Module 1: The Basics of Logical Analysis
1.1 Building Blocks of Logic
Let’s jump right in and examine the fundamental building blocks of logic: propositions and arguments.
1.1.1 Propositions
Reasoning involves making claims or statements that we back up with reasons. Something we claim, state, or assert is a proposition. (Be aware that the term statement
may be used interchangeably in this course with the term proposition
.)
Propositions are expressed by declarative sentences. They are things that can be true or false. ‘This textbook can be read online.’ is a declarative sentence; it expresses the proposition that the textbook is an ebook you can read on your device, which is true.
Other kinds of sentences do not express propositions. For example:
- Imperative sentences issue commands. ‘Sit down and be quiet.’ is an imperative sentence; it doesn’t make a claim, or express something that might be true or false. Either it’s obeyed or it isn’t.
- Interrogative sentences ask questions: ‘Who will win the World Cup this year?’ is an interrogative sentence; it too does not assert anything that might be true or false.
Although some advanced logics have been developed to deal with imperatives and questions, we do not address them in an introductory-level course. Only declarative sentences express propositions, and so they are the only kind of sentences we will deal with at this stage in the study of logic.
Check Your Understanding
1.1.2 Arguments
Recall from the unit overview that logic is the study of reasoning. The fundamental unit of reasoning is the argument. In logic, ‘argument’ does not mean a disagreement, a shouting match; rather, we define the term precisely in this way:
Argument: a set of propositions, one of which, the conclusion, is (supposed to be) supported by the others, the premises.
The component parts are defined as follows:
- The conclusion is the proposition that is the claim being backed up with reasons.
- The premises are propositions that provide reasons or evidence to support the argument’s conclusion.
When we are reasoning by drawing an inference from a set of statements, then the inference we draw is the conclusion of an argument, and the statements from which it’s drawn are the premises.
Note: In logic, the term inference
is used in several related ways. Typically it refers to the process of basing a conclusion on evidence, or reasoning —as in the verb to infer.
It may also be used to refer to the conclusion/claim itself. In addition, an argument consisting of a single premise and conclusion may be referred to as an inference.
Returning to our definition of argument,
we include the parenthetical hedge—supposed to be
—in this definition of “argument” to make room for bad arguments. Remember, in Logic, we’re evaluating reasoning. Arguments can be good or bad, logically correct or incorrect. A bad argument, very roughly speaking, is one where the premises fail to support the conclusion; a good argument’s premises actually do support the conclusion by giving good reasons for believing it. We don’t judge arguments based on whether or not they succeed in convincing— there are logically bad arguments that can be quite persuasive. Rather, the logical enterprise is to identify the kinds of reasoning that ought to be persuasive.
Check Your Understanding
