Having put these principles into a clear light, and examined all other possible objections to them, it will behoove me to admit that they are not free from the defect common to almost all propositions in philosophy, that of being more or less vague and open to unwarrantable exaggeration. To be able to doubt a proposition, if it means to doubt it this instant, can include only actual doubt. If the time be extended changes of mind may take place. Doubt may also be so slight that it is not decidedly recognizable. It is easy to find propositions of which we cannot positively say whether they can be doubted or not. Nevertheless, I undertake to show that the principles are sufficiently definite for the purposes of logic.

      I next undertake something like an enumeration of the indubitable propositions. I shall not affirm that my enumeration is complete, but shall only mention those which must be taken account of in logic. Nor shall I name all the individual propositions; for they will be different for different persons and even for the same person at different times. But I shall enumerate categories of them. These will be enumerated in the form of propositions which are not themselves indubitable in advance of the proofs of them which I shall adduce. Nor can these proofs be apodictic. They will leave room for hypothetical doubts; but I do not think they will leave any really possible doubt in the reader's mind.

      I have not decided upon the order of my enumeration; nor will I be positive that upon reconsideration I may not slightly alter my present statement. But the propositions which I shall show to be beyond criticism will be pretty nearly as follows.

      I will first mention judgments descriptive of one's own state of thought. These will include perceptual judgments, that is, judgments as to the character of present percepts, such as "The sky is blue". They will also include judgments as to the meanings which the person making the judgment himself attaches to words and other signs. Thus, if I say to myself "There seems to be a horse", then, that being true in the sense I attach to the word "horse", I am quite sure that there is an animal. For I am quite sure that by a horse I mean a kind of animal. It is true that I am sometimes in doubt exactly what I do mean. Precisely where shall I draw the line between "many persons" and "not many persons"? Moreover, I may blunder about my meaning. I may declare that in saying the sky is blue I therein imply that it is not orange-colored, although, in fact, when I said the sky was blue I was not referring at all to the possibility of its being orange- colored. But I shall show that nevertheless all judgments concerning one's own thought are in the only reasonable sense of the words beyond criticism.

      The proposition here laid down, that all judgments concerning the contents of our own thought are beyond criticism, is not itself beyond criticism. It is a matter to be argued out; and some logicians virtually deny it. Their doctrine is that it is only the first impressions of sense or other immediate consciousness that are to be accepted without criticism. But I deny both branches of this opinion, and hold that the first impressions of sense and all immediate consciousness are of the most dubious character, while certain propositions whose psychological genesis may be traced are nevertheless quite indubitable. I will undertake to put this beyond all real doubt.

      Another class of propositions beyond criticism results from the application of one indubitable judgment to another. For example, if I say that a judgment is false, I am referring to something out of thought. For what I mean is that the proposition refers to a subject and misrepresents it, which it could not do if it referred only to the contents of thought. Consequently, the following proposition is not confined to the thought of the person who judges it: "There is such a thing as a false proposition." Now two things are indubitable; first, that to say that that proposition, if it were enunciated, would be false would imply that that proposition was not enunciated, and second, the perceptual judgment that one hears that proposition enunciated. Consequently, the proposition is beyond criticism; and this is an important result. It will be observed that I do not deny that its being beyond criticism is itself a proposition requiring careful examination. Various objections might be made to it. For example, it may be said that Hegel does not admit it, so that it cannot be so incapable of doubt. I reply that it might be doubted if we overlooked what we actually perceive, as Hegel does. But if he would open his eyes to the fact that his own opinion is denied, it would at once become impossible for him to retain that opinion.

      Another class of judgments exempt from criticism refers to objects of the mind's own creations.

      Logic, however, does make positive assertions of a very general nature. What do they rest upon? I undertake to show that certain kinds of judgments are indubitable, that they appear evident and are beyond all criticism, and that accepting these as certain, it becomes evident that certain methods of procedure must in the long run lead science to the truth, supposing that |66| they lead to any results at all, and supposing that there is any such thing as the truth; and that this remains true no matter how the universe is constituted, and whether we instinctively approve of the reasoning or not. I thus oppose both the English logicians, who hold that the validity of empirical reasoning depends upon the universe having a special constitution, and the German logicians, who hold that the validity of all reasoning ultimately consists in a feeling of rationality. But it will be observed that I limit my position, for the present, to the reasoning of science, leaving the practical reasonings of the individual for further consideration. Of this programme of my logic (a very partial view of it) I limit myself in this memoir to satisfying every attentive reader of the truth of the first part; namely that some judgments are exempt |67| from criticism and that certain specified kinds of judgments belong to that class. I do not in this number profess to lay open the whole theory of such judgments nor to render their indubitable character perfectly clear and comprehensible; because to do that would require certain conceptions which it is not necessary here to develop in order to show that the fact is as I say, however it may come about.

