Digital Companion to C. S. Peirce
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1896 | The Regenerated Logic | CP 3.442

possibility may be understood in many senses; but they may all be embraced under the definition that that is possible which, in a certain state of information, is not known to be false.

1897 | The Logic of Relatives | CP 3.527

I formerly defined the possible as that which in a given state of information (real or feigned) we do not know not to be true. But this definition today seems to me only a twisted phrase which, by means of two negatives, conceals an anacoluthon. We know in advance of experience that certain things are not true, because we see they are impossible. Thus, if a chemist tests the contents of a hundred bottles for fluorine, and finds it present in the majority, and if another chemist tests them for oxygen and finds it in the majority, and if each of them reports his result to me, it will be useless for them to come to me together and say that they know infallibly that fluorine and oxygen cannot be present in the same bottle; for I see that such infallibility is impossible. I know it is not true, because I satisfy myself that there is no room for it even in that ideal world of which the real world is but a fragment. I need no sensible experimentation, because ideal experimentation establishes a much broader answer to the question than sensible experimentation could give.

1897-8 | Mems for 8 Lectures | MS [R] 945:2

A possibility of some sort is […] a particular tinge of consciousness. I do not say that possibility is a consciousness exactly but the tinge of a consciousness, a potential consciousness. However, the distinction is little more than verbal.

1902 | Possibility, Impossibility, and Possible | DPP 2:313-314; CP 6.364-367

The term is used to express a variety of meanings which, although distinct in themselves, yet flow readily into one another. These meanings may best be grouped according as they have (1) an ontological objective value, or a logical subjective value; and (2) according as they are used antithetically to actuality or necessity. The antithetical point of view is the most convenient from which to begin.

Possibility may mean that something is (1) not actual, or (2) that, while it possesses actual existence, that existence lacks causal or rational necessity.

(1) As opposed to the actual, the phrase has again a double meaning. (a) Taken objectively, it may mean something as yet undeveloped, since not presenting itself in actually objectified form, but capable of doing so at some future time, when all the conditions of its realization occur: latent, potential being. This implies capacity for realization; and, if this capacity be taken in an active sense, connotes some inherent tendency to actuality, which, if not thwarted, leads to final completeness of being. This involves the active sense of potentiality, of force, etc. It is close to the literal sense of the term (posse, can be). This is the dominating sense in Greek philosophy, being connected with Aristotle’s teleological theory of development. (b) Taken logically, it denotes that there is some ground for asserting actuality, but not sufficient to justify a positive statement: may, as distinct from can, be. Thus, possibly it will rain tomorrow. It has to do with degrees of certainty in judging.

(2) As opposed to the necessary, the term has also a double sense. (a) It may mean chance, contingency, as an objective fact. Chance again, has a double meaning: (i) something not derivable or explainable causally by reference to antecedent facts. There are those who assert the reality of such chance. On this view there are many possibilities in store in the future which no amount of knowledge would enable us to foresee or forestall. Indeterministic theories of the will assert possibilities of this sort also. (ii) Chance may mean that which, while necessary causally, is not necessary teleologically; the unplanned, the fatalistic. From this point of view the “possible” is that which unexpectedly prevents the carrying-out of a purpose or intention. It leads up to the logical sense (b), according to which the possible, as opposed to the necessary, is anything whose existence cannot be derived from reason; that, the existence of which, rationally speaking, might be otherwise. It is opposed to mathematical or metaphysical necessity, where existence cannot be otherwise than as it is. In this sense the objective actual may be only (logically) possible; the present rain-storm is actual, but since it does not follow from a necessity of thought, but only from empirical antecedents, it is not necessary, and hence just a contingent possibility. [—] In the sphere of mathematics, logic, and metaphysics there is no possibility in the strict sense; all that exists exists of necessity. In the physical and practical spheres which deal with the space and time world the notion of possibility has full sway. Everything is possible which does not contradict the laws of reason; that which is inconceivable, which violates the law of reason, is impossible. The impossible is the self-contradictory.

The nominalistic definition (nominalistic in its real character, though generally admitted by realists, as Scotus, i. dist. 7, qu. unica) that that is possible which is not known not to be true in a real or assumed state of information is, like many nominalistic definitions, extremely helpful up to a certain point, while in the end proving itself quite superficial. It is not that certain things are possible because they are not known not to be true, but that they are not known not to be true because they are, more or less clearly, seen to be possible.

1902 [c.] | Reason's Rules | MS [R] 599:36

The possible is that which in a given state of information is not known not to be true.

1905 | Issues of Pragmaticism | CP 5.454

Restricting the word to its characteristic applicability, a state of things has the Modality of the possible – that is, of the merely possible – only in case the contradictory state of things is likewise possible, which proves possibility to be the vague modality. One who knows that Harvard University has an office in State Street, Boston, and has impression that it is at No. 30, but yet suspects that 50 is the number, would say “I think it is at No. 30, but it may be at No. 50,” or “it is possibly at No. 50.” Thereupon, another, who does not doubt his recollection, might chime in, “It actually is at No. 50,” or simply “it is at No. 50,” or “it is at No. 50, de inesse.” Thereupon, the person who had first asked, what the number was might say, “Since you are so positive, it must be at No. 50,” for “I know the first figure is 5. So, since you are both certain the second is a 0, why 50 it necessarily is.” That is to say, in this most subjective kind of Modality, that which is known by direct recollection is in the Mode of Actuality, the determinate mode. But when knowledge is indeterminate among alternatives, either there is one state of things which alone accords with them all, when this is in the Mode of Necessity, or there is more than one state of things that no knowledge excludes, when each of these is in the Mode of Possibility.

1905 [c.] | The Branches of Geometry; Existential Graphs [R] | MS [R] 96

We certainly have the notion of objective possibility, whether there be such a thing or not. It may be defined as that mode of being which is not subject to the principle of contradiction since if it be merely possible that A is B, it is possible that A is not B. [—] How can the principle of contradiction fail to apply to anything? By something being held in reserve and not expressed.

1908 | The Bed-Rock Beneath Pragmaticism | MS [R] 300:39

...the Possible is an ingredient of the Truth which, in consequence of its vagueness, must remain a thought and can never be more than an idea except by taking on a definiteness that does belong to it in itself