Wittgenstein: On Certainty, §66—78

66. I make assertions about reality, assertions which have different degrees of assurance. How does the degree of assurance come out? What consequences has it? We may be dealing, for example, with the certainty of memory, or again of perception. I may be sure of something, but still know what test might convince me of error. I am e.g. quite sure of the date of a battle, but if I should find a different date in a recognized work of history, I should alter my opinion, and this would not mean I lost all faith in judging.

67. Could we imagine a man who keeps on making mistakes where we regard a mistake as ruled out, and in fact never encounter one? E.g. he says he lives in such and such a place, is so and so old, comes from such and such a city, and he speaks with the same certainty (giving all the tokens of it) as I do, but he is wrong. But what is his relation to this error? What am I to suppose? 

68. The question is: what is the logician to say here? 

69. I should like to say: "If I am wrong about this, I have no guarantee that anything I say is true." But others won't say that about me, nor will I say it about other people. 

70. For months I have lived at address A, I have read the name of the street and the number of the house countless times, have received countless letters here and given countless people the address. If I am wrong about it, the mistake is hardly less that if I were (wrongly) to believe I was writing Chinese and not German. 

71. If my friend were to imagine one day that he had been living for a long time past in such and such a place, etc.etc., I should not call this a mistake, but rather a mental disturbance, perhaps a transient one. 

72. Not every false belief of this sort is a mistake. 

73. But what is the difference between mistake and mental disturbance? Or what is the difference between my treating it as a mistake and my treating it as mental disturbance? 

74. Can we say: a mistake doesn't only have a cause, it also has a ground? I.e., roughly: when someone makes a mistake, this can be fitted into what he knows aright. 

75. Would this be correct: If I merely believed wrongly that there is a table here in front of me, this might still be a mistake; but if I believe wrongly that I have seen this table, or one like it, every day for several months past, and have regularly used it, that isn't a mistake?

76. Naturally, my aim must be to give the statements that one would like to make here, but cannot make significantly. 

77. Perhaps I shall do a multiplication twice to make sure, or perhaps get someone else to work it over. But shall I work it over again twenty times, or get twenty people to go over it? And is that some sort of negligence? Would the certainty really be greater for being checked twenty times?

78. And can I give a reason why it isn't?

(Wittgenstein: On Certainty, §66—78)

Leibniz, science, and theology

From The New Atlantis — "At fourteen, he enrolled at the University of Leipzig to study philosophy. “I was very young when I began to meditate,” he would later write, “and I was not quite fifteen when I strolled for whole days in a grove to take sides between Aristotle and Democritus.” Even then, Leibniz was nagged by the tension between the teleological account of nature inherited from Aristotle and engrained in academia, and the new mechanical physics, represented by Galileo and Descartes, that hearkened back to the ancient Greek atomist Democritus. Early in Leibniz’s career, mechanism won out and led him to focus on mathematics, but, as we shall see, he later appropriated into his system something akin to the substantial forms of Aristotle. "For reasons not entirely known, Leibniz was denied the doctor’s degree of law at Leipzig and left the city, never to live there again. After quickly finishing, defending, and publishing his dissertation at the University of Altdorf at age twenty, he turned down the offer of a professorship, presumably to pursue his independent work of reforming the sciences — a project involving far more than the academy."