The greater the numbert of cases in which a thing of sort A has been found associated with a thing of sort B (without failure), the more probable it is that A is always associated with B Under the same circumstance, a sufficient number of cases of the association of A with #B will make it nearly certain that A is always associated with B, and will make this general law approach certainty without limit

anything implied by a true proposition is true

Laws of Thought (note they are pretty arbitrary lol)

  1. Law of Identity (Whatever is, is)
  2. Law of Contradiction (Nothing can both be and not be)
  3. Law of excluded middle (everything must either be or not be)

Empiricists - All knowledge is gained from experience (Locke, Berkeley) Rationalists - In addition to experience, there are innate ideas and principles (Descartes, Leibniz)

innate logic independent of experienceis still elicited and caused by experience - ‘a priori’ some knowledge is a priori, the experience which makes us think of it does not suffice to prove it, but merely directs our attention that we see its truth without requiring any proof from experience

but empiricists were right thAat nothing can be known to exist except by experience help knowledge is empirical when it relies in full or part on experience

deduction - general 2 general, general 2 particular induction - particular 2 particular, particular 2 general

a priori (2+2=4) deduction empirical generalisation induction (because all empirical ggeneralisations are more uncertain than the instances of them)

pre-kant people believed that all a priori knowledge was analytic, achieved by the laws of thought

Hume (prekant) believed that the connection in some cases was synthetic. previously the rationalists thought effecet could be deduced from cause with enough knowledge made a proposition that nothing could be known a priori about the connexion of cause and effect also that all arithmetic and geometry were synthetic, not analytic e.g. 7+5=12; 7 and 5 have to be put together to give 12; the idea of 12 is not contained in them, nor even in the idea of adding them together

how is pure maths possible? - empiricist pure: our mathematical knowledge is derived by induction from particular instances - validity of general principle cannot be proved by induction - certainty of general principle can be known from consideration of a single instance, and gain nothing from repeat instances

kant thinks we have a physical and private object (of our nature, space time causality comparison), we know the phenomenon which is a product of us and the thing itself limits scope and fails to explain certainty relations are constructs of the mind (‘in’ a room), however it is true that an earwig is in your room even if you know it or not.

a priori knowledge applies to what is mental and not mental