Digital Companion to C. S. Peirce
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1866 | Lowell Lectures on The Logic of Science; or Induction and Hypothesis: Lecture VI. Practical Maxims of Logic | W 1:441

The inductive or hypothetic conclusion, therefore, stands to one of its premisses in the relation of a deductive or syllogistic premiss to its conclusion, the second premiss of the induction or hypothesis remaining a premiss in this explaining syllogism. It is in fact a sufficient definition of a scientific inference to say that it is the inference of one of the premisses of a syllogism from the other premiss and from the conclusion. If fact, every such inference is valid, that is to say, lends an additional probability to the proposition inferred, altho’ the fact indicated by this proposition may still remain entirely unknown or even grossly improbable.

1868 | Some Consequences of Four Incapacities | W 2:237; CP 5.307

The association of ideas is said to proceed according to three principles – those of resemblance, of contiguity, and of causality. But it would be equally true to say that signs denote what they do on the three principles of resemblance, contiguity, and causality. There can be no question that anything is a sign of whatever is associated with it by resemblance, by contiguity, or by causality: nor can there be any doubt that any sign recalls the thing signified. So, then, the association of ideas consists in this, that a judgment occasions another judgment, of which it is the sign. Now this is nothing less nor more than inference.

1880 | On the Algebra of Logic | W 4:164; CP 3.160

A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief. The representation to ourselves that we have a specified habit of this kind is called a judgment. A belief-habit in its development begins by being vague, special, and meagre; it becomes more precise, general, and full, without limit. The process of this development, so far as it takes place in the imagination, is called thought. A judgment is formed; and under the influence of a belief-habit this gives rise to a new judgment, indicating an addition to belief. Such a process is called an inference; the antecedent judgment is called the premise; the consequent judgment, the conclusion; the habit of thought, which determined the passage from the one to the other (when formulated as a proposition), the leading principle.

1891 | Review of William James's "The Principles of Psychology" | CN 1:107; W 8:235; CP 8.63

…unconscious inference differs essentially from inference in the narrow sense, all our control over which depends upon this, that it involves a conscious, though it may be an indistinct, reference to a genus of arguments.

1893 | Grand Logic: Division III. Substantial Study of Logic. Chapter VI. The Essence of Reasoning | CP 4.55

…inference has at least two elements: the one is the suggestion of one idea by another according to the law of association, while the other is the carrying forward of the asserting element of judgment, the holding for true, from the first judgment to the second. That these two things suffice [to] constitute inference I do not say…

1893 [c.] | Grand Logic: Book I. Of Reasoning in General. Introduction. The Association of Ideas | CP 7.443-4

When an idea bearing the stamp of experience suggests another, that other in many cases itself carries that same stamp, which is carried forward in suggestion and thus a derivative authority from experience is conferred upon an idea which may have neither the vividness nor the other marks of directer experience. This sort of suggestion is inference. The law of association will divide inference into inferences by contiguity and inferences by resemblance, meaning by these latter inference from the occult inward nature of ideas or of the soul.

All inferences are really performed under the influence of the law of association. But all psychical actions divide into two great classes, those which are performed under the uncontrolled governance of association and those in which by the “agency” of consciousness, – whatever that may mean, – the actions come under self-criticism and self-control. The latter class of actions may be pronounced good or bad; the former could not be otherwise than they were.

1895 | Short Logic | EP 2:11-12

Reasoning is the process by which we attain a belief which we regard as the result of previous knowledge. [—]

Again, a given belief may be regarded as the effect of another given belief, without our seeming to see clearly why or how. Such a process is usually called an inference; but it ought not to be called a rational inference, or reasoning. A blind force constrains us. [—]

The word illation signifies a process of inference. Reasoning, in general, is sometimes called ratiocination. Argumentation is the expression of a reasoning.

1901 | Hume's Argument against Miracles, and the Idea of Natural Law (Hume) | MS [R] 873:3 (var.); HP 2:912

Inference is any act of deliberate assent, in any degree, however slight, which a man accords to a proposition because he thinks that assent warranted by his already accorded assent to another proposition or propositions, called the premisses.

1911 | A Logical Critique of Essential Articles of Religious Faith | MS [R] 852:2

The word Reasoning may be used as the name either of a mental action or of a mental occupation. In the latter sense, it is that occupation of the mind in which one casts about for arguments, considers them, and draws a conclusion from them. In the former sense, it is a synonym of inference, or the passage from an argument to a conclusion.

1913 | An Essay toward Improving Our Reasoning in Security and in Uberty | EP 2:463

When it happens that a new belief comes to one as consciously generated from a previous belief, - an event which can only occur in consequence of some third belief (stored away in some dark closet of the mind, as a habit of thought) being in a suitable relation to that second one, - I call the event and inference, or a reasoning.

nd | Fragments [R] | MS [R] 839

An argumentation within one’s own mind, by which the thinker is more or less inclined to believe something, or by which he sees that something must be true, is called an inference.