By Jacques Derrida
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Part of Descartes's -36answer is that there are certain very simple and general notions that may serve as the starting points for explaining whole classes of seemingly diverse phenomena: The exclusive concern of mathematics is with questions of order or measure, and it is irrelevant whether the measure in question involves numbers, shapes, stars, sounds or any other object whatsoever. This made me realise that there must be a general science which explains all the points that can be raised concerning order and measure, irrespective of the subject matter, and that this science should be termed mathesis universalis ( AT X.
The argument so far has left unscathed a large number of seemingly quite unproblematic sense-based judgements such as 'I am holding my hand in front of my face'; these, it seems, I would be mad to doubt. But now the second wave of doubt arrives: it is possible that even the judgement that I am holding my hand up could be false; for I might at this very moment be dreaming--not holding my hand up before my eyes, but asleep in bed with my eyes closed. 3. The possibility that I am now dreaming leaves unscathed my belief in the existenoe of at least general kinds of things such as heads, hands, and faces (for though a particular judgement about this hand may be false if I am dreaming, dreams are presumably formed from ingredients taken from real life).
15 What Mersenne did propose, however, was that 'the entire argument be set out in geometrical fashion (more geometrico), starting from a number of definitions, postulates and axioms' ( ATV II. 128; CSM II. 92). Descartes replied that in the Meditations he had deliberately avoided the standard geometrical technique 'which ancient geometers usually employed in their writings'. This traditional method was known as the 'method of synthesis', and Descartes conceded that it had the advantage of providing rigorous demonstrations where 'each step is contained in what has gone before' so that 'the reader, however argumentative or stubborn he may be, is compelled to give his assent' ( AT VII.