      The paper, in order to be convincing, as I mean that it shall be, will necessarily be largely occupied with matters really irrelevant, although to nearly every reader they will appear to be most pertinent. For the ground here fairly bristles with sophistical objections which, at this stage of the investigation, I shall have developed no logical method for dispatching. I shall not in this prospectus of the paper allude to them further.

      My general principle, which I easily prove, is that |68| so far as operations are beyond our ken, we cannot control them; and so far as we cannot control them it is idle to inquire whether they are performed well or performed ill; and so far as this inquiry is idle, "ought" and "ought not" have no meaning, and criticism, in the philosophical sense, is out of the question.

      There is one of those irrelevant apparent difficulties that perhaps I had better just touch upon. Namely, to say that a judgment is beyond criticism is to say that it not only ought to be [but] forcibly must be treated as infallible. But, of course, no judgment really is literally infallible. Although such judgments are not subject to external criticism, they may be drawn with so much deliberation as greatly to diminish the chance of a judgment not of that class being mistaken for one of that class. This is a specimen of the kind of objection which will require elucidation.

      |69| I shall go on to apply my principle to show the following classes of judgments are exempt from logical criticism:

      First, judgments to the effect that the content of our consciousness includes certain elements, or in other words analyses of consciousness in the form of judgments. In particular, there are two important varieties of such judgments. One of these consists of perceptual judgments. For example, when I say "The sky is blue", I am not speaking of any external reality but mean only that when I look up I have a sensation of blueness. It is conceivable that this judgment, being an entirely different sort of mental product from a sensation, should misrepresent the sensation. But if we cannot help making that judgment, and up to date there is not the slightest ground for a suspicion that we ever can make it otherwise than we do, it is utter nonsense to inquire whether it is made right or wrong. Whether we can judge |70| otherwise or not of the percept before us is, no doubt, a question to be carefully considered. But as soon as it is settled that we cannot, criticism is silenced. Should it be proved that we cannot help judging as we do within the next three months, then until that time had elapsed we should have to treat the judgment as infallible. The other variety of this class of judgments which merits mention consists of judgments concerning our own meaning. Suppose, for example, I have convinced myself that I am looking at a horse, and that I explicitly make this judgment. Then, I conclude that I am looking at a perissid ungulate. For what I mean by a horse is a perissid ungulate. In other words, I analyze the meaning of the word horse, in the sense in which I use it. It is certain that blunders are frequently committed in such analyses. Yet if I am persuaded that no amount of deliberation could cause me to judge |71| otherwise than that what I now mean be a horse is necessarily a perissid ungulate, then that powerlessness to judge otherwise must cut off all dispute. The following dialogue might be imagined:

      A second class of judgments that are beyond criticism consist of those which would answer the question, what would you do under such and such circumstances, supposing you were to act so as to be deliberately satisfied with what you were doing? A man might reply, If I were to undergo such an experience, in the light |72| of it I might change my mind; but supposing I remained as I now am, and acted deliberately, I cannot help thinking that I should do so and so. Intentions are sunk deep in the dark lake of consciousness. A man may not descry his own, accurately. Figures on the surface of consciousness may interfere with his insight into himself. Still, if he really cannot otherwise judge his present deliberate intent, there is nothing for it but to accept his judgment of that present intention. Such judgments of how one would behave under circumstances of a general description occur every time a man reasons. For in all reasoning, there is an accompanying judgment that from analogous premisses one would, if he considered the matter sufficiently, draw an analogous conclusion. Whether the facts would bear him out or not is, of course, another question.

      A third class of judgments not open to criticism are judgments concerning objects created by one's |73| own imagination. Imagine, for example, an endless succession of objects. Then there will be there two distinct endless sequences; namely that of the objects in the oddly numbered places, and that of the objects in the evenly numbered places. That this is so is not to be discovered by merely analyzing what one had in mind. The judgment is the result of a psychical process of experimentation, considerably like an induction. But it differs from any kind of reasoning in not being subject to control. It is true that after one has once lit up the idea that there are two endless series whose members so alternate, the analysis of that idea does show that it will be applicable to any endless series; and this analysis can be thrown into the form of a proof that it will be so. Yet this proof will rest on some proposition which is simply self- evident. But as long as one only has the idea of the simple endless series, one may think forever, and not discover the theorem, until something suggests that other idea to the mind. What I call the theorematic reasoning |74| of mathematics consists in so introducing a foreign idea, using it, and finally deducing a conclusion from which it is eliminated. Every such proof rests, however, upon judgments in which the foreign idea is first introduced, and which are simply self- evident. As such, they are exempt from criticism. Judgments of this kind are the very foundation of logic except insofar as it is an experiential science. If a proposition appears to us, after the most deliberate review, to be quite self-evident, and leave no room for doubt, it certainly cannot be rendered more evident; for its evidence is perfect already. Neither can it be rendered less evident, until some loophole for doubt is discovered. It is, therefore, exempt from all criticism. True, the whole thing may be a mistake. The sixteenth proposition of the first book of Euclid affords an example. The second postulate was that every terminated right line can be continuously prolonged. Kai peperasmenên eutheian kata to suneches ep' eutheias ekballein. This |75| is by no means saying that it can be prolonged to an indefinitely great length. He, however, virtually has proved (in prop. 2) that from the extremity of a straight line can be drawn continuously with that line a line of any given length. He imagines, then,a triangle .

