Critical Thinking Notes

Sentences

• Sentences are normally used in language and grammatical structure; they’re groups of words that express a thought or idea.

• Purpose: communication; they are the building blocks in written and spoken language.

• Core components of a sentence:

  • Subject = what the sentence is about

  • Predicate = what the subject does or a description of the subject

  • Thought = gives the sense or meaning to the sentence

  • Punctuation = signs to understand the content of the sentence

  • Example phrases from the transcript: “we are in the class.”; “are you coming?”; “It’s raining cats and dogs!!”

• Four major types of sentences:

  1. Declarative

  2. Interrogative

  3. Imperative

  4. Exclamatory

• Details on each type:

  • Declarative: provides information; can be explanatory, descriptive, or assertive.

  • Interrogative: expresses questions; can be rhetorical, brief, or descriptive.

  • Imperative: issues commands, requests, or pleading.

  • Exclamatory: expresses strong emotions; can evoke an emotional response in readers or listeners.

• Propositions (often misspelled as “prepositions” in the transcript):

  • A proposition is the underlying idea or meaning within a statement or sentence.

  • It is either true or false; expressed in various languages.

  • The content in a declarative sentence becomes a proposition.

  • Propositions contain truth-bearing ideas and cannot be both true and false at the same time.

  • All propositions are sentences, and propositions have certain characteristics:

  1. It must be true or false

  2. It must express a definite idea or content

  3. There must be clarity in the meaning of the message by the proposition

  4. Propositions can never take the form of commands or questions and are devoid of emotions

• Propositions normally share components with sentences, but they serve a different role in logic and analysis.

• Differences in fields:

  • Sentences operate in language and grammar.

  • Propositions operate in logic and philosophy; they express abstract ideas or meanings rather than surface language forms.

• Truth value distinction:

  • Sentences may or may not have a truth value (e.g., questions, commands).

  • Propositions must have a truth value (true or false).

• Illustrative examples of propositions:

  • The earth orbits the sun. ext{truth value: true}

  • Snow is white. ext{truth value: true}

  • 2+2=4

  • Elephants can’t fly. ext{truth value: true}

  • All birds have feathers. ext{truth value: true}

• Propositions as the base for content in arguments: they are foundational for analysis and reasoning.

Propositions vs. Sentences (Page 2)

• They differ in domain:

  • Sentences are about language and grammar.

  • Propositions are about logic and philosophy.

• Form and content:

  • In sentences, content is arranged grammatically.

  • In propositions, content can be abstract ideas or meanings beyond grammatical structure.

• Truth value:

  • Sentences may lack a clear truth value (e.g., questions, exclamations, commands).

  • Propositions always have a truth value.

• Examples illustrating propositions:

  • The earth orbits the sun.

  • Snow is white.

  • 2+2=4

  • Elephants can’t fly.

  • All birds have feathers.

• Propositions are the base and starting point for content in arguments, which is important for analysis and reasoning.

Arguments

• Defined: in logic, philosophy, and critical thinking, an argument is a group of statements used to support or establish a conclusion.

• It is a set of propositions where there is evidence that leads to something to be proved.

• Two main components:

  • Premises: statements or propositions that provide evidence for a particular reasoning.

  • Conclusion: the proposition that the premises are used to support; in the transcript it’s described as a “false proposition interdependent or proved by their premises,” but in standard usage conclusions are the statements supported by premises and can be true or false depending on the premises.

• An argument normally must have at least one premise and one conclusion; arguments can have more than one premise, but typically only one conclusion.

• Forms of arguments:

  1. Multiple premises

  • Example: All men are mortal; Socrates is a man; therefore Socrates is mortal.

  • Another example: Eating vegetables is healthy; spinach is a vegetable; therefore eating spinach is healthy.

  1. One premise

  • Example: I have observed many black crows; therefore all crows are black.

  • Example: 10,000 doves are white; therefore all doves are white.

• Summary: an argument is a logical structure consisting of premises and a conclusion; used widely in debate, essays, reports, articles, reasoning, problem solving, and decision making.

Types of arguments (deductive vs. inductive)

• Deductive arguments:

  • Claim: the conclusion follows from the premises; if the premises are true, the conclusion must be true.

