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Letters to Paul Carus

Now we can regard the Interpretant in 3 ways, or rather there are 3 distinct things which may properly be regarded as the Interpretant. For any thing that the sign, as such, effects may be considered as the Interpretant. And this may be 1^st something merely subjective, the vague determination of the consciousness effected by the sign, 2^ndthe actual event that some signs by virtue of really acting as such bring about. For instance, let the sign be a military word or command. Then the instant action of the whole rank of men will be the Dynamical Interpretant, as I call it.

The third sense in which we may properly speak of the Interpretant is that in which I speak of the Final Interpretant meaning that Habit in the production of which the function of the Sign, as such, is exhausted.

As for the validity of the hypothesis, the retroduction, there seems at first to be no room at all for the question of what supports it, since from an actual fact it only infers a may-be (may-be and may-be not). But there is a decided leaning to the affirmative side and the frequency with which that turns out to be an actual fact is to me quite the most surprising of all the wonders of the universe.

A good account of Quantitative Induction is given in my paper in Studies in Logic, By Members of the Johns Hopkins University, and its two rules are there well developed. But what I there call hypothesis is so far from being that, that it is rather Quantitative than Qualitative Induction. At any rate, it is treated mostly as Quantitative. Hypothesis proper is in that paper only touched upon in the last section.

… the division of the elementary kinds of reasoning into three heads was made by me in my first lectures and was published in 1869 in Harris’s Journal of Speculative Philosophy. I still consider that it had a sound basis. Only in almost everything I printed before the beginning of this century I more or less mixed up Hypothesis and Induction … .

The general body of logicians had also at all times come very near recognizing the trichotomy. They only failed to do so by having so narrow and formalistic a conception of inference ( as necessarily having formulated judgments for its premises) that they did not recognize Hypothesis (or, as I now term it, retroduction) as an inference … .

Then there are 3 divisions that relate to the Object. One according to the form under which the Sign presents its Object. This is of course the object as the sign represents it, i.e. the Immediate Object.

…the essential character of induction is that it infers a would-be from actual singulars. These singulars must, in general, be finite in multitude and then […] the inductive conclusion can be (usually) but indefinite, and can never be certain…

Now we can regard the Interpretant in 3 ways, or rather there are 3 distinct things which may properly be regarded as the Interpretant. For any thing that the sign, as such, effects may be considered as the Interpretant. And this may be 1^stsomething merely subjective, the vague determination of the consciousness effected by the sign, 2^ndthe actual event that some signs by virtue of really acting as such bring about. [—]

I only make use of one division according to the 1^st of the above, the Initial Interpretant, as I call it.

… any thing that the sign, as such, effects may be considered as the Interpretant.

The names which I would propose for general adoption for the three different kinds of acceptability of propositions are

The last alone seems to be capable of a certain degree of exactitude or measurement

By plausibility, I mean the degree to which a theory ought to recommend itself to our belief independently of any kind of evidence other than our instinct urging us to regard it favorably. All the other races of animals certainly have such instincts; why refuse them to mankind? Have not all men some notions of right and wrong as well as purely theoretical instincts? For example, if any man finds that an object of no great size in his chamber behaves in any surprising manner, he wonders what makes it do so; and his instinct suggests that the cause, most plausibly, is also in his chamber or in the neighbourhood. It is true that the alchemists used to think it might be some configuration of the planets, but in my opinion this was due to a special derangement of natural instinct. Physicists certainly today continue largely to be influenced by such plausibilities in selecting which of several hypotheses they will first put to the test.

Pragmatism (pragmaticism) might be defined as that mode of thinking that never results in a concept that is equivalent to a noun substantive, since all that it thinks is an assertion, or a qualified assertion such as “suppose that (so and so),” or else it is equivalent to an expression of the speaker’s will not asserting it so much as exhibiting it.

…Pragmatism or the doctrine of pragmatic clarification […] consists in a clear conception of that Habit of Conduct in which any given concept would work out its actualization.

