(source)Man is a rope, tied between beast and overman — a rope over an abyss…
What is great in man is that he is a bridge and not an end: what can be loved in man is that he is an overture and a going under
(source)For believe me! — the secret for harvesting from existence the greatest fruitfulness and the greatest enjoyment is: to live dangerously! Build your cities on the slopes of Vesuvius! Send your ships into uncharted seas! Live at war with your peers and yourselves! Be robbers and conquerors as long as you cannot be rulers and possessors, you seekers of knowledge! Soon the age will be past when you could be content to live hidden in forests like shy deer! At long last the search for knowledge will reach out for its due: — it will want to rule and possess, and you with it!
It is quite certain that at the bottom of all skepticism there is an abstract certainty that is the foothold of doubt and is like the line one draws as the base upon which the figure is sketched. Therefore it is quite certain that nothing is accomplished even by the most rigorous attempt of Greek skepticism to round off the hovering of skepticism by emphasizing that the statement about doubt must not be understood as a position, but it still does not follow that doubt overcomes itself. The basic certainty that sustains doubt can at no moment hypostatize itself as long as I am doubting, because doubt continually leaves it in order to doubt. If I want to keep on doubting, I shall never in all eternity advance any further, because doubt consists precisely in and by passing off that certainty as something else. If I hold on to the certainty as certainty for one single moment, I must also stop doubting for that moment. But then it is not doubt that cancels itself; it is I who stop doubting. Therefore a mediocre doubter will be most likely to succeed in gaining certainty, and next a doubter who merely joins categories in order to see how they look the best without bothering in the least to carry out any of them. — I cannot stop returning to this point, because it is so decisive. If it is the case that doubt overcomes itself, that by doubting everything one in this very doubt wins truth without a break and an absolutely new point of departure, then not one single Christian category can be maintained, then Christianity is abolished.
(source)Everyone knows that the most difficult leap, even in the physical realm, is when a man leaps into the air from a standing position and comes down again on the same spot. The leap becomes easier in the degree to which some distance intervenes between the initial position and the place where the leap takes off. And so it is also with respect to a decisive movement in the realm of the spirit. The most difficult decisive action is not that in which the individual is far removed from the decision (as when a non-Christian is about to decide to become one), but when it is as if the matter were already decided.
The concept is based on the following analogy: The rules of language are analogous to the rules of games; thus saying something in a language is analogous to making a move in a game. The analogy between a language and a game demonstrates that words have meaning depending on the uses made of them in the various and multiform activities of human life.
Davidson points out that beliefs and meanings are inseparable. A person holds a sentence true based on what he believes and what he takes the sentence to mean. If the interpreter knew what a person believed when that person held a sentence to be true, the meaning of the sentence could then be inferred. Vice versa, if the interpreter knew what a person took a sentence to mean when that person held it to be true, the belief of the speaker could be inferred. So Davidson doesn’t allow the interpreter to have access to beliefs as evidence, since the interpreter would then be begging the question. Instead, Davidson allows that the interpreter can reasonably ascertain when a speaker holds a sentence true, without knowing anything about a particular belief or meaning. That will then allow the interpreter to construct hypotheses relating a speaker and an utterance to a particular state of affairs at a particular time.
Davidson argues that because the language is compositional, it is also holistic: sentences are based on the meanings of words, but the meaning of a word depends on the totality of sentences in which it appears. That holistic constraint, along with the requirement that the theory of truth is law-like, suffices to minimize indeterminacy just enough for successful communication to occur.
Hume asks on what grounds we come to our beliefs about the unobserved on the basis of inductive inferences. He presents an argument in the form of a dilemma which appears to rule out the possibility of any reasoning from the premises to the conclusion of an inductive inference. There are, he says, two possible types of arguments, “demonstrative” and “probable”, but neither will serve. A demonstrative argument produces the wrong kind of conclusion, and a probable argument would be circular. Therefore, for Hume, the problem remains of how to explain why we form any conclusions that go beyond the past instances of which we have had experience
Gödel said that every non-trivial (interesting) formal system is either incomplete or inconsistent:
1. There will always be questions that cannot be answered, using a certain set of axioms;
2. You cannot prove that a system of axioms is consistent, unless you use a different set of axioms .
-CS PeirceThus, the uncertainty of the mental law is no mere defect of it, but is on the contrary of its essence. The truth is, the mind is not subject to “law,” in the same rigid sense that matter is. It only experiences gentle forces which merely render it more likely to act a given way than it otherwise would be. There always remains a certain amount of arbitrary spontaneity in its action, without which it would be dead.
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