Combining Texts

Ideas for 'Thinking About Mathematics', 'fragments/reports' and 'Naturalism in Mathematics'

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7 ideas

12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / b. Recollection doctrine
We can't seek for things if we have no idea of them [Epicurus, by Diog. Laertius]
     Full Idea: We could not seek for anything if we had not some notion of it.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.21
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
To name something, you must already have an idea of what it is [Epicurus, by Diog. Laertius]
     Full Idea: We could not give names to things, if we had not a preliminary notion of what the things were.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.21
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
Epicurus says colours are relative to the eye, not intrinsic to bodies [Epicurus, by Plutarch]
     Full Idea: Epicurus says that colours are not intrinsic to bodies but a result of certain arrangements and positions relative to the eye, which implies that body is no more colourless than coloured.
     From: report of Epicurus (fragments/reports [c.289 BCE], Fr 30) by Plutarch - 74: Reply to Colotes §1110
     A reaction: This seems to me such a self-evident truth that I am puzzled as to why anyone would claim that colours are real features of bodies. Epicurus points out that entering a dark room we see no colour, but then colour appears after a while.
12. Knowledge Sources / B. Perception / 5. Interpretation
Sensations cannot be judged, because similar sensations have equal value, and different ones have nothing in common [Epicurus, by Diog. Laertius]
     Full Idea: Sensation is out of reach of control, because one sensation cannot judge another which resembles itself, as they have equal value, and different sensations have different objects.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20
     A reaction: Scepticism about the possibility of purely empirical knowledge; an interesting comment on the question of whether perceptions contain any intrinsic knowledge.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
     Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge.
     From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1)
     A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach.
12. Knowledge Sources / D. Empiricism / 1. Empiricism
The criteria of truth are senses, preconceptions and passions [Epicurus, by Diog. Laertius]
     Full Idea: The criteria of truth are the senses, the preconceptions, and the passions.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20
12. Knowledge Sources / D. Empiricism / 4. Pro-Empiricism
Reason can't judge senses, as it is based on them [Epicurus, by Diog. Laertius]
     Full Idea: Reason cannot judge the senses, because it is based on them.
     From: report of Epicurus (fragments/reports [c.289 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 10.20