Logic and Critical Thinking: Unit 2 Review

What are the three categorical operations?

Conversion, obversion, and contraposition.

In categorical logic, what are complements?

The logical opposite of a term, such as 'non-S' for 'S'.

What does 'logical equivalence' mean in categorical logic?

When two statements necessarily have the same truth value under all circumstances.

What are 'immediate inferences'?

Inferences drawn directly from a single categorical proposition without requiring another premise.

To which two standard forms can all valid categorical syllogisms be reduced?

AAA-1 (First Barbara) and AII-1 (First Darii).

Name the two immediate inference fallacies related to operations.

Illicit conversion and illicit contraposition.

What are 'contradictions' in logic?

Two statements that cannot both be true and cannot both be false at the same time.

What is the Modern (Boolean) Square of Opposition?

It illustrates the logical relationships (primarily contradictions) between A, E, I, and O propositions, based on Boolean interpretation, assuming no existential import for universal statements.

How can contradiction be used to challenge an argument's soundness?

By demonstrating that the conclusion contradicts known facts or widely accepted premises, thereby challenging the truth of its premises even if the argument is valid.

What is the purpose of reducing the number of terms in arguments?

To simplify complex arguments so they can be analyzed using standard categorical logic methods.

Define 'Enthymemes' and list their orders.

Syllogisms with one unstated (implied) premise or conclusion. They can be 1st, 2nd, or 3rd order depending on which part is missing.

What is a 'Sorites' and how is it typically tested for validity?

A chain of categorical syllogisms where the conclusion of one becomes a premise for the next. It is tested by putting it in standard form and using Three-Circle Venn diagrams for each constituent syllogism.

What is the importance of translating ordinary language into A, E, I, O categorical logic language?

To standardize statements for precise logical analysis and to fit them into the structure of categorical propositions.

In the context of categorical syllogisms, why is careful translation of statements crucial?

To correctly identify the subject and predicate terms, quantifiers, and quality (affirmative/negative), especially when dealing with ambiguous or implicitly stated information, to ensure accurate syllogism formation.

Differentiate between 'validity' and 'soundness' in arguments.

Valdity refers to the logical structure of an argument: if the premises are true, the conclusion must be true. Soundness means an argument is both valid and all its premises are actually true.

How are Syllogistic Rules used to test for argument validity?

By checking if the argument violates any of the five specific rules that govern valid categorical syllogisms; a violation indicates a fallacy and invalidity.

How are Three-Circle Venn Diagrams used to test validity in categorical syllogisms?

By shading or placing 'X's to represent the premises and then observing if the conclusion is necessarily depicted in the diagram, often by comparing to a separate two-circle conclusion diagram.

What are the two components of our perspective on reality, according to the "Blind Men and the Elephant" story?

Our perspective is both empirical (senses) and intellectual (principles).

According to the discussion of Siccar Point, why can two people perceive the same thing empirically but understand it differently?

They are using different principles.

What is the value of disagreeing with others, as discussed?

A disagreement is an opportunity to discover one’s own principles and to consider revising a principle for greater reliability.

What are the two persistent questions that each individual aims to answer?

"What should I believe?" and "What should I do?"

Define philosophy.

Philosophy is the rational search for true answers to questions fundamental to human existence.

What are the three main branches of philosophy, and what does each study?

Metaphysics: The study of reality. Epistemology: The study of knowledge. Axiology: The study of value.

Provide an example of a metaphysical question.

How old is Earth?

Provide an example of an epistemological question.

By what means can we determine the age of Earth?

Provide an example of an axiological question.

Of what importance is knowing the age of Earth?

What are the five types of sentences?

Questions, commands, interjections, nonsense, and statements.

Which type of sentence can be either true or false?

Statements.

List some synonyms for "statement."

Belief, opinion, claim, view, proposition.

In the "Logic Tree," what is the primary distinction when analyzing a passage of language use?

Whether it is an argument (something is being proven) or a non-argument.

Differentiate between a deductive and an inductive argument.

Deductive: Attempts to guarantee the conclusion. Inductive: Attempts to make the conclusion probable.

When assessing if premises do their job in a deductive argument, what terms are used?

Valid (if they succeed) or Invalid (if they fail).

When assessing if premises do their job in an inductive argument, what terms are used?

Strong (if they succeed) or Weak (if they fail).

When all premises of a valid deductive argument are true, what is the argument considered?

Sound.

When all premises of a strong inductive argument are true, what is the argument considered?

Cogent.

Define "Topic" in discursive structure.

A category of things.

Define "Issue" in discursive structure.

A question about a topic, for which Yes and No are the only options.

Define "Position" in discursive structure.

Yes or No on an issue.

Define "Reasoning (argument)" in discursive structure.

A set of statements in which a conclusion is allegedly drawn from premises.

What is "Criticism (test)" in discursive structure?

A testing of the reasoning for validity or soundness.

What is a "Reply" in discursive structure?

A defense of or revision to one’s reasoning.

Who developed categorical logic and when?

Aristotle, in the 4th century BCE.

What is the fundamental unit of categorical logic?

The category, which is the name of a set of things.

How many categories does a categorical statement interrelate?

Two categories.

List the four types of categorical statements, their standard form, and designation.

A: All S are P (universal affirmative). E: No S are P (universal negative). I: Some S are P (particular affirmative). O: Some S are not P (particular negative).

How is 'All S are P' represented in a Venn diagram?

Shade the S crescent (the part of S that is not P).

How is 'No S are P' represented in a Venn diagram?

Shade the football shape (the intersection of S and P).

How is 'Some S are P' represented in a Venn diagram?

Place an 'X' in the football shape (the intersection of S and P).

How is 'Some S are not P' represented in a Venn diagram?

Place an 'X' in the S crescent (the part of S that is not P).

In the categorical statement 'All S are P', which term(s) are distributed?

The subject term (S).

In the categorical statement 'No S are P', which term(s) are distributed?

Both the subject term (S) and the predicate term (P).

In the categorical statement 'Some S are P', which term(s) are distributed?

Neither the subject term (S) nor the predicate term (P).

In the categorical statement 'Some S are not P', which term(s) are distributed?

The predicate term (P).

In categorical syllogisms, what is "Mood"?

The letter names of the premises and conclusion (e.g., AAA, EIO).

In categorical syllogisms, what does "Figure" refer to?

The arrangement of the middle terms.

How is the "Form name" of a categorical syllogism determined?

It is the combination of the mood and the figure (e.g., AAA-1).

What is the first step when analyzing an argument written in paragraph form?

Identify the conclusion, often with the help of indicator words.

When using a three-circle Venn diagram to test a categorical syllogism, how should the three circles be labeled?

Middle term in the middle, minor term to the left, and major term to the right.

When diagramming a syllogism with a three-circle Venn diagram, which parts of the argument are directly represented on the diagram?

Only the premises.

After diagramming the premises on a three-circle Venn diagram, what is the next step to test for validity?

Create a separate two-circle Venn diagram for the conclusion, labeled properly.

How do you determine if a categorical syllogism is valid using the Venn diagram method?

By asking if the diagram for the conclusion is entirely contained within the diagram for the premises. If 'Yes,' it's valid; if 'No,' it's invalid.

If a categorical syllogism is found to be invalid using the Venn diagram method, what additional step should