§1 Understanding Logic

Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning. Traditionally centered around the analysis of argument forms and patterns, logic provides the “laws of thought” that allow us to evaluate the relationship between our claims and our conclusions.

While psychology explores how people actually think, logic is a normative discipline—it focuses on how we ought to think if we wish to be rational. By refining a system of rules, we can better identify good patterns of reasoning and separate them from muddled or bad forms. This skill is essential for improving our own reasoning and evaluating the constant stream of claims we encounter daily.

1.1 Building Blocks: Statements and Arguments

An argument is not a quarrel or a verbal fight; it is a technical structure consisting of a set of sentences. One or more of these sentences—the premise(s)—are intended to provide support for, or reasons to believe, another sentence—the conclusion.

All arguments are composed of statements (or propositions).

• Statements: Sentences that possess a truth value, meaning they are either true or false. (e.g., “Jupiter is a planet” or “Olympia is the capital of Washington”).

• Non-statements: Sentences that do not assert a fact and therefore lack a truth value. These include questions (“What time is it?”), commands (“Go study!”), and exclamations (“Awesome!”).

1.2 The Two Pillars: Deduction and Induction

All arguments aim to support a conclusion, but they differ fundamentally in their intent—the way the premises are meant to relate to the conclusion.

• Deductive Reasoning: Aims to provide conclusive support. In a deductive argument, the intent is for the conclusion to follow with absolute necessity. If the premises are true, the truth of the conclusion is guaranteed. We ask: Do the premises attempt to prove the truth of the conclusion?

• Inductive Reasoning: Aims to provide probable support. The intent is for the conclusion to be likely given the premises. Even if the premises are true, it remains possible for the conclusion to be false, though it is statistically or logically improbable. We ask: Do the premises attempt to increase the likelihood of the conclusion?

1.3 Identifying Arguments in the Wild

To determine if an argument is present, look for the inferential relationship: the process of reasoning where patterns and relationships are recognized between statements. This often involves indicator words that signal which part of the text provides support and which part is being supported.

1.4 Standard Form

To evaluate an argument clearly, it is helpful to place it into standard form. This involves taking an argument from a passage and organizing the premises (P1, P2, etc.) so they lead directly to the conclusion (C), marked by the “therefore” symbol ($\therefore$).

Example in Standard Form:

• P1: The amount of money spent per student has been decreasing for years.

• P2: At current funding levels, the state cannot fulfill its constitutional obligation to provide education.

• $\therefore$ C: Public schools deserve increased financial assistance.

1.5 Distinguishing Non-Arguments

It is important to distinguish arguments from other types of communication that may appear similar but lack the intent to provide rational support for a claim. Common non-arguments include:

• Warnings and Advice: Alerts to danger or recommendations for behavior without evidence.

• Beliefs and Opinions: Expressions of personal judgment without supporting reasons.

• Reports and Expositions: Information-sharing or elaborating on a subject without establishing a proof.

• Explanations: Descriptions of why or how an event occurred (taking the event as a given), rather than proving that it occurred.

• Conditionals: “If…then” statements that lay out conditions but do not establish that the conditions or the results are actually true.