Pascal. 66. In the Thoughts of Pascal we find many striking remarks on the logic of that science with which he was peculiarly conversant, and upon the general foundations of certainty. He had reflected deeply upon the sceptical objections to all human reasoning, and, though sometimes out of a desire to elevate religious faith at its expense, he seems to consider them unanswerable, he was too clear-headed to believe them just. “Reason,” he says, “confounds the dogmatists, and nature the sceptics.”[805] “We have an incapacity of demonstration, which one cannot overcome; we have a conception of truth which the others cannot disturb.”[806] He throws out a notion of a more complete method of reasoning than that of geometry, wherein everything shall be demonstrated, which, however, he holds to be unattainable;[807] and perhaps on this account he might think the cavils of pyrrhonism invincible by pure reason. But as he afterwards admits that we may have a full certainty of propositions that cannot be demonstrated, such as the infinity of number and space, and that such incapability of direct proof is rather a perfection than a defect, this notion of a greater completeness in evidence seems neither clear nor consistent.[808]
[805] Œuvres de Pascal, vol. i., p. 205. Il faut que chacun prenne parti, et se range nécessairement ou au dogmatisme, ou au pyrrhonisme; car qui penseroit demeurer neutre seroit pyrrhonien par excellence; cette neutralité est l’essence du pyrrhonisme, p. 204. I do not know that I understand this; is it not either a self-evident proposition or a sophism?
[806] P. 208.
[807] Pensées de Pascal, part i., art. 2.
[808] Comme la cause qui les rend incapables de démonstration n’est pas leur obscurité, mais au contraire leur extrême évidence, ce manque de preuve n’est pas un défaut, mais plutôt une perfection.
67. Geometry, Pascal observes, is almost the only subject, as to which we find truths wherein all men agree. And one cause of this is that geometers alone regard the true laws of demonstration. These as enumerated by him are eight in number. 1. To define nothing which cannot be expressed in clearer terms than those in which it is already expressed. 2. To leave no obscure or equivocal terms undefined. 3. To employ in the definition no terms not already known. 4. To omit nothing in the principles from which we argue unless we are sure it is granted. 5. To lay down no axiom which is not perfectly evident. 6. To demonstrate nothing which is as clear already as we can make it. 7. To prove everything in the least doubtful, by means of self-evident axioms, or of propositions already demonstrated. 8. To substitute mentally the definition instead of the thing defined. Of these rules, he says, the first, fourth, and sixth are not absolutely necessary in order to avoid error, but the other five are indispensable. Yet, though they may be found in books of logic, none but the geometers have paid any regard to them. The authors of these books seem not to have entered into the spirit of their own precepts. All other rules than those he has given are useless or mischievous; they contain, he says, the whole art of demonstration.[809]
[809] Œuvres de Pascal, i., 66.
68. The reverence of Pascal, like that of Malebranche, for what is established in religion does not extend to philosophy. We do not find in them, as we may sometimes perceive in the present day, all sorts of prejudices against the liberties of the human mind clustering together, like a herd of bats, by an instinctive association. He has the same idea as Bacon, that the ancients were properly the children among mankind. Not only each man, he says, advances daily in science, but all men collectively make a constant progress, so that all generations of mankind during so many ages may be considered as one man, always subsisting and always learning; and the old age of this universal man is not to be sought in the period next to his birth, but in that which is most removed from it. Those we call ancients were truly novices in all things; and we who have added to all they knew the experience of so many succeeding ages, have a better claim to that antiquity which we revere in them. In this, with much ingenuity and much truth, there is a certain mixture of fallacy, which I shall not wait to point out.
69. The genius of Pascal was admirably fitted for acute observation on the constitution of human nature, if he had not seen everything through a refracting medium of religious prejudice. When this does not interfere to bias his judgment, he abounds with fine remarks, though always a little tending towards severity. One of the most useful and original is the following: “When we would show anyone that he is mistaken, our best course is to observe on what side he considers the subject, for his view of it is generally right on this side, and admit to him that he is right so far. He will be satisfied with this acknowledgment that he was not wrong in his judgment, but only inadvertent in not looking at the whole of the case. For we are less ashamed of not having seen the whole, than of being deceived in what we do see; and this may perhaps arise from an impossibility of the understanding’s being deceived in what it does see, just as the perceptions of the senses, as such, must be always true.”[810]
[810] Id., p. 149. Though Pascal here says that the perceptions of the senses are always true, we find the contrary asserted in other passages; he is not uniformly consistent with himself.