     If Euclid had not been able to save his sixteenth proposition by means of the third postulate about the circle, he could not have saved it at all. For his first postulate is not that only one right line can join two points as its terminals, but merely that there is a right line from one point to the other. Êitêsthô apo pantos sêmeiou epi pan sêmeion eutheian grammên agagein. He does not postulate that only one straight line can be drawn through two points, but only that all right angles are equal. That postulate would have enabled him to prove that only one unlimited straight line cannot be drawn between two points (a proposition he does not give because he deals only with what is limited), but not that there were not two limited straight lines having those points as terminals. Had he omitted from his definition of the circle the clause represented in our language by the single word 'within' (tôn entos |78| tou schêmatos keimenôn), as some moderns would have had him do, he would have had no logical way of proving that the sum of the angles of a plane triangle do not exceed two right angles. Still, as long as he continued to overlook the possibility of Fig.2, his proof would have appeared convincing, and there would have been no criticism to make upon it. In all these cases, of whatever class, it is only the act of judging that is exempt from criticism in the strict sense of an inquiry whether an operation has been performed rightly or wrongly. There is nothing to prevent the resulting proposition from being confronted with objections showing that there is something wrong somewhere. For example, though the act of judging that the sky looks blue is itself exempt from criticism, yet one can imagine a person to be so thoroughly persuaded of the falsity of Goethe's theory of colors that, not seeing any other way of accounting |79| for the sky's seeming blue, that he might suspect that it does not seem blue. Again if a man analyzing his idea of matter deliberately judges that he means by 'matter' something which in its nature is not a representation of anything, his judgment would, as an act, not be open to any criticism; but still, that would not prevent a Berkeley from raising the difficulty that since we can have no experience or imagination of anything but representations, there does not seem to be any possible way in which a man ever could attach such a meaning to a word consistently. So again, certain saints have declared that they would go voluntarily and deliberately to Hell, if such were the will and good pleasure of the Lord; but a Hobbes would not be prevented from suspecting that they had deceived themselves, since Hell means a state of utter dissatisfaction, and it is absurd to say that a person could find any |80| satisfaction in complete dissatisfaction. So in the present case, had Euclid omitted the word 'within' or rather the corresponding Greek phrase, from his definition of the circle, it might have occurred to him that he was provided with no postulates about straight lines in a plane that were not equally true of great circles on a sphere, and therefore, since a spherical triangle may have the sum of its angles anything up to six right angles, or even ten, if you please, there must be something wrong with the proof that this is impossible in a plane.

      This third class of judgments exempt from criticism coincides with that of evident judgments or judgments of evident propositions. For 'evident' means manifest to any mind who clearly apprehends the proposition, no matter how lacking in experience he may be. The truth of a perceptual judgment, analysis of meaning, |81| or declaration of intention, is manifest only to the one person whose experience it concerns. It is only when we judge concerning creatures of the imagination that all minds are on a par, however devoid of experience some of them may be.

       When a mathematical demonstration is clearly apprehended, we are forced to admit the conclusion. It is evident; and we cannot think otherwise. It is, therefore, beyond all logical criticism; and the forms of syllogism cannot lend it any support. Pure mathematics, therefore, stands in no need of a science of logic. Methodeutically, mathematics is its own logic; and the notion that a calculus of logic can be of any help to mathematics, unless merely as another mathematical method supplying a speedier process of demonstration (which is just what a logical calculus rather opposes), is futile. Mathematics, however, is of great aid to logic. The reasoning of mathe|82|matics is also an instructive subject for logical analysis, teaching us many things about the nature of reasoning. But although a mathematical demonstration, once completely apprehended, is evident, indubitable, beyond control, and beyond criticism, yet the process of arriving at it is certainly a matter of skill and art, subject to criticism, and controlled by anticipated criticism. This control implies that different ways of proceeding are considered hesitatingly; and until the demonstration is found there is doubt of the conclusion. The theorem is not self-evident or it could not really be proved. But over what elements of the process is the control exercised? Over two: the invention of the proof, and the acceptance of the proof. But the process of invention of the proof is not of the nature of that demonstrative reasoning which we call mathematical. There is nothing evident about it except that, as it turns out, it evidently answers the purpose. |83| It is, in fact, a piece of probable reasoning in regard to which a good logical methodeutic may be a great aid. As to the acceptance of the proof, after it is framed all the artifices which may be employed to assist it are of the nature of checks. That is to say, they are merely equivalent to a careful review of the proof itself in which some minor details may be varied in order to diminish the chances of error. In short, this is an operation by which the proof is brought fully and clearly before the mind. That the proof is absolute is evident and beyond criticism. The theorem which was not evident before the proof was apprehended, now becomes itself entirely evident, in view of the proof. Such reasoning forms the principal stage of logic. It is not itself amenable to logic for any justification; and although logic may aid in the discovery of the proof, yet its result is tested in another way. This disposes of the German objection that to use reasoning in order to deter|84|mine what methods of probable reasoning will lead to the truth begs the whole question, so that the only way is to admit that the validity of reasoning consists in a feeling of reasonableness.

