Peirce's Definitions of Scientific Truth...

Truth

(see also Real )(if need be, highlight this entire post to read easier, the red and gray elements)

"To say that a thing is Real is merely to say that such predicates as are true of it, or some of them, are true of it regardless of whatever any actual person or persons might think concerning that truth. Unconditionality in that single respect constitutes what we call Reality.[---] I call "truth" the predestinate opinion, by which I ought to have meant that which would ultimately prevail if investigation were carried sufficiently far in that particular direction." ('A Sketch of Logical Critics', EP 2.457-458, 1911)

"Unless truth be recognized as public, - as that of which any person would come to be convinced if he carried his inquiry, his sincere search for immovable belief, far enough, - then there will be nothing to prevent each one of us from adopting an utterly futile belief of his own which all the rest will disbelieve. Each one will set himself up as a little prophet; that is, a little "crank," a half-witted victim of his own narrowness.

But if Truth be something public, it must mean that to the acceptance of which as a basis of conduct any person you please would ultimately come if he pursued his inquiries far enough; - yes, every rational being, however prejudiced he might be at the outset. For Truth has that compulsive nature which Pope well expressed:

The eternal years of God are her's.

But, you will say, I am setting up this very proposition as infallible truth. Not at all; it is a mere definition. I do not say that it is infallibly true that there is any belief to which a person would come if he were to carry his inquiries far enough. I only say that that alone is what I call Truth. I cannot infallibly know that there is any Truth." (Letter to Lady Welby, SS 73, 1908)

"The purpose of every sign is to express "fact," and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the perfect Truth, the absolute Truth, and as such (at least, we may use this language) would be the very Universe. Aristotle gropes for a conception of perfection or entelechy, which he never succeeds in making clear. We may adopt the word to mean the very fact, that is, the ideal sign which should be quite perfect, and so identical, - in such identity as a sign may have, with the very matter denoted united with the very form signified by it. The entelechy of the Universe of being, then, the Universe qua fact, will be that Universe in its aspect as a sign, the "Truth" of being. The "Truth," the fact that is not abstracted but complete, is the ultimate interpretant of every sign." ('New Elements', EP 2:304, c. 1904)

"... to believe the absolute truth would be to have such a belief that under no circumstances, such as actually occur, should we find ourselves surprised." ('Reason's Conscience: A Practical Treatise on the Theory of Discovery; Wherein Logic Is Conceived as Semeiotic', MS 693: 166, 1904)

"Every man is fully satisfied that there is such a thing as truth, or he would not ask any question. That truth consists in a conformity to something independent of his thinking it to be so, or of any man's opinion on that subject. But for the man who holds this second opinion, the only reality, there could be, would be conformity to the ultimate result of inquiry. But there would not be any course of inquiry possible except in the sense that it would be easier for him to interpret the phenomenon; and ultimately he would be forced to say that there was no reality at all except that he now at this instant finds a certain way of thinking easier than any other. But that violates the very idea of reality and of truth." (Harvard Lectures on Pragmatism, CP 5.211, 1903)

"Truth is a character which attaches to an abstract proposition, such as a person might utter. It essentially depends upon that proposition's not professing to be exactly true. But we hope that in the progress of science its error will indefinitely diminish, just as the error of 3.14159, the value given for π, will indefinitely diminish as the calculation is carried to more and more places of decimals. What we call π is an ideal limit to which no numerical expression can be perfectly true. If our hope is vain; if in respect to some question - say that of the freedom of the will - no matter how long the discussion goes on, no matter how scientific our methods may become, there never will be a time when we can fully satisfy ourselves either that the question has no meaning, or that one answer or the other explains the facts, then in regard to that question there certainly is no truth. But whether or not there would be perhaps any reality is a question for the metaphysician, not the logician. Even if the metaphysician decides that where there is no truth there is no reality, still the distinction between the character of truth and the character of reality is plain and definable. Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth. [---] In the above we have considered positive scientific truth. But the same definitions equally hold in the normative sciences. If a moralist describes an ideal as the summum bonum, in the first place, the perfect truth of his statement requires that it should involve the confession that the perfect doctrine can neither be stated nor conceived. If, with that allowance, the future development of man's moral nature will only lead to a firmer satisfaction with the described ideal, the doctrine is true." ('Truth and Falsity and Error', DPP 2 / CP 5.565-566, 1902)

