Hume Term Paper

New Proposed Thesis

• Question: what does he mean by "math" and how can he claim that math is true?
  • There is an underlying principle that nature has inlaid
  • is math true because it cooresponds to that underlying principle, or because it is internally consistent?
    • math is internally consistent, and it also seems to explain things that the principle does, but it can't be used to discover that principle
  • he states that Euclid demonstrated "truths" (4.1)
  • if we can only know truths about math, etc, can we not know truths about our own world?
• Outline
  • Thesis: When Hume says "math", he is referring to an internally consistent system of reasoning, and when he claims that it is true, he is claiming that it is true to itself, not necessarily to our experience.
  • Math = an "affirmation, which is either intuitively or demonstratively certain" (4.1)
    • internally consistent reasoning
    • it's a system that does not necessarily coincide with our world (if there never were a circle, this system would still work, etc.)
    • even though math is its own separate system, its conclusions can still coorespond w/ our system (mixed, applied mathematics) (4.13)
    • but is mixed math as "true" as pure math is? no
      • it's based on experience of the underlying principles, not pure reason
      • but we can somewhat know the underlying principles, but without certainty
        • There is an underlying principle behind what we sense in nature (lots of evidence for this)
  • what about non-Euclidean geometry?
  • I haven't read much Hume

Old Proposed Thesis

Problem: Towards the end of paragraph 22 of Section 5, Hume makes a statement that seems to undermine his previous arguments. He seems to say that nature has created a course among our thinking that corresponds with the course of the external objects.

“As nature has taught us the use of our limbs, without giving us the knowledge of the muscles and nerves, by which they are actuated; so has she implanted in us an instinct, which carries forward the thought in a correspondent course to that which she has established among external objects”

Solution: This paper will show that this section does not actually conflict with his previous arguments.

Questions

• According to Reid…
  • has nature implanted a natural course among external objects?
  • can we know that our ideas of cause/effect follow that course as well?

Notes

• thoughts follow and are bound to impressions
• "nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact"
• can't extrapolate past experience to future predictions???
• the ultimate things that run the phaenomena are undiscoverable (pg 112, 4.12)
• he really emphasizes our inability to know cause/effect through reason; only through experience
• there are really principles behind the phaenomena (e.g. something is nutritious to eat, and we can discover that, but we can't discover why) 4.16
  • we assume that similar qualities are always accompanied by similar secret powers (principles) (5.4) by custom of habit
• arguments from experience can only be probable (4.19)
• experience = "the great guide of human life" (4.20)
• reason is incapable of drawing from a thousand examples something that it coulnd't draw from one example; custom can do that
  • so, inferences from experience are custom, not reason
• "All belief of matter of fact or real existence is derived merely from some object, present to the memory or senses, and a customary conjunction between that and some other object." (5.8)
  • can we actually learn anything of history? (5.7)
• there really is a defined course in nature, and our succession of ideas matches with it.