chaos theory, which could only serve to amplify her point.
The notion that the universe is determined fails. — Banno
..it's clear you did not take the time and effort to understand it... — tim wood
Now, in philosophy we understand that what appears as infinite is really indefinite, or indeterminate, — Metaphysician Undercover
If it is a given that the account of the position of the box and a given ball are accurate, then why would there be errors? — Harry Hindu
Do you understand the ratio between the circumference and diameter of a circle to be a number? — tim wood
Del Santo's reply to the ontological point is, in part,
...a finite volume of space can only hold a finite quantity of information. But if a measurement within that volume were made to infinite precision, that measurement would consist in infinite information. Hence, infinite precision is not possible. — Banno
Given infinitesimals there seems to be no reason to conclude that an infinite amount of information could not be "held" within what we would think of as a finite volume of space. — Janus
No, it's an irrational ratio, — Metaphysician Undercover
Of course, I do not intend to banish from physics the idea of a real number. It is indispensable for the application of analysis. What I mean is that a physical situation must be described by means of real numbers in such a way that the natural uncertainty in all observations is taken into account.'
Referring to figure 1, consider a (classical) par- ticle that is bound to move in a one-dimensional cavity with perfectly elastic walls and total length l. If the particle has a perfectly determinate (i.e. with infinite precision) initial position x(t = 0) = x0 and velocity ⃗v(t = 0) = ⃗v0 , classical physics then allows to predict, also with infinite precision, the future positions x(t) and velocities ⃗v(t) for any time instant t.
The alternative explanation being offered by Del Santo is that the initial velocity does not correspond to some real number, but instead to some region of the real numbers. — Banno
See, your guy. He, your guy in your quote, does not have a problem with real numbers as numbers. — tim wood
But what's the point?In fact “as soon as one realizes that the mathematical real numbers are not really real, i.e. have no physical significance, then one concludes that classical physics is not deterministic.
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