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Single Idea 9185

[filed under theme 12. Knowledge Sources / E. Direct Knowledge / 2. Intuition ]

Full Idea

Bolzano was determined to expel Kantian intuition from analysis, and to prove from first principles anything that could be proved, no matter how obvious it might seem when thought of in geometrical terms.

Clarification

'Analysis', in mathematics, is the theory of real numbers

Gist of Idea

Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved

Source

report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Michael Dummett - The Philosophy of Mathematics 2.3

Book Ref

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.129

A Reaction

This is characteristic of the Enlightenment Project, well after the Enlightenment. It is a step towards Frege's attack on 'psychologism' in mathematics. The problem is that it led us into a spurious platonism. We live in troubled times.

The 26 ideas with the same theme [direct awareness of knowledge]:

79 Intuition grasps the definitions that can't be proved [Aristotle]
16111 Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
12543 Intuition gives us direct and certain knowledge of what is obvious [Locke]
8736 Kantian intuitions are of particulars, and they give immediate knowledge [Kant, by Shapiro]
16911 Intuition is a representation that depends on the presence of the object [Kant]
23246 Faith is not knowledge; it is a decision of the will [Fichte]
9185 Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
16900 Intuitions cannot be communicated [Frege, by Burge]
14830 Intuition only recognises what is possible, not what exists or is certain [Nietzsche]
21221 Direct 'seeing' by consciousness is the ultimate rational legitimation [Husserl]
10040 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
11079 How do I decide when to accept or obey an intuition? [Wittgenstein]
23957 We often trust our intuitions as rational, despite their lack of reflection [Solomon]
4948 Intuition is the strongest possible evidence one can have about anything [Kripke]
13408 Intuition and thought-experiments embody substantial information about the world [Papineau]
23101 Intuitions don't prove things; they just receptivity to interpretations [Kekes]
16534 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe]
9374 If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian]
9592 Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence [Williamson]
20181 When analytic philosophers run out of arguments, they present intuitions as their evidence [Williamson]
20182 The word 'intuitive' often plays not role at all in arguments, and can be removed [Cappelen]
11078 Intuition is only outside the 'space of reasons' if all reasons are inferential [Hanna]
11077 Intuition includes apriority, clarity, modality, authority, fallibility and no inferences [Hanna]
11080 Intuition is more like memory, imagination or understanding, than like perception [Hanna]
14891 There is no reason to think our intuitions are good for science or metaphysics [Ladyman/Ross]
17734 It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins]