J
James1215
Guest
Objections to point 2: pure reason does not give us knowledge.
Maths does not contain any such propositions as ‘experience is required for knowledge [because…]’ or ‘the human body cannot function for long without respiration [because…]’. Is 1+1=2 this sort of proposition? No, 2 is contained within 1+1 and is not an extension but an intrinsic part of 1+1. I agree maths is certain, but it cannot be uncertain given that it is a system of self-consistent logic. How is maths descriptive or methodological? Yes mathematicians engage in complex thought processes, but that does not mean they gain anything but human insight into the elaboration of what is already given in principle; that is different from a methodology which takes one some epistemological distance. It would be done in a moment by a computer, or by a more intelligent person. I agree that the ‘knowledge’ one gains within maths is ‘beyond sense experience’ because one can go further and say there is no intersection between mathematics and the observed. The latter does not confirm the former, and the former does not illuminate the latter unaided.
That point is where I may have introduced confusion. No amount of testing is needed to show that pi=pi, but what knowledge does pi give us? Does it tell us the radius of the Earth or the circumference? No it doesn’t, because maths is nothing without our empirical observation that the earth is not actually spherical. We have to use or not use mathematical models according to empirical observation and therefore, according to experience. Pure reason does not give us knowledge.
Dubito! The reason I asked you to formulate that again is so that I do not attack a straw man. How is engaging in a project where one tries to doubt one’s existence a methodology for knowledge? Firstly, it is irrational to think that one’s senses are totally illusory (to doubt them); secondly, if one achieves doubt of everything, one has no knowledge. If I doubt everything, I doubt that I’m doubting. I doubt that I exist. What possible certainty is left?
Therefore, the examples provided to show that reason alone does produce knowledge are lacking. It remains that 1. experience is used for knowledge 2. we cannot seem to do without it.
Maths does not contain any such propositions as ‘experience is required for knowledge [because…]’ or ‘the human body cannot function for long without respiration [because…]’. Is 1+1=2 this sort of proposition? No, 2 is contained within 1+1 and is not an extension but an intrinsic part of 1+1. I agree maths is certain, but it cannot be uncertain given that it is a system of self-consistent logic. How is maths descriptive or methodological? Yes mathematicians engage in complex thought processes, but that does not mean they gain anything but human insight into the elaboration of what is already given in principle; that is different from a methodology which takes one some epistemological distance. It would be done in a moment by a computer, or by a more intelligent person. I agree that the ‘knowledge’ one gains within maths is ‘beyond sense experience’ because one can go further and say there is no intersection between mathematics and the observed. The latter does not confirm the former, and the former does not illuminate the latter unaided.
That point is where I may have introduced confusion. No amount of testing is needed to show that pi=pi, but what knowledge does pi give us? Does it tell us the radius of the Earth or the circumference? No it doesn’t, because maths is nothing without our empirical observation that the earth is not actually spherical. We have to use or not use mathematical models according to empirical observation and therefore, according to experience. Pure reason does not give us knowledge.
Dubito! The reason I asked you to formulate that again is so that I do not attack a straw man. How is engaging in a project where one tries to doubt one’s existence a methodology for knowledge? Firstly, it is irrational to think that one’s senses are totally illusory (to doubt them); secondly, if one achieves doubt of everything, one has no knowledge. If I doubt everything, I doubt that I’m doubting. I doubt that I exist. What possible certainty is left?
Therefore, the examples provided to show that reason alone does produce knowledge are lacking. It remains that 1. experience is used for knowledge 2. we cannot seem to do without it.