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9558
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All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
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Full Idea:
If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.
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From:
Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics
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A reaction:
This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.
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19089
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Our whole conception of an object is its possible practical consequences [Peirce]
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Full Idea:
Consider what effects, which might conceivably have practical bearings, we conceive the objects of our conceptions to have. Then, our conception of these effects is the whole of our conception of the object.
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From:
Charles Sanders Peirce (How to Make our Ideas Clear [1878], EP i.132), quoted by Albert Atkin - Peirce 2 'early'
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A reaction:
This is his 1878 version, which was fine-tuned later in life. He seems to have extended his principle to include possibilities, as well as the mere objects. That is, he moved beyond mere nominalism.
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7660
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We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce]
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Full Idea:
A belief has just three properties: first, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit.
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From:
Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.28)
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A reaction:
Peirce probably believed that Bismarck breathed oxygen, but was unaware of his belief, and no one ever dreamed of acting on such a belief, unless Bismarck was gasping for air.
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2748
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A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
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Full Idea:
Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
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From:
report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
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A reaction:
This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.
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