Combining Philosophers

Ideas for Archimedes, Ren Descartes and David Conway

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7 ideas

12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
Clear and distinct truths must be known all at once (unlike deductions) [Descartes]
     Full Idea: We require two conditions for intuition, namely that the proposition appear clear and distinct, and then that it be understood all at once and not successively. Deduction, on the other hand, implies a certain movement of the mind.
     From: René Descartes (Rules for the Direction of the Mind [1628], 11)
     A reaction: A nice distinction. Presumably with deduction you grasp each step clearly, and then the inference and conclusion, and you can then forget the previous steps because you have something secure.
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes]
     Full Idea: The human soul possesses something divine in which are deposited the first seeds of useful knowledge, which, in spite of the negligence and embarrassment of poorly done studies, bear spontaneous fruit.
     From: René Descartes (Rules for the Direction of the Mind [1628], 04)
     A reaction: This makes clear the religious underpinning which is required for his commitment to such useful innate ideas (such as basic geometry)
Our thinking about external things doesn't disprove the existence of innate ideas [Descartes]
     Full Idea: You can't prove that Praxiteles never made any statues on the grounds that he did not get from within himself the marble from which he sculpted them.
     From: René Descartes (Reply to Fifth Objections [1641], 362)
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes]
     Full Idea: A triangle has a determinate nature, which I did not fabricate, and which does not depend on my mind. This is evident from the fact that various properties can be demonstrated regarding it, such as that its three angles are equal to two right angles.
     From: René Descartes (Meditations [1641], §5.64)
What experience could prove 'If a=c and b=c then a=b'? [Descartes]
     Full Idea: Please tell me what the corporeal motion is that is capable of forming some common notion to the effect that 'things which are equal to a third thing are equal to each other'.
     From: René Descartes (Comments on a Certain Broadsheet [1644], p.366)
'Nothing comes from nothing' is an eternal truth found within the mind [Descartes]
     Full Idea: The proposition 'nothing comes from nothing' is not to be considered as an existing thing, or the mode of a thing, but as a certain eternal truth which has its seat in our mind and is a common notion or axiom.
     From: René Descartes (Principles of Philosophy [1646], I.49)
     A reaction: There is a tension here, in his assertion that it is 'eternal', but 'not existing'. How does one distinguish an innate idea from an innate truth? 'Eternal' sounds like an external guarantee of truth, but being 'in our mind' sounds less reliable.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
I aim to find the principles and causes of everything, using the seeds within my mind [Descartes]
     Full Idea: I have tried to find in general the principles or first causes of everything which is or which may be in the world, ..without taking them from any other source than from certain seeds of truth which are naturally in our minds.
     From: René Descartes (A Discourse on Method [1637], §6.64)