Deductive Logic
I found this while googling logic.
INTRODUCTION.
§ 1. LOGIC is divided into two branches, namely–
(1) Inductive,
(2) Deductive.
§ 2. The problem of inductive logic is to determine the actual truth
or falsity of propositions: the problem of deductive logic is to
determine their relative truth or falsity, that is to say, given such
and such propositions as true, what others will follow from them.§ 3. Hence in the natural order of treatment inductive logic precedes
deductive, since it is induction which supplies us with the general
truths, from which we reason down in our deductive inferences.§ 4. It is not, however, with logic as a whole that we are here
concerned, but only with deductive logic, which may be defined as The
Science of the Formal Laws of Thought.§ 5. In order fully to understand this definition we must know exactly
what is meant by ‘thought,’ by a ‘law of thought,’ by the term
‘formal,’ and by ‘science.’§ 6. Thought, as here used, is confined to the faculty of
comparison. All thought involves comparison, that is to say, a
recognition of likeness or unlikeness.§ 7. The laws of thought are the conditions of correct thinking. The
term ‘law,’ however, is so ambiguous that it will be well to determine
more precisely in what sense it is here used.§ 8. We talk of the ‘laws of the land’ and of the ‘laws of nature,’
and it is evident that we mean very different things by these
expressions. By a law in the political sense is meant a command
imposed by a superior upon an inferior and sanctioned by a penalty for
disobedience. But by the ‘laws of nature’ are meant merely certain
uniformities among natural phenomena; for instance, the ‘law of
gravitation’ means that every particle of matter does invariably
attract every other particle of matter in the universe.§ 9. The word ‘law’ is transferred by a metaphor from one of these
senses to the other. The effect of such a command as that described
above is to produce a certain amount of uniformity in the conduct of
men, and so, where we observe uniformity in nature, we assume that it
is the result of such a command, whereas the only thing really known
to us is the fact of uniformity itself.§ 10. Now in which of these two senses are we using the term ‘laws of
thought’? The laws of the land, it is plain, are often violated,
whereas the laws of nature never can be so [Footnote: There is a sense
in which people frequently speak of the laws of nature being violated,
as when one says that intemperance or celibacy is a violation of the
laws of nature, but here by 'nature' is meant an ideal perfection in
the conditions of existence.]. Can the laws of thought be violated in
like manner with the laws of the land? Or are they inviolable like the
laws of nature?§ 11. In appearance they can be, and manifestly often are violated-for
how else could error be possible? But in reality they can not. No man
ever accepts a contradiction when it presents itself to the mind as
such: but when reasoning is at all complicated what does really
involve a contradiction is not seen to do so; and this sort of error
is further assisted by the infinite perplexities of language.§ 12. The laws of thought then in their ultimate expression are
certain uniformities which invariably hold among mental phenomena, and
so far they resemble the laws of nature: but in their complex
applications they may be violated owing to error, as the laws of the
land may be violated by crime.§ 13. We have now to determine the meaning of the expression ‘formal
laws of thought.’§ 14. The distinction between form and matter is one which pervades
all nature. We are familiar with it in the case of concrete things. A
cup, for instance, with precisely the same form, may be composed of
very different matter-gold, silver, pewter, horn or what not?§ 15. Similarly in every act of thought we may distinguish two
things–(1) the object thought about,
(2) the way in which the mind thinks of it.
The first is called the Matter; the second the Form of Thought.
§ 16. Now Formal, which is another name for Deductive Logic, is
concerned only with the way in which the mind thinks, and has nothing
to do with the particular objects thought about.
Keep working that brain, steam isn’t coming out yet.
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