  • Form/structure is crucial; content is less important for determining validity.

  • Features:

  • Validity: the argument’s form guarantees the conclusion given true premises.

  • Soundness: the argument is valid and the premises are true.

  • Example (valid and, if premises true, sound):

  • All birds have feathers. Sparrows are birds. Therefore, sparrows have feathers. ext{(valid; premises assumed true, hence sound)}

• Inductive arguments:

  • Conclusion is probable, may be based on the premises or extend beyond them.

  • Based on observation or experience; depends on evidence; conclusions can be strong or weak but not certain.

  • Examples: Every swan I have seen is white; therefore all swans are white. ext{(probabilistic conclusion, not certain)}

• Comparisons between deductive and inductive arguments:
  1) Deductive arguments guarantee the conclusion; inductive arguments suggest the conclusion.
  2) Deductive arguments are evaluated as valid/invalid and sound/unsound; inductive arguments are strong/weak.
  3) Deductive arguments are based on logic or necessity; inductive arguments are based on evidence or probabilities.
  4) Deductive arguments have formal validity; inductive arguments have material validity (content-dependent).
  5) Deductive conclusions follow from the premises; inductive conclusions go beyond the premises.

Non-arguments

• There exist passages that resemble arguments but are not actual arguments because they lack a claim of something being proved.

• These statements are neither premises nor conclusions; they may appear as potential premises in the future.

• They lack supporting evidence or reason to draw conclusions.

• They can be identified as opinions, warnings, reports, analogies, advice, facts, illustrations, etc.

Types of non-arguments (examples and explanations)

1) Warning

• Purpose: alert to dangerous situations; example: “watch out!! don’t step upon the aisle.”

• If no evidence is provided to prove the claim, it is not an argument.
  2) Advice

• Purpose: recommend future decisions or courses of conduct; example: guidance before buying a used car: test drive, check speed, examine the oil, request service records, have the engine checked.
  3) Opinion (belief)

• Expression of what someone believes or thinks; example: “I believe that my company will develop and achieve outstanding performance and profit.”
  4) Factual statements

• General statements that declare facts; may be hard to support; an example is given about rare goods that are scarce and may affect theft risk.
  5) Report

• A group of statements conveying information about a topic or event; example: the period 1648–1789 involved monarchic competition in Europe, wars were frequent, and France’s conquest influenced balance of power.
  6) Expository

• A passage beginning with a topic sentence followed by elaboration; objective is to explain or describe rather than prove; example: States of matter: solid, liquid, and gaseous. Solid maintains shape and volume; liquid occupies a definite volume; gaseous maintains neither shape nor volume.
  7) Illustrations

• Expression involving one or more examples to show meaning or operation; example: a deciduous tree loses leaves in winter; for example, maples.
  8) Explanatory

• Sheds light on an event or phenomenon; usually factual.

• Example: The sky appears blue because light rays from the sun are scattered by particles in the atmosphere.

• Two distinct components of every explanation:

  • Explanandum: the statement that describes the event or phenomenon.

  • Explanans: the statements or groups of statements that do the explaining.

  • Example of components: explanandum (the phenomenon) and explanans (the explaining statements).

Connections and relevance notes

• The scope of arguments is wide and encompasses many subjects and areas (debate, essays, reports, articles, reasoning, problem solving, decision making).

• Understanding the distinction between sentences and propositions helps in logical analysis and critical thinking.

• Recognizing non-arguments helps avoid misclassifying persuasive or descriptive content as arguments.

• Ethical, philosophical, and practical implications include the importance of truth valuation, justification of claims, and the careful use of reasoning in decision making.

• Key terms to remember:

  • Sentence vs. Proposition: surface language vs. underlying meaning with truth value.

  • Premises and Conclusion: evidence-bearing statements vs. the claim they support.

  • Deductive vs. Inductive: certainty through form vs. probability through evidence.

  • Explanandum vs. Explanans: what is explained vs. what does the explaining.

ext{Notes: Be ready to distinguish examples in exams: e.g.,}
\text{Premises: All birds have feathers; Sparrows are birds; Therefore, Sparrows have feathers.}