Lecture 2 (Chatper 2) + Article

When is a sentence ambiguous?

A sentence is ambiguous in a given context when there is more than one possible way of interpreting it in that context. If there is more than one proposition it could plausibly be taken to express in that context.

Lexical Ambiguity (Definition, Cause, and Resolution)

• Definition: A property of individual words or phrases that occurs when a single term has two or more distinct meanings (i.e., picks out two or more different extensions).

• Sentence Impact: An ambiguous word can import its ambiguity into an entire sentence, making it open to multiple competing interpretations (e.g., "He is a curious child" → inquisitive vs. strange; "by the penguins" → attacked by them vs. next to them).

• Resolution: In practice, lexical ambiguity is resolved through context and background knowledge, which indicate the most probable intended meaning.

Syntactic Ambiguity (Definition, Cause vs. Lexical, and Resolution)

• Definition: A sentence-level ambiguity occurring when the grammatical arrangement (syntax) of words allows a sentence to express two or more distinct propositions.

• Contrast with Lexical Ambiguity: It is caused by the structure/grouping of the words (often ambiguous modifier attachments), not by an individual word having multiple meanings.

• Example: "The power company will announce that the electricity supply is to be cut off tomorrow." (Does "tomorrow" attach to the announcement or the cut-off?)

• Add the coriander, finely chopped (if desired)

• Resolution: Rewriting and restructuring the sentence so modifiers clearly attach to their intended target (e.g., "Tomorrow, the power company will announce...").

Vagueness (Definition, Distinction from Ambiguity, and Types)

• Definition: A property of words or phrases whose meaning is indefinite or whose boundaries of application (extension) are fuzzy and demarcated without precise cut-offs.

• Contrast with Ambiguity: Ambiguity involves a word having two or more distinct meanings (e.g., ball = toy vs. dance); vagueness involves an indefinite, fuzzy boundary for a term's application (e.g., bald, big pay rise).

• Two Main Types:

  • Rhetorical / Cluster: Emotionally charged terms whose application is left deliberately imprecise to sway an audience or hide weak positions (e.g., radical, weapons of mass destruction).

    • Borderline / Continuum: Descriptive terms whose clear concepts lack sharp cut-off points along a spectrum (e.g., city vs. town, orange vs. yellow).

Primary vs. Secondary Connotation (Definitions, Logical Test, and Role in Rhetoric/Metaphor)

• Primary Connotation: The defining rule stating the necessary and sufficient conditions for a term's application (e.g., ram= "male sheep"). Lacking a primary trait creates a logical contradiction (a "female ram" cannot exist).

• Secondary Connotation: The typical associations, expectations, or non-defining characteristics attributed to a term (e.g., ram = woolly, has horns, eats grass). Lacking these traits is not a contradiction.

• Critical Thinking Impact:

  • Vagueness: When the line between primary and secondary traits blurs (e.g., feminist, left-wing), terms become vague and rhetorically loaded.

    • Metaphor: Metaphors activate secondary connotations while ignoring false primary ones (e.g., calling someone a "pig" evokes untidiness or greed, not swine biology).

Rhetorical Question.

Rhetorical questions take the form of a question but indirectly assert a proposition

(Whereas a declarative sentence directly asserts a proposition)

Implicitly Relative Sentences (Definition, The "Comparison Class" Problem, and Resolution)

• Definition: Sentences that make a comparison or evaluation without explicitly stating the group, baseline, or standard of comparison being used (e.g., "Taxes are high", "Uncle Eddie is a fast runner").

• The Comparison Class Problem: The truth or falsity of the claim depends entirely on the omitted reference group. Compared to Olympic sprinters, Uncle Eddie is slow (claim is false); compared to other 94-year-olds, he may be very fast (claim is true).

• Secondary Issue (Compounded Vagueness): Even after identifying the comparison class, relative adjectives (fast, low, above-average) lack sharp cutoff thresholds along their scale.

  • Critical Thinking Resolution: Identify the missing comparison class and make it explicit before evaluating whether the claim is true, false, or supported by evidence.

Quantifiers in Critical Thinking (Definition, the 3 Main Problems, and Counterexamples)

• Definition: Words or phrases specifying how many/much of something exists or how frequently an event occurs (all, most, some, few, rarely, never).

• Three Core Problems:

  1. Imprecise Use: Using absolute/universal quantifiers (all, never) when only a qualified generalization (most, often) is warranted.

  2. Inherent Vagueness: Indefinite terms like some or few lack precise thresholds, making them easy to twist rhetorically.

  3. Omission (Implicit Quantifiers): Leaving out quantifiers entirely ("Politicians are corrupt"), which defaults to a sweeping universal reading rather than the speaker's likely limited experience.

• Counterexample: A single specific exception cited to refute a universal claim (e.g., pointing to one non-sponsored pro athlete to defeat "All pro athletes get sponsorship deals").

Hard vs. Soft Generalisations (Definitions, Counterexamples, and Rhetorical Risks)

• Hard Generalisation: A universal claim meant to apply without exception (all, every, no, never). Refuted by a single counterexample.

• Soft Generalisation: A claim about what is typically or generally true (most, usually, on average). Isolated exceptions do not disprove it.

• The Trap: Quantifier-free claims ("People play less sport when they get older") are usually meant softly, but critics often attack them as if they were hard claims.

• Rhetorical Danger: Even factually true soft generalisations about demographic groups risk being misunderstood as hard claims, mistaken for innate/genetic traits, or causing offence by ignoring the systemic explanations behind the facts.

The "You Can Never Generalise" Paradox:

The claim that "all generalisations are false" is self-refuting—if true, it defeats itself because it is a generalisation. Furthermore, many generalisations are demonstrably true (e.g., "All cities in the UK have a bus service").

Rhetorical Force vs. Implicature (Definitions, Distinction, and Role of Context)

• Rhetorical Force: The emotional or suggestive tone conveyed by linguistic conventions (loaded words) surrounding a proposition without altering its factual content (e.g., "bunked off early" vs. "left early").

• Implicature: Meaning that is left unsaid, but which an informed listener reasonably infers based on the context of the utterance (e.g., answering "She hasn't been expelled" to imply poor academic performance).

• Core Difference: Rhetorical force lives in the emotive phrasing of the words themselves; implicature depends on what is left unstated in a specific context.

Necessary vs. Sufficient Conditions (Definitions and Example)

• Necessary Condition: A condition an entity must meet to qualify as X (without it, it cannot be X).

  • Example: Being a sheep is necessary to be a ewe.

• Sufficient Condition: A condition or set of conditions that is enough on its own to guarantee an entity is an X.

  • Example: Being a female sheep is sufficient to be a ewe.

• Relationship: A feature can be necessary without being sufficient (a ram is a sheep, but not a ewe), and sufficient without being necessary (being a ewe guarantees being a sheep, but not all sheep are ewes).

Testing Definitions in Critical Thinking (Role of Counterexamples)

• Goal: Definitions aim to state precisely the necessary and sufficient conditions for a category.

• Testing Method: We challenge proposed conditions using counterexamples:

  1. Too broad: Something meets the conditions but clearly does not belong (e.g., defining a square as "a 4-sided planar figure" allows diamonds/rhombuses).

  2. Too narrow: Something clearly belongs but fails the proposed rule.

• Outcome: When a counterexample is identified, we must either refine the definition to fix the criteria or adjust what we include in the category.

What is a statement implicature?

• The objective standard: An implicature is not just whatever secret meaning the speaker had in their head. A statement only carries an implicature if a listener who knows the context would reasonably take that meaning to be intended.

  • Unintended implicature: Because of this standard, you can accidentally create an implicature you didn't mean to make. For example, if someone asks, "Do you like my haircut?" and you answer, "Well, your shoes look great," the implicature is that you dislike the haircut—even if you genuinely just wanted to compliment their shoes.

Rhetorical Ploys (Core Definition, Key Categories, and Crucial Distinctions) (Dont have to know the exact differences)

• Core Definition: Verbal techniques that aim to influence belief, choice, or behavior through psychological, emotional, or linguistic manipulation rather than by offering rational reasons (arguments).

• Four Primary Categories:

  1. Emotional Appeals: Novelty, popularity, fear/scare tactics, pity/guilt, cuteness/sexiness, ridicule.

  2. Repetitive Demands: Direct attack (bare commands) and hard sell (persistent repetition).

  3. Linguistic Deception: Equivocation (shifting word meanings/averages), trading on implicature (inviting false inferences with plausible deniability), many questions (presupposing guilt inside a question).

  4. Deflection: Smokescreens, whataboutism, and tone policing.

• Two Crucial Distinctions:

  • Appeal to Fear vs. Genuine Warning: Scare tactics induce unwarranted alarm to force compliance; genuine warnings are evidence-based, informative alerts from knowledgeable agents.

  • Smokescreen vs. Red Herring: A smokescreen is a purely rhetorical distraction; a red herring is a bad argument that provides irrelevant premises.

Referesher what is a primary/secondary connotation?

Secondary connotation refers to the typical associations, non-essential traits, or stereotypical features connected with a word that are not part of its strict definition (primary connotation).

• Primary Connotation (The Rule/Definition): The necessary and sufficient conditions. Lacking this is a logical contradiction.

  • Ram → "male sheep"

  • Bachelor → "unmarried adult male"

• Secondary Connotation (The Associations/Stereotypes): Common characteristics people expect or associate with the word, but which are not strictly required. Lacking these is not a contradiction.

  • Ram → woolly, has horns, butts heads, eats grass. (A bald, hornless male sheep is still a ram.)

  • Bachelor → messy apartment, drinks beer, dates around. (A neat, sober, non-dating unmarried man is still a bachelor.)

The Key Test

Ask yourself: "Can something lack this trait and still strictly be that thing?"

