logic 9/9

Cogency and Its Relation to Soundness (Inductive vs Deductive)

The lecture begins by clarifying terms for reasoning. Even if premises are true and the argument is strong, the conclusion can still be false. In inductive arguments, we classify them as cogent if all premises are true and as uncogent if either the argument is weak or at least one premise is false. This mirrors the way soundness and unsoundness work for deductive (valid) arguments: sound means valid and with true premises; unsound means not sound. The speaker emphasizes that we will focus on a practical approach to testing inductive arguments by elimination and assessment rather than trying to determine truth values of premises in every case.

Prediction as the First Elimination Step in Induction

The first elimination step for inductive arguments is to check whether the conclusion is a prediction about the future. A prediction is a future contingent sentence: it is about something that may be true or false in the future but is not currently settled. The lecturer uses the notion of future contingents to illustrate this, noting that English lacks a true future tense; we typically encode future events with words like will or going to. An example discussed is whether a hurricane will hit us this year. If the conclusion asserts a future contingent event, the claim is a prediction regardless of the type of reasoning supporting it. The measles example and the emerging disease discussion (COVID reference) emphasize how predictions are treated as future contingents in evaluation.

Causal Inferences: Causes, Effects, and Invisible Forces

Causation is presented as something often inferred from invisible forces. The lecturer stresses that causation is not directly observable; we infer it from effects and mechanisms. Causal inferences can proceed in two directions: from cause to effect or from effect to cause. Several concrete examples are used:

  • A rock-and-pen experiment: gravity causes the pen to land in a trash can when thrown; the observer notes gravity as a causal force despite not directly seeing gravity itself.
  • In biomedical studies, researchers look for causal forces to understand how to produce desired effects (developing medicines) or prevent undesired effects.
  • Everyday causal reasoning about baking: undercooked brownies are explained by insufficient leavening (cause to effect), and brownies that fail to rise are linked to leavening issues.

The lecture emphasizes keeping causation separate from mere correlation and recognizing that causal claims rely on identifying and understanding the underlying forces that produce observable effects.

Analogy Arguments and the Burden of Proof

An argument from analogy is introduced as a reasoning pattern that rests on comparing two things and claiming that what holds for one will hold for the other. The example used is: Firemen are like soldiers; you shouldn’t blame firefighters for fires or soldiers for wars. The discussion highlights a key point: the argument must specify relevant similarities. Simply saying two things are alike is not enough; the premises must state similarities that justify the analogy. The instructor notes that students often supply extra premises (additional similarities) that can strengthen the argument, but the original argument’s stated similarity may be weak or nonexistent. The burden of proof remains with the argument creator: if the similarities aren’t stated, one should not assume them. The exchange also touches on the need to avoid adding extraneous considerations that aren’t part of the argument being evaluated.

Inductive Generalization: From Sample to Population

Inductive generalization moves from a selected sample to a broader population. It is a statistical form of reasoning, and numerical indicators should cue its use. The speaker gives several examples:

  • A poll of 10,000 men across the US finds that 85% believe they are better looking than average. The conclusion is that American men as a group believe they are better looking than average.
  • A parallel poll of 10,000 American women shows 80% believing they are better looking than average.
    The key caution is distinguishing between “most” and “all.” The argument about “most American men” is weaker than asserting that all American men believe they are better looking. The discussion also explores the difference that sample size and representativeness make in generalizing to a population.
  • Additional inductive generalization examples appear later: equal property splits in divorce with reported effects on living standards for men vs. women; the prevalence of cold weather in Super Bowl history; plant physiology experiments where frost events lead to plant death.
  • The speaker emphasizes recognizing when a statement uses terms like most, many, or a proportion and interpreting these as inductive generalizations rather than deductive claims of universality.

