# Cartesian coordinates

<mathematics, graphics> (After René Descartes, French philosopher and mathematician) A pair of numbers, (x, y), defining the position of a point in a two-dimensional space by its perpendicular projection onto two axes which are at right angles to each other. x and y are also known as the abscissa and ordinate.

The idea can be generalised to any number of independent axes.

Compare polar coordinates.

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# Cartesian doubt

<epistemology> in his Meditations, Descartes (1596-1650) proposed discarding any kind of belief that could be doubted, that might be false. Initially, he was inclined to doubt all the evidences of his senses (pointing out that it seemed impossible to tell for sure whether he was at any point aswake or asleep). The doubt that Descartes introduced into philosophy has been a characteristic feature as many philosophers since have supposed that we have no secure rational basis for believing in the existence of a world external to our sense experience, etc. private language argument, the

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# Cartesian interactionist dualism

<philosophy of mind, ontology> the view that

1) ontological independence is the criterion for the identification of substance, that is x = substance iff, for any y different from x, x exists independently of y

2) following (1), strictly speaking, there is only one substance, that is God = substance

3) if x is ontologically dependent only on God, then x = substance in a weak sense

4) the mental and the material are two weak-substances and;

5) both can have causal effects on the other.

Luciano Floridi <luciano.floridi@philosophy.ox.ac.uk>

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# Cartesianism

<metaphysics, epistemology, philosophical school, dualism, innatism> Cartesianism is the name applied in philosophy to the doctrines of Descartes, and to the tradition of modern philosophy that arose out of his thought. In a way, much modern philosophy is just a footnote to, or working out of, Descartes. Some signature ideas and ideals of Cartesianism are dualism and rationalism, a combination of idealism in the spiritual realm and of mechanism in the physical realm. (References from automatism and mechanism.)

Based on [The Ism Book]

Edited by Giovanni Benzi

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# Cartesian product

<mathematics> (After Renee Descartes, French philosopher and mathematician) The Cartesian product of two sets A and B is the set

```	A x B = {(a, b) | a in A, b in B}.

```
I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets.

If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "Cartesian coordinates" of points in that space.

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# Cartesian scepticism

<epistemology> 1. sceptical views against the absolute reliability of empirical and mathematical knowledge.

2. any of a class of sceptical views against empirical knowledge based on the argument that claims to empirical knowledge are defeated by the possibility that we might be deceived insofar as we might be, for example, dreaming, hallucinating, deceived by demons, or brains in vats.

Chris Eliasmith - [Dictionary of Philosophy of Mind] Homepage

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