旧日的存档： kingdom of coins

King Coin’s Palace
Enter King Coin, Minister of Science, several other coins.

King Coin: Know that we have divided
into two kingdom: that of heads and that of tails.
Eternal quest of flipping
sets two force equivalent through chaos.
Of all the scientists, I shall summon several devoted to study of chances,
and the theory shall not be intellectual game.
But our proper pursuit of soul and act.

King Coins casts a magic .
Enter Laplace

Laplace: I am flattered to be summoned, King Coins. I have always been a devoted servant to emperors and kings, and it is my honor that my theory of chance would perform in in the ruling of a kingdom.[ Laplace, although a fruitful scientist, was sometimes the target of contempt for his political insincerity. However, in applying probability theory into the studying and ruling of population of France, his motivation is more mathematical. See Gilspie, 4.]

Minister: Please begin, Laplace

Laplace:Let us first consider the simplest case: If a even coin is flipped, the two outcomes— tail-side and head-side are equally likely.[ Laplace first proposed his definition of chance in Mémoire sur les suites récurro-récurrentes et sur leur usages dans la théorie des hasards,published in Savants étranges 6, 1774, p. 353-371. Oeuvres 8, p. 5-24. This definition is very much the same as the classic definition of probability in modern textbook. However, thought out his most philosophical writings, Laplace seems to dwindle between a subjectivism and a objectivism account of probability. This dialogue would focus on the subjectivism side of Laplace for sake of simplicity.]

Minister: I’m listening, my friend, and that certainly correspond to our instinct.

Laplace: In any cases like this, in which we are unable to find substantial difference between each outcome, we have to assume that the ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.

Minister:So these are your definition of probability.

King Coin casts a magic
Enter C.S.Peirce

Laplace: As it be,there should be no real probability at all!

Minister: What? You just demolished your all previous talks!

Laplace: Please be patient, my friend, and let us consider again from the beginning: The coin’s state is actually determined by its previous physical state the moment before landing, would you not agree?

Minister: I guess that should the basic premise of determinism, but I will allow it.

Laplace: And the exact physical state before landing was determined by previous state!

Minister: IAccepting the idea of determinism.

Laplace: With such assumption, there cannot be a genuine probability floating and hovering above the caustic chain! Were there a omniscient being, it would know any single future flipping coin’s side by simply looking at the current state and calculate. On the contrary, our inability to predict and understanding of the coin as a system of probability, is just the result of our ignorance.

C.S.Peirce: So you were saying that chances do not really play a part in natural phenomena, it’s only a result of our ignorance.

Laplace: I think you have made my point clear.

C.S.Peirce: Your argument is based on determinism, searching for the certainty of universe. However, to extend my opinion, I might have to turn away from simple system and to biology, and let us both took determinism for granted at the moment.

Laplce: As I now do have a lot of time to Research In Peace, I do read a little about evolution and biology.

C.S.Peirce:And you would agree, that with the evolution species become multifarious, humankind more complex?

Laplace: That’s true.

C.S.Peirce: But uniformity does not originate variety on its own, which is to say that same condition two cases would only generate identical result. The determinism here is surely unable to explained the fact that nevertheless our world is becoming a more varied place It is a irreversible process, contrary to what determinism has presumed. Many more challenges, such as the problem of consciousness, of feeling free to change one’s action despite that the given condition of mechanical status is fixed, but I will rest my counterargument for the moment and go for the its influence on the theory of chance: The chance could not be a derivation of one’s epistemological status: what one perceives has no real macro effect on the dice system being considered.[ Peirce actually had four phenomena which he thought determinism would not be able to explain: growth, complexity, regularity and consciousness, in Collected Papers of Charles Sanders Peirce, Vols. i-vi ed. See Turley.]

King Coin casts a magic
Enter Strevens

Strevens: On the last sentence I agree with Peirce, a physical system like the even dice has its own probabilities, and one’s knowledge would not change the fact.

C.S.Peirce: Exactly, chances should be of empirical content, and can be corroborated with statistical research.

Laplace: Of course I am not talking about a random one’s knowledge would change the the dice side. Knowledge of the dice, which could be easily tampered and would surely have no effect is not ignorance itself, what one does not know about the system could be a natural and accurate depiction of the system.

