V. Logic and Knowledge (From Mills work System of Logic)
A. Deduction: (inference from general to particular)
1. Definition:
All deductive or demonstrative sciences are inductive and are based on experience. The
2. The Syllogism
Syllogism contains the major premise as an inductive generalization. For instance, in the syllogism,
P1 All human beings are mortal.
P2. Socrates is a human being.
Conclusion: Therefore, Socrates is mortal.
The conclusion is presumed in the first premise since we cannot say that “All human beings are mortal” unless we are already convinced of the mortality of each individual man including Socrates.
A general statement, such as “All human beings are mortal” is just a rule, like a memorandum that summarizes what we know of individuals; so a general statement is really about individuals and we infer from the general to the particular in a syllogism. IN a syllogism then we do not really infer from a general to a particular, but we interpret the general rule in the major premise to make sure that it is applied correctly. The syllogism still has value however because arguing from a “general principle presents a larger object to the imagination than individual statements” and provides a superior means of testing a claim by pointing out conclusions to be examined. Mill does not make the distinction between “validity” and “soundness common in present day logic.
3. Geometry
The points, lines, circles, and squares of geometry are copies of the imperfect or approximate points, lines circles, and squares we encounter in our experience e. The points, lines, circles, and squares we encounter in our experience. The points, lines, circles, square, and axioms of geometry are not a priori necessary truths based upon definitions or else some separate realm of concepts; rather they are experiential, or experimental, truths and should be regarded as approximations. Since we can explain geometry quite well as being based upon experience, the burden of proof here rests with anyone who wants to claim otherwise. The “necessity” of geometry cannot be based on the view which is held by some that any other axioms are inconceivable since there is a long history of the rejection of prior claims about inconceivability as knowledge increased.
4. Arithmetic and Algebra.
There is no separate realm of abstract numbers because we always encounter numbers in experience associated with objects. That is, we do not experience the number 10 but rather 10 books, 10 pencils, 10 miles, etc. We jus think we are dealing with a separate, abstract number because we can associate a given number with a variety of different objects. The fundamental truths of number are based upon early and constant experiences and are thus inductive generalizations.