"These characters equally apply to pure mathematics. [---] A proposition is not a statement of perfectly pure mathematics until it is devoid of all definite meaning, and comes to this -- that a property of a certain icon is pointed out and is declared to belong to anything like it, of which instances are given. The perfect truth cannot be stated, except in the sense that it confesses its imperfection. The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. [---] But whether there is any reality or not, the truth of the pure mathematical proposition is constituted by the impossibility of ever finding a case in which it fails. This, however, is only possible if we confess the impossibility of precisely defining it." ('Truth and Falsity and Error', DPP 2 / CP 5.567, 1902)

"But even if it were impossible to distinguish between truth and reality, that would not in the least prevent our defining what it is that truth consists in. Truth and falsity are characters confined to propositions. A proposition is a sign which separately indicates its object. Thus, a portrait with the name of the original below it is a proposition. It asserts that if anybody looks at it, he can form a reasonably correct idea of how the original looked. A sign is only a sign in actu by virtue of its receiving an interpretation, that is, by virtue of its determining another sign of the same object. This is as true of mental judgments as it is of external signs. To say that a proposition is true is to say that every interpretation of it is true. [---] Thus, a false proposition is a proposition of which some interpretant represents that, on an occasion which it indicates, a percept will have a certain character, while the immediate perceptual judgment on that occasion is that the percept has not that character. A true proposition is a proposition belief in which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended." ('Truth and Falsity and Error', DPP 2 / CP 5.569, 1902)

"All the above relates to complex truth, or the truth of propositions. This is divided into many varieties, among which may be mentioned ethical truth, or the conformity of an assertion to the speaker's or writer's belief, otherwise called veracity, and logical truth, that is, the concordance of a proposition with reality, in such way as is above defined.

(2) The word truth has also had great importance in philosophy in widely different senses, in which it is distinguished as simple truth, which is that truth which inheres in other subjects than propositions.

Plato in the Cratylus (385B) maintains that words have truth; and some of the scholastics admitted that an incomplex sign, such as a picture, may have truth.

But truth is also used in senses in which it is not an affection of a sign, but of things as things. Such truth is called transcendental truth. The scholastic maxim was Ens est unum, verum, bonum. Among the senses in which transcendental truth was spoken of was that in which it was said that all science has for its object the investigation of truth, that is to say, of the real characters of things. It was, in other senses, regarded as a subject of metaphysics exclusively. It is sometimes defined so as to be indistinguishable from reality, or real existence. Another common definition is that truth is the conformity, or conformability, of things to reason. Another definition is that truth is the conformity of things to their essential principles.

(3) Truth is also used in logic in a sense in which it inheres only in subjects more complex than propositions. Such is formal truth, which belongs to an argumentation which conforms to logical laws." ('Truth and Falsity and Error', DPP 2 / CP 5.570-573, 1902)

"By a true proposition (if there be any such thing) I mean a proposition which at some time, past or future, emerges into thought, and has the following three characters:

1st, no direct effort of yours, mine, or anybody's, can reverse it permanently, or even permanently prevent its asserting itself;

2nd, no reasoning or discussion can permanently prevent its asserting itself;

3rd, any prediction based on the proposition, as to what ought to present itself in experience under certain conditions, will be fulfilled when those conditions are satisfied.

By a reality, I mean anything represented in a true proposition.

By a positive reality or truth, I mean one to which all three of the above criteria can be applied, - of course imperfectly, since we can never carry them out to the end.

By an ideal reality or truth, I mean one to which the first two criteria can be applied imperfectly, but the third not at all, since the proposition does not imply that any particular state of things will ever appear in experience. Such is a truth of pure mathematics.

By an ultimate reality or truth, I mean one to which the first criterion can be in some measure applied, but which can never be overthrown or rendered clearer by any reasoning, and upon which alone no predictions can be based. Thus, if you are kicked by a horse, the fact of the pain is beyond all discussion and far less can it be shaken or established by any experimentation." (Letter to Georg Cantor, NEM 3:773, 1900)

"The question therefore is, how is true belief (or belief in the real) distinguished from false belief (or belief in fiction). Now, as we have seen in the former paper, the ideas of truth and falsehood, in their full development, appertain exclusively to the experiential method of settling opinion. [---]
On the other hand, all the followers of science are animated by a cheerful hope that the processes of investigation, if only pushed far enough, will give one certain solution to each question to which they apply it. [---] This activity of thought by which we are carried, not where we wish, but to a fore-ordained goal, is like the operation of destiny. No modification of the point of view taken, no selection of other facts for study, no natural bent of mind even, can enable a man to escape the predestinate opinion. This great hope is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. (' How to Make Our Ideas Clear', CP 5.406-407, 1878)