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Charles PeirceWritings of C. S. Peirce 6 (1886-1890), pp. 354-356
/354/The first thing to remark about reasoning is that it is a passage from one belief to another. The propositions embodying the earlier and later beliefs are called respectively the premises and conclusion: the latter is said to be inferred or concluded from the former by the process of inference or reasoning.
But that one belief is subsequent to another signifies nothing, unless it also results from that other. When this is the case we have something like inference: it may be called by that name in a broad sense. Only if we are not conscious that the resulting belief is caused by one already adopted, we cannot watch the process nor control it; so that there can be no art of reasoning applicable to inference in that sense. Therefore, the name of reasoning is best confined to those processes in which we are directly aware that the concluded belief is an effect of another. [The editors of Writings 6 suggest comparing the passage above with W4:245 (1881), W5:327, 328 (1886), and W5:372 (1886).]
But when we say that one belief is determined by another, what do we mean, precisely what positive and sensible facts do we refer to?
In answering this, it will be useful to have a bit of reasoning before us as an example. What is the sum of the angles of a plane polygon? Let the polygon be cut in two by means of a diagonal between two vertices, the two parts similarly cut in two, and so on until the pieces are reduced to triangles. Each such cut leaves the total sum of all the angles the same, increases the number of polygons by one, and increases the number of sides by two. Thus, the number of cuts increased by one gives the number of polygons, and if these are all triangles, three times this or thrice the number of cuts plus three is the number of their sides; but this is also equal to twice the number of cuts /355/ plus the number of sides of the original polygon; so that the number of cuts plus three is the original number of sides. Then, the number of triangles is the original number of sides less two; and as each triangle has two right angles, the sum of the angles of a polygon is twice as many right angles as it has sides less four right angles.
We are thus led to believe that the sum of the angles of the N-gon is 2N - 4 right angles, because they are equal to the angles of N - 2 triangles having each the sum of its angles equal to two right angles. The question is what we are conscious of which induces us to use this word "because." As the etymology of the word shows, it implies that we feel a compulsion upon us to believe the conclusion, which compulsion we refer to the premises as its subject. There is a sense of compulsion in all belief; we are compelled to see what we see. But the compulsion of reason produces a different sensation. It seems to derive its force from our most intimate self. But all this is of little interest to the logician as such, who need not care how men feel, nor even too much how they think, but rather how they ought to think and will think when they reflect. What is far more essential to the significance of the "because," in that it is more important to the fulfilling of the function expressed by that word, is the implication that the conclusion is derived from the contemplation of an ideal construction. This ideal construction is not a mere product of casual experience; but is regarded as something that will hold good everywhere and always. In whatever world we may find ourselves, we are confident that the truth of premises such as those of the inference before us would be accompanied by the truth of such a conclusion, according to a rule which commends itself to our intelligence. [The editors of Writings 6 say: "From 1880 on, Peirce was interested in what is currently referred to as possible-worlds semantics for modal logic (see W4:170, 1880, and CP 2.349, c. 1896). The crux lies in the distinction between the de inesse conditional, which only states that "here and now either the antecedent is false or the consequent is true," and the ordinary hypothetical, which asserts that "in a certain possible state of things throughout a certain well understood range of possibility either the antecedent is false or the consequent true" (NEM 4:169, 1898). The latter needs a worked-out theory of quantification, so that possible states of things can be quantified over. … Peirce's later development in logic, especially his Existential Graphs, are in large part aimed at sophisticating the expression of this "possible worlds" approach." W6:425] We have in the above example the idea of the measurement of angles by superposition; and we see clearly that measuring them in this way the sum of the angles of the polygon will be equal to that of the triangles into which it is dissected, in every case whatever. In regard to the number of triangles, the reasoning has intentionally been left rather loose, so as to resemble our ordinary inferences. But except in certain vaguely conceived cases, this part of the reasoning also is seen to hold in every possible world.
The next character of reasoning to be noticed is that it is capable of being right and wrong. It is unnecessary at this time to open the difficult question of what the truth of a proposition consists in. Suffice /356/ it that some propositions are what we wish them to be; they are true. Others are not; they are false. An inference is good or bad according to the character of the habit which governs it. A habit of inference such that we can assure ourselves that from true premises it will in every possible case lead to a true conclusion is good reasoning. But if it is within the bounds of possibility (that is, of what we do not know to be false) that an inference governed by the habit in question should have true premises and a false conclusion, then it is not demonstrative, and if it pretends to be [. . .] [According to the editors of Writings 6, the view that the possible is that which we do not know to be false, which is later called by Peirce the nominalistic conception of possibility, was rejected by him in 1897: "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" (CP3.527, 1897).]
End: Peirce's "Reasoning"
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