A Companion to Rationalism by Nelson Alan;

Author:Nelson, Alan;
Language: eng
Format: epub
ISBN: 4433095
Publisher: John Wiley & Sons, Incorporated
Published: 2012-09-03T16:00:00+00:00

Conclusion

Rationalist philosophers often condemn the imagination as a source of error and confusion, and urge us to detach ourselves from it in order to attain knowledge. Notwithstanding these criticisms, rationalists as varied as Plato, Descartes, and Malebranche maintain that the imagination is necessary in mathematics. The claim here is not simply that the imagination provides a useful – albeit ultimately dispensable – aid to the intellect in mathematics, but that it is constitutive of mathematical thinking. They also hold that mathematical thinking provides a stepping stone to a higher form of cognition, to the cognition of a first principle of knowledge.

The bulk of this chapter has been devoted to showing how, according to the Cartesian rationalists, the imagination is constitutive of mathematical thinking and how such thinking provides a stepping stone to a first principle. Concerning the first issue, both Descartes and Malebranche hold that mathematics takes a single object – extension or intelligible extension. But they maintain that the imagination provides different ways of conceiving this single object (i.e., different distinct imaginings). The imagination serves to delimit (intelligible) extension in our thought, so that we cognize it as some figure or other. The imagination also plays an essential role in the conception of the properties or truths that pertain to geometrical figures.

As for the second issue, both Descartes and Malebranche recognize what many philosophers today take as self-evident, that it is extremely difficult to form a non-imagistic representation of extension. Descartes thinks that such perceptions are possible but rare, and attained only after great effort, whereas Malebranche denies that we even are capable of absolutely pure cognitions of intelligible extension. They concur, however, in thinking that the imagination, as controlled and purified by geometry, provides a stepping stone to a (relatively) pure cognition of extension. The imagination can serve this function precisely because in mathematics we are already conceiving (intelligible) extension in a very distinct manner, especially as compared with our everyday thoughts. Malebranche also holds that, unlike the mind’s other modifications, the imagination leaves a greater share of attention for ideas in God. These ideas are intrinsically pure and distinct. The more attention that we can devote to them, the purer our perceptions will be.

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