Tuesday, May 26, 2009

Logic Primer 2: The Building Blocks of Logic

Now we will discuss some of the basic building blocks in the study of logic. In general, everything else is built upon these essentials.

The first building block is the proposition. A proposition is something that may be asserted or denied. Propositions can be true or false; hence, they have a truth-value. In other words, a proposition is a true or false statement that says something about reality. Other statements, such as commands, questions, or exclamations are not true or false – they are not propositions.

An argument is “any group of propositions of which one is claimed to follow from the others, which are regarded as providing support or grounds for the truth of that one.”1 When you have a number of propositions that lead to a conclusion, you have an argument. The conclusion of an argument is the statement that follows from the supporting propositions, which are called premises. To reiterate: an argument is composed of premises that lead to a conclusion. A conclusion without premises is not an argument; it is merely an opinion.

The building blocks of arguments can often be recognized by telltale words. The words that point to the conclusion can be called conclusion-indicators:

“Therefore, hence, thus, so, accordingly, in consequence, consequently, as a result, it follows that, we may infer, which shows that…” These are all words or phrases that often point to the conclusion of an argument.

The telltale words for premises can be called premise-indicators:
“Since, because, for, as, follows from, as shown by, as indicated by, the reason is that…” These are some of the words that can point to premises.2

One point should be noted when seeking to identify arguments. There is a difference between an argument and an explanation. As Copi explains:
Many passages, both written and spoken, that appear to be arguments are in fact not arguments but explanations. The occurrence of certain premise- or conclusion-indicators such as “because,” “for,” and “therefore” cannot settle the matter, since those words may be used in both explanations and arguments. What we need to know the intention of the author of the passage.3
So the careful thinker must discern the difference between explanations and arguments by looking closely at context and intention.

Arguments come in two kinds—they are either deductive or inductive. These are important terms to differentiate. When an argument is deductive, it means that the conclusion follows from the premises necessarily and conclusively. When a deductive argument is valid, it means that if the premises are true, the conclusion must be true. An inductive argument, on the other hand, is not a conclusive argument. When an argument is inductive, it simply means that that the conclusion may be true to a certain degree of probability. Copi clarifies:
A deductive argument is one whose conclusion is claimed to follow from its premises with absolute necessity, this necessity not being a matter of degree and not depending in any way on whatever else may be the case. In sharp contrast, an inductive argument is one whose conclusion is claimed to follow from its premises only with probability, this probability being a matter of degree and dependent upon what else may be the case.4
One way to look at this is as follows: in a deductive argument, no amount of additional information can change the conclusion of the argument. In an inductive argument, the conclusion may change when new information is discovered. Deductive arguments are certain, whereas inductive arguments are probable to some degree.

When an argument is structured correctly, it is called a valid argument. When an argument is not correctly structured, it is called invalid. An argument cannot be true or false, only valid or invalid. Truth or falsity only applies to statements or propositions. The conclusion of an argument can be true or false (because the conclusion is a statement), but the argument is only either valid or invalid.

Finally, when an argument is valid, and all of its premises are true, it is called a sound argument. This is the kind of argument the good thinker is looking for.

Here are some resources that will get you started:

Audio resource:
- Logic MP3 Resources.

Helpful books:
- A Rulebook for Arguments by Anthony Weston
- Logic by Gordon Clark

Some web links:
- Introduction to Logic from ODU
- Propositional Logic from Internet Encyclopedia of Philosophy
- online Logic Primer

Tomorrow we will look at thinking logically.

1 Copi & Cohen, p. 6.
2 Ibid., pp. 21,22. These are a brief adapted summary of some of Copi & Cohen’s conclusion and premiss-indicators.
3 Ibid., p. 35.
4 Ibid., p. 45.


Lee said...

Makes sense... thanks

Chad said...


Thank you for doing this logic series. I plan to feature it on my blog in the near future and look forward to working through the resources this summer.

Keep up the good work!


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