None of the books contain a definition of mathematical probability (which is what I mean by “probability” however measured) which will hold water. For the sake of simplicity, I will define it in a particular example. If, then, I say that the probability that if a certain die be thrown in the usual way it will turn up a number divisible by 3 (i.e., either 3 or 6) is 1/3, what do I mean? I mean, of course, to state that that die has a certain habit or disposition of behaviour in its present state of wear. It is a would be and does not consist in actualities or single events in any multitude finite or infinite. Nevertheless a habit does consist in what would happen under certain circumstances if it should remain unchanged throughout an endless series of actual occurrences. I must therefore define that habit of the die in question which we express by saying that there is a probability of 1/3 (or odds of 1 to 2) that if it be thrown it will turn up a number divisible by 3 by saying how it would behave if, while remaining with its shape, etc. just as they are now, it were to be thrown an endless succession of times. Now it is very true that it is quite impossible that it should be thrown an infinite succession of times. But this is no objection to my supposing it, since that impossibility is merely a physical, or if you please, a metaphysical one, and is not due to any logical impossibility to the occurrence in a finite time of an endless succession of events each occupying a finite time. For when Achilles overtook the tortoise he had to go through such an endless series (endless in the series, but not endless in time) and supposedly actually did so.

… the division of the elementary kinds of reasoning into three heads was made by me in my first lectures and was published in 1869 in Harris’s Journal of Speculative Philosophy. I still consider that it had a sound basis. Only in almost everything I printed before the beginning of this century I more or less mixed up Hypothesis and Induction … .

The general body of logicians had also at all times come very near recognizing the trichotomy. They only failed to do so by having so narrow and formalistic a conception of inference ( as necessarily having formulated judgments for its premises) that they did not recognize Hypothesis (or, as I now term it, retroduction) as an inference … .

When one contemplates a surprising or otherwise perplexing state of things (often so perplexing that he cannot definitely state what the perplexing character is) he may formulate it into a judgment or many apparently connected judgments; he will often finally strike out a hypothesis, or problematical judgment, as a mere possibility, from which he either fully perceives or more or less suspects that the perplexing phenomenon would be a necessary or quite probable consequence.

That is a retroduction. Now three lines of reasoning are open to him. [—]

Or, second, he may proceed still further to study the phenomenon in order to find other features that the hypothesis will explain (i.e. in the English sense of explain, to deduce the facts from the hypothesis as its necessary or probable consequences). That will be to continue reasoning retroductively, i.e., by hypothesis.

As for the validity of the hypothesis, the retroduction, there seems at first to be no room at all for the question of what supports it, since from an actual fact it only infers a may-be (may-be and may-be not). But there is a decided leaning to the affirmative side and the frequency with which that turns out to be an actual fact is to me quite the most surprising of all the wonders of the universe.

A sign in general is 1^st something Real, that is 2^nd applicable to an object different from itself and already known to the person to whom it is a sign, and 3^rd is capable of interpretation in the mind of that person, so that it will (or would if accepted as veracious sign) have some effect upon him of a kind it was calculated or fit to have.

The names which I would propose for general adoption for the three different kinds of acceptability of propositions are

The last alone seems to be capable of a certain degree of exactitude or measurement

[—]

By verisimilitude I mean that kind of recommendation of a proposition which consists in evidence which is insufficient because there is not enough of it, but which will amount to proof if that evidence which is not yet examined continues to be of the same virtue as that already examined, or if the evidence not at hand and that never will be complete, should be like that which is at hand. All determinations of probability ultimately rest on such verisimilitudes. I mean that if we throw a die 216 times in order to ascertain whether the probability of its turning up a six at any one throw differs decidedly from 1/6 or not, our conclusion is an affair not of probability as Laplace would have it, by assuming that the antecedent probabilities of the different values of the probability are equal, but is a verisimilitude or as we say a “likelihood.”