Arguments from Authority and Tests of Source Credibility

Another inductive pattern is argument from authority: an expert or cited source is used to support a claim. The lecturer highlights simple cue phrases such as says or states to identify authority-based arguments. Examples include: a traffic report from a person named Dennis or a claim that CNN said four people are dead in a building collapse. The reliability of authorities is discussed, including the idea that media outlets have a duty to inform rather than guarantee truth, and the broader issue of whether an authority is qualified or credible. The lecturer promises to return to standards for evaluating such authorities later, noting that there can be good and bad uses of authority in arguments (including the risk of unqualified authority). The discussion also touches on eyewitness testimony and how the credibility of reports affects inductive strength.

Probabilistic and Correlational Induction: Prediction and Causal Links

Concrete prediction-based inductive reasoning reappears in several examples: sea level rise along Virginia’s shores is predicted to rise between 16 inches and 4 feet in the next century, illustrating probabilistic forecasts with numeric ranges. The lecture also distinguishes between predicting on the basis of evidence (prediction) and using causal reasoning to infer linkages between events, as with the link between recipe memory and test-taking memory (analogy).

Logic, Possible Worlds, and Logical Possibility

A substantial portion of the lecture is devoted to formal concepts in logic and possible-world semantics. Important distinctions include:

  • Possible world theory: a proposition is possibly true if it is true in at least one possible world. A proposition is logically possible if it can be conceived without contradiction.
  • True propositions are true in the actual world; possibly true propositions may be true in some possible world but not the actual one.
  • Logically possible vs physically possible vs probable. A proposition is logically possible if it does not entail a contradiction but may be contrary to what actually happens.
  • The poster examples include alternate histories and thought experiments where changing a single variable yields a different world, illustrating how logic analyzes counterfactuals.

Logical Laws and Relations: Identity, Excluded Middle, Non-Contradiction, and Symmetry

The lecture moves into formal logic and standard laws. Key points include:

  • Law of Identity: Everything is identical to itself. This is expressed as for all p, p = p. In symbols: orall pigl(p = pigr).
  • Law of Excluded Middle: A proposition is either true or false: p
    rightarrow p ext{ is not the case; } p ext{ or }
    eg p. In symbols: p \, ext{∨}\,
    eg p. (Often presented as a law: p \lor
    eg p.)
  • Law of Noncontradiction: A proposition cannot be both true and false at the same time:
    eg(p \land \neg p).
  • The Equivalence and Identity notions are illustrated with a simple demonstration about whether two people or identities are the same and how we track whether an object remains the same under change.
  • Reflexivity, Symmetry, and Transitivity: The lecture defines and tests these relations using ordinary-language examples and then moves to mathematical-like statements. Reflexivity means any thing relates to itself (a = a). Symmetry means if a = b then b = a. Transitivity means if a = b and b = c, then a = c. Examples are given: the Weekend and Abel; brothers Adam and John; jealousy relations; biological kinship (siblings, cousins) to illustrate transitivity and symmetry in real-world relations.
  • The exercise with “Does a like b, and does b like c, imply a like c?” shows that these relations are not always transitive in ordinary language, highlighting the distinction between mathematical relations and everyday associations.

Ordinary Language Analysis and the Move to Formal Logic

The lecturer distinguishes ordinary language (OL) from formal logic (FL). Ordinary language analysis (OLA) is used to understand how everyday terms function and to ensure that concepts align with commonsense understanding. In logic, one must sometimes switch to formal notation and symbolic language. The goal is to translate intuitive reasoning into precise, formal structures, which can require deprogramming preconceived beliefs about how language works. The talk also touches on linguistic concepts such as can vs may, possible vs probable, and the utility of double modals and double negatives in reasoning—learning to parse arguments without relying on informal stylistic cues.

