We use logic every day to figure out test questions, plan our budgets, and decide who to date. We borrow from the vocabulary of logic when we say, "Brilliant deduction" or even "I don't want to argue about it." In the study of logic, however, each of these terms has a specific definition, and we must be clear on these if we are to communicate.
Vocabulary
Proposition --
T or F in an argument, but not alone. Can be a premise or conclusion. Is not equal to a sentence.
Premise --
Proposition used as evidence in an argument.
Conclusion --
Proposition used as a thesis in an argument.
Argument --
A group of propositions of which one is claimed to follow from the others.
Induction --
A process through which the premises provide some basis for the conclusion
Deduction --
A process through which the premises provide conclusive proof for the conclusion.
Argument Indicators: Premise Indicators: Conclusion Indicators:
should
must
ought
necessarily
since
because
for
as
inasmuch as
for the reason that
first ...
therefore
hence
thus
so
consequently
it follows that
one may infer
one may conclude
When dealing with persuasive writing, it will be helpful for you to outline the argument by premises and conclusions. By looking at the structure of the argument, it is easy to spot logical error.
Universities are full of knowledge. The freshmen bring a little in, and the seniors take none away, and knowledge accumulates.
-- Harvard President A. L. Lowell
Premise 1
Premise 2
Premise 3
Conclusion Freshmen bring a little (knowledge) in
Seniors take none away
Knowledge accumulates
Universities are full of knowledge
Example 2
(Here, the conclusion of one argument is used as a premise in another. This is very common.)
Even though there may be a deceiver of some sort, very powerful and very tricky, who bends all his efforts to keep me perpetually deceived, there can be no slightest doubt that I exist, since he deceives me; and let him deceive me as much as he will, he can never make me be nothing as long as I think I am something. Thus, after having thought well on this matter, and after examining all things with care, I must finally conclude and maintain that this proposition: I am, I exist, is necessarily true every time that I pronounce it or conceive it in my mind.
-- Rene Descartes, *Meditations*
Argument 1 Premise 1:
Conclusion of Argument 1
Argument 2 Premise 1:
Conclusion:
To be deceived ... I must exist
When I think that I exist I cannot be
deceived about that
I am, I exist, is necessarily true ... .
Exercises
Find the Arguments and Outline them in These Statements:
1. Ask the same for me, for friends should have all things in common.
-- Plato, Phaedrus
2. Matter is activity, and therefore a body is where it acts; and because every particle of matter acts all over the universe, every body is everywhere.
-- Collingwood, The Idea of Nature
3. The citizen who so values his "independence" that he will not enroll in a political party is really forfeiting independence, because he abandons a share in decision©making at the primary level: the choice of the candidate.
-- Felknor, Dirty Politics
Reaching Logical Conclusions
This article is reprinted from pages 78-79 of Pearson-Allen: Modern Algebra , Book One. In the book it is one of several between-chapter articles that add interest and provike thought on subjects related to the topics discussed in the text.
Consider the two statements:
1. Any member of a varsity squad is excused from physical education.
2. Henry is a member of the varsity football squad.
Our common sense tells us that if we accept these two statement as true, then we must accept the following third statement as true:
3. Henry is excused from physical education.
We say that the third statement follows logically from the other two.
In drawing logical conclusions it does not matter whether the statements we accept as true are reasonable or sensible. This is because we depend entirely upon the form of the statements and not upon what we are talking about. Thus, if we accept the following statements as true:
1. All whales are mammals;
2. All mammals are warm-blooded animals;
3. All warm-blooded animals are subject to colds;
then we must conclude that
