Notes on Hume's Treatise

by G. J. Mattey

PART III. OF KNOWLEDGE AND PROBABILITY

§ XI. Of the probability of chances.

To get the full force and evidence of the system, its consequences are considered. The system can be used to explain other sorts of reasoning.

Probability has been said by philosophers to be that reasoning which is not based on the comparison of ideas alone (as is knowledge ), and all arguments from cause and effects are on this definition probable. But we commonly attribute to causal arguments "a superior kind of evidence," as in e.g. "the sun will rise to-morrow," or "all men must dye." We will call these proofs, which are derived from the cause/effect relation and "are entirely free from doubt and uncertainty." Then probability is evidence which is accompanied by uncertainty.

Probability "or reasoning from conjecture" is divided into two types: what arises from chance and from causes.

Chance, lack of cause (though not real in itself) leaves the imagination indifferent, so its object is called contingent, as opposed to cause, which determines our thoughts "and in a manner forces us to survey such certain objects, in such certain relations." Chance restores the initial condition of indifference which existed before the production of the habit.

No chance can be superior to any other, for if there is any inclination there is no indifference, thus allowing for a cause. "This truth is not peculiar to my system, but is acknowledg'd by every one, that forms calculations concerning chances."

We must allow causes to be intermixed with chance to make "calculations concerning the laws of hazard," which then can be applied to otherwise indifferent situations to give superior combinations of chances. There is "a conjunction of necessity in some particulars, with a total indifference I others." Otherwise, "every notion, that the most extravagant fancy can form, is upon a footing of equality." So we mix the fact that a die must fall on one side with the indifference concerning which side will turn up.

How does a superior combination of chances influence our opinion? It is neither by demonstration or probability (the argument concerning causes is here repeated). We cannot prove with certainty that an event will fall on the side of the odds, on pain of violating the notion of chance. If we say we know with certainty that it is more probable that it will happen on the side with the odds, what is the notion of probability? It can only be "number of chances," in which case nothing is added: "we do no more than affirm, that where there is a superior number of chances thre is actually a superior, and where there is an inferior there is an inferior; which are identical propositions, and of no consequence." So how can a superior number of chances produce assent?

Suppose a die has one number of spots on four sides and another number on two. 1) there are certain causes, such as gravity, solidity and figure which determine its fall, 2) there are six sides, which are supposed to be indifferent, 3) a certain number is written on each side.

The mind must consider the motion of the die when it is let go: habit dictates this. It will turn up one side, as the results of intermingled causes. Chance then has it that all sides are equally probable. The imagination does not have all sides turned up (impossible) or any one side (contrary to hypothesis), but "divide[s] its force equally among them." The vivacity is thus split. The sides with the same figure unite the dispersed force, and this proportional to their numbers. "The impulses of the former [four sides] are, therefore, superior to those of the latter." The inferior takes out its share of the superior, and we are left with the difference.

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