Strevens:Even if the lacked knowledge—the ignorance- is a useful indication for the exact side the coin would be flipped, the relation should be a secondary one rather than a direct reflection or a genuine cause. As a bystander belief changes his ignorance changes but the change would have no impact on the actual probability of the dice system, so that ignorance itself could not constitute the cause probability.

Minister: I have understood your point. Now Peirce, how would you define your empirical content of your probability?

C.S.Peirce: The probability of the flipped dice being tails is not be a proposition or an event or a state nor is it a type of event or state an argument should be assigned to the probability with premisses and a conclusion. In this case, the premisses are the conditions of the random throwing of the even dice, the conclusion the side of the flipped coin.
When conducting an empirical research of the probabilities, we should start by simple repeat of the same experiment, and mark each result, the denominator of the probability to be the total tests hold ,the numerator the time of the conclusion(the tails side). As we repeats and remarks, the denominator is growing infinitely large, and we can see the probability of the argument to be the limit of the crucial ratio .

Laplace: You seem to understand probability in the chain of trials, yet in this single dice flipping event, where only one experiment is taken, what statistics data has to offer to become denominator or numerator are only 0 and 1, that never reflects the result.
And when speaking of statistics, the stablitiy of numbers, such as the letters or lotteires sent in France remained fairly constant, which calls for a stochastic proof rather than a explanation of “growth”, but I will leave it here for now[ See Sheynin, 127]

C.S.Peirce: I admit that the probability could not be measured accurately in one single trial, but in one single experiment there is the derivation from laws of nature, being a universal chance.

Laplace: Which should have no effect on the real world.

C.S.Perice: Quite opposite, the unviersal chance is a delicate nature that is embedded in every systems and presents the lightest violation of nature per se, and it is the violation of nature that unable us to predict the side precisely, but not vice versa. In your theory, probability is a mathematical representation of chance, but chance should be taken to mean real departures from the laws of nature, lawlessness. So the influence of chance is actually everywhere.

Strevens:Then I am afraid that both of your are to mingle a epistemological question with a physical one, as we are again faced with the question of proper knowledge of the coin system, and I doubt that the latter problem could be be a substantial base of the former one.

Strevens:The coin-flipping coin itself could provide a powerful counterexample!
Suppose we have flipped the even coin for a hundred times, and each times we encountered the result of coin being the head.
Would it be rational to suppose that the flipped coin is more likely to be head-side.[ . The question of wheel of fortune is first proposal by Henri Poincaré (1905) and adopted in a modified version
by Hans Reichenbach (1949). This proposal is similar in certain ways to Strevens’s, and took for granted, without explaining, an important inference from symmetry to probability.
]

Minister: No, it would be irrational, the probability should be still hold to be 50%.

Strevens: You are right. We consider it as an accident. It suggests that, far from being based on ignorance, our knowledge of the actual probability is actually based on knowledge of the certain system.

Laplace: Yet without inferential evidence on how the dice should be thrown randomly,the exact physical probability can not be determined! If, say, the thrower is a experienced cheater, the physical probability might turns out to be other than 50%. And how would you arrive the conclusion of probability from the premise of symmetry?

Strevens: The experienced cheater would contradicts our presuppositions that the system is perfectly symmetric! However, we could still use a different example, to show that probability in a deterministic system can still be derived directly from symmetry. Allow me in diverging from the current affairs of the coin kingdom to look at what happens around a wheel of fortune.

(Strevens took out a red and black wheel)

Strevens:Look at this wheel of fortune, consisted in equally wide red and black sections(without the zeroes), the wheel rotates around the fixed central axis, while a fixed pointer with which we can see the outcome. The wheel itself is a Suppose the wheel starts to rotate when the pointer is at the area of 0 at a given speed. And what are the chances of the pointer stopping at a black section?

C.S.Peirce:50%, equal to the probability of it stopping at a red section

Works Cited

Gillispie, Charles Coulston. “Probability and Politics: Laplace, Condorcet, and Turgot.” Proceedings of the American Philosophical Society 116, no. 1 (February 15, 1972): 1–20.

Turley, Peter T. “Peirce on Chance.” Transactions of the Charles S. Peirce Society 5, no. 4 (October 1, 1969): 243–254.

Sheynin, O. B. “P. S. Laplace’s Work on Probability.” Archive for History of Exact Sciences 16, no. 2 (December 8, 1976): 137–182.

Strevens, M. “Inferring Probabilities from Symmetries.” Noûs 32, no. 2 (1998): 231–246.