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Early Modern Philosophy reveals some interesting stuff about the nature and power of science and mathematics. Some of the philosopher that talked about this stuff was Descartes in his Meditation, Hume, and Kant.
Descartes Meditations are concerned with the scientific method. Descartes was a French mathematician and he invented Analytic Geometry and Cartesian Coordinates. Descartes used something called the Method of doubt. He is not a skeptic. His doubt is a tool that he uses to search for certainty. He adopts this skeptical hypothesis in his search. One of his hypotheses was the Dream Hypothesis. In his Dream Hypothesis he says, for all I know I might be dreaming. He is calling all sense based a posteriori beliefs into doubt. In Meditation I Descartes says, “any sense experience may be recreated in a dream, dream experiences are not veridical, therefore any sense experience may be non-veridical and so subject to doubt.” Mathematical truths and truths of reason survive his hypothesis. An example in one of the videos was, whether I am awake or asleep 2+3=5 and a square has four sides. I think mathematics is important to science because it helps you figures things out about the world with evidence. If you did not have math, I don’t think science could work. Almost everything you do in science involves math. Math can help prove the science.
Hume also talked about the nature of scientific thought. Hume was a British Empiricist. He believed that human understating is limited and many judgments thought to be rational actually rely on other faculties. He also believes that humanity is seeking understanding fundamental principles of science or Metaphysics. In the video is said “Metaphysics tries to penetrate into subjects utterly inaccessible to the understanding.” Hume says, “universal doubt would be doubt of our knowledge.” He also says, “if such universal doubt would be attainable, it would be incurable.” Hume advocates a limited skepticism. He thinks the only objects of abstract science or mathematics are quantity and number. This is the limit of a priori reasoning. Abstract reasonings will help you with mathematics.
Kant also had some things to say about science and metaphysics. He believes that general features of reality may be discovered by pure reason which is a priori. He says “Any possible experience has a certain structure and this structure is the foundation for metaphysics.” According to Kant our understanding shapes reality, prior to our experience of it. Intuition is what is immediately given to us which is the Forms of intuition. He also believes that we do not see space. We see things in space and we do not experience time. We experience events in time. He says objects are intuited in space and time and Kant refers to mathematics as “pure intuition.” Time is linear and that is arithmetic. Kant gives the example that 7+5=12 and he says that he can analyze the sum of seven and 5 as long as you please and you will never find 12 in it. He is saying that it is not an analytic statement and you have to go outside of the concepts with the help of intuition. Kant says that mathematics only makes sense through possible application to objects of experience.
All of these early modern philosophers reveal some interesting stuff about the nature and power of science and mathematics. It was important for them to think this way and come up with the ideas that they came up with to help make science and mathematics what it is today because I do not think you can have science without mathematics.
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