Cognitive vs Emotive Meaning in Language and Persuasion

A significant portion discusses two levels of meaning in language: cognitive (informational content) and emotive (emotional impact). The speaker argues that when language is used to persuade, it often tries to evoke emotion, and the listener must distinguish the informational content from the emotional influence. The example of propaganda and emotionally charged political texts is used to illustrate how motive and emotion can be embedded within language and how critical evaluation should focus on the argument structure rather than purely on emotional appeals. The speaker also demonstrates with a pair of exercises using thumbs to indicate positive or negative sentiment elicited by language, emphasizing awareness of the emotive potential of rhetoric.

Putting It All Together: Goals for the Course and Practice with Arguments

The overall aim is to move from ordinary language use toward formal logical structures, enabling students to analyze arguments more effectively. The instructor emphasizes three major tasks: understanding the laws of thought (as opposed to merely repeating terms), mastering the distinction between logical possibility and actual truth, and building skills to translate everyday reasoning into formal representations. The lecture ends with a broader reflection on how logic, language, and thought interact and how disciplined analysis can improve critical thinking and argumentative clarity.

Key Concepts and Formulas Summary

  • Cogent vs uncogent (inductive): Cogent if premises are true and support the conclusion; uncogent if weak or premises false.
  • Prediction (future contingent sentence): Conclusion about a future event; the argument is a prediction regardless of the supporting reasoning.
  • Causation: Inference about invisible forces; can proceed from cause to effect or effect to cause; examples include gravity and leavening in baking.
  • Analogy: Compare two things and argue that similarities justify transferring conclusions; requires explicit similarities; burden of proof on the arguer.
  • Inductive generalization: From a sample to a population; use of numbers and proportions; distinguish between most and all; be cautious about representativeness and generalization.
  • Argument from authority: Premises rely on what an authority says; credibility depends on the authority’s relevance and qualifications.
  • Possible world semantics: A proposition is possibly true if true in at least one possible world; logically possible if it can be conceived without contradiction.
  • Laws of thought (logic):
    • Identity: orall pigl(p = pigr)
    • Excluded middle: p \,\lor \, \neg p
    • Noncontradiction: \neg(p \land \neg p)
  • Logical relations: Reflexivity (a = a), Symmetry (if a = b then b = a), Transitivity (if a = b and b = c then a = c).
  • Possible vs impossible: Distinguish logically possible, physically possible, and logically impossible; use possible-worlds to analyze counterfactuals.
  • Can vs may; double modals; ordinary language vs formal notation: Translating OL into FL improves clarity and reduces misinterpretation.

Examples Referenced in the Lecture (Key Takeaways)

  • Prediction examples: Hurricane hitting the US; sea level rise prediction: 16 inches to 4 feet in the next century.
  • Causation examples: Gravity causing a pen to land in a trash can; leavening issues affecting rise of brownies.
  • Analogy example: Firefighters and soldiers; lack of explicit similarities weakens the argument if similarities are not stated.
  • Inductive generalizations: 10,000 men claim they’re better looking; 10,000 women claim they’re better looking; most vs all; divorce study showing different standard-of-living effects for men vs women; Super Bowl weather history.
  • Authority and testimony: CNN reports versus qualified expertise; eyewitness testimony credibility.
  • Possible worlds and counterfactuals: Trump as president in the actual world; hypothetical alternates with Obama, Harris, etc.
  • Logical laws demonstrations: Identity, excluded middle, noncontradiction; examples showing why contradictions undermine reasoning.
  • Ordinary language analysis: Distinguishing cognitive meaning from emotive impact; propaganda examples; the role of language in guiding beliefs and actions.

Ethical and Practical Implications

  • Critical evaluation of arguments requires more than accepting premises; one must assess strength, relevance, and the truth of premises, especially in inductive reasoning.
  • Recognizing the emotive power of language helps avoid being misled by rhetoric; focus on the argument’s structure and evidence.
  • Understanding possible worlds and logical possibility supports clearer analysis of counterfactual scenarios and hypothetical claims, which is essential in philosophy, science, and public discourse.
  • The discussion of authority cautions against over-reliance on experts without assessing their scope, methods, and credibility; skepticism can be warranted