• If no (it is logically impossible) → Primary connotation.

• If yes (it is just a common association or stereotype) → Secondary connotation.

Buzzwords, Jargon, and Acronyms (Definitions, Social Functions, and Critical Remedy)

• Buzzwords: Trendy words loaded with rich secondary connotations (e.g., "change", "elites") used vaguely to trigger emotional reactions rather than convey specific policy or substance.

  • Remedy: Rephrase claims in neutral language before analyzing them.

• Jargon: Specialized vocabulary that obscures meaning for outsiders and creates an exclusive "in-crowd."

  • Nuance: Legitimate among domain experts; problematic when used on laypeople to confuse or intimidate.

• Acronyms: Initialisms (e.g., MVP, KPI) that mimic jargon by shutting out anyone who cannot decode them.

Spin vs. Gas-lighting (Definitions, Mechanisms, and Public Impact)

• Spin: The deliberate use of rhetorical framing and euphemistic jargon to cast controversial actions in a positive, technically respectable light (e.g., framing corporate bailouts as "injecting liquidity").

• Gas-lighting: Manipulative rhetoric that undermines a target's confidence in their own memory, perception, or sanity through persistent denial, contradiction, and discrediting.

• Public Realm Use: Politicians or institutions gas-light when they flatly deny past statements or obvious facts despite clear evidence, forcing observers to doubt their own senses.

What is the difference between normative and rational models?

• Rational models define decisions purely by internal consistency (e.g., transitivity across choices) regardless of what choices are made.

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• Normative models are prescriptive; they dictate which choice is optimal by measuring it against an external standard or criterion (such as maximizing financial reward).

What is the difference between expected value and expected utility, and how are they similar?

Similarity: Both models evaluate choices by multiplying an outcome's worth by its probability to identify the optimal choice.

• Difference:

Expected value uses objective, absolute monetary worth.

• Expected utility uses subjective, personal worth (utility) attached to an outcome based on an individual's immediate needs or circumstances (e.g., a guaranteed small amount of money has higher utility to someone who is starving).

How do we know that people not make rational decisions?

Description Invariance Violations: Changing how a problem is framed (e.g., gains vs. losses, or categorizing money into "psychic budgets") flips preferences, even when the mathematical outcomes are identical.

Procedure Invariance Violations: People make different choices depending on how preferences are elicited (e.g., direct choice vs. setting a selling price).

• Sunk Cost Fallacy: People allow past, unrecoverable investments of time or money to dictate current decisions.

Can utility theory explain why people gamble in casinos?

Yes. While casino games have a negative expected monetary value (the house always has an edge), people may perceive the subjective utility of winning a life-changing sum (or the entertainment value derived from playing) as worth the relatively small, low-utility loss of the wager

What are the three heuristics that people use to estimate probabilities, and how do they work!

Representativeness: Judging the likelihood of an event or category membership by how closely it matches our prototype, stereotype, or typical features of a process (e.g., assuming a sequence of coin tosses that looks irregular is more likely than a patterned one).

Availability: Judging an event's likelihood by how easily and quickly concrete instances or examples come to mind (e.g., assuming words beginning with r are more numerous because they are easier to recall).

• Anchoring and Adjustment: Beginning an estimate with an initial starting value (the "anchor," suggested by the problem or a quick partial calculation) and then adjusting upward or downward. In practice, these adjustments are almost always insufficient.

What type of information do people typically ignore when making choices!

Sample Size: People fail to recognize that smaller sample groups are much more likely to deviate from true averages than larger groups.

Base Rates: People overlook the general prevalence or baseline frequency of an event in a population, especially when provided with specific descriptive or anecdotal information (such as eyewitness reports or diagnostic test accuracy).

What is the core of Gigerenzer's argument about why the problems posed to participants in typical choice experiments are unfair and make people look more foolish than they really are?

Evolutionary adaptation to natural frequencies: Gigerenzer argues that the human mind evolved in preliterate environments to track natural frequencies (e.g., "8 out of 100 people"), not abstract probabilities or percentages (e.g., "0.8%").

• Because standard laboratory tasks present information in a format (probabilities) that does not match our cognitive architecture, participants appear irrational. When the exact same problems are framed using natural frequencies, participants routinely perform at much higher levels and account for base rates accurately.

What is the extension of a term?

The thing the term refers to.
Ball: Extension could be
→ Actual, ball for playing
→ Ball formal dance

Lecture Definition of Primary / Secondary Connotation

Tsunami
Primary: Something falls within the extension of a term if, and only if thee conditions are met. (E.g. large ocean wave)

Secondary:
Characteristics that the things with the extension usually exhibit, but not necessarily:
E.g. cause of many deaths and major economic damage

Metaphor works on the basis of the secondary connotation:
E.g A tsunami of Islamisation!

What is a logical benchmark?

What is a probabilistic benchmark?

What is a Rational Decision benchmark?

p→q logic Irrationality