      A fourth kind of judgment which must be regarded as beyond criticism, although they are reached by a sort of process of reasoning, are those in which a proposition is presented to perception, the meaning of which proposition either supports or conflicts with what is presented to sense. I will give a couple of examples to show what I mean, because such propositions throw much light upon logic. Take the proposition, "Some actually enunciated proposition is false". The meaning of this proposition is such that the falsity of that meaning, that is, the non-enunciation of any false proposition, would conflict with this proposition's enunciating what we perceive that it does enunciate. Therefore, the proposition must be true, |85| that a false proposition is actually enunciated. Yet it is quite possible to imagine a paradisiacal world in which no false proposition should ever have been suggested. We cannot, therefore, say that there necessarily must be a false proposition, but only that the existence of this proposition constitutes the certainly that a false proposition is enunciated, although the assertion of this proposition itself is perfectly true. This forces us to recognize the correct and extremely important logical doctrine, namely, that every proposition asserts two things, first whatever it is meant to assert, and secondly, its own truth. Unless both these are true, the proposition is false. Although, therefore, the meaning or matter of this proposition is true, the proposition itself may be false; and it will be so in case there is no other false proposition than itself.

      Suppose however we find a piece of paper quite blank except for these two [sic: read "three"] sentences:

Now, disregarding the implication by the first sentence of its own truth, is whatever it says of the second true? If so, it is false that something that the third sentence on this paper says of the first is false. Then whatever the third sentence says of the first is true. Then something that the first says of the second is false, contrary to the hypothesis. Then we are driven to assume that something that the second sentence says of the third is true. Then, something that the third says of the first is false. Hence, whatever the first sentence says of the second is true, again contrary to the hypothesis. I prove by an elaborate necessary argument that the only admissible solution is that every proposition, even if not asserted, necessarily and essentially involves as part of its meaning that the reality, or truth of things, or the real universe, is truly repre|88|sented by what it says, and that the three sentences are true in other respects, but false in their inseparable implication that they represent any truth of being, or the real universe in any respect. This they fail to do because, though each refers to the others, yet together they do not represent any real being independent of being represented.

      This brings me to the examination of the matter of the hope which we entertain concerning the matter in hand when we start any inquiry. I find it convenient to use the term proposition to denote that meaning of a sentence which not only remains the same in whatever language it is expressed, but is also the same whether it be believed or doubted, asserted (by somebody's making himself responsible for it), or commanded (by somebody's expressing that he holds another responsible for it), or put as a question (when somebody expresses an attempt to induce another to make himself responsible for it). Now I prove in a man|89|ner which will command veritable assent, that every proposition whether it be believed, doubted, asserted, commanded, or put interrogatively, supposed, etc. essentially represents itself to represent an absolute reality, the very same for all propositions, which is definite (that is, subject to the principle of contradiction) and individual (that is, subject to the principle of excluded middle). This reality is not in any respect constituted by being represented as so constituted in any definite proposition or representation. That there is such an absolute reality we hope; and in every inquiry we hope that the proposition which is put in the interrogative mood represents that reality. If a proposition represents that reality and represents it rightly in whatever respect it represents it, the proposition is true. If the proposition does not represent the absolute reality or in any respect represents it wrongly, it is false.

      |90| I further show that we hope that any inquiry which we undertake will result in a complete settlement of opinion. We never need abandon that hope. The representation of the reality in such destined opinion is the reality.

      It follows that the methodeutic task of logic is to find such methods as must hasten the progress of opinion toward its ultimate bourn.

      It is plain that I cannot outline the contents of all my proposed [memoirs] as I have done this since such an outline would fill five hundred pages of manuscript. I can only say that this first memoir is not one of those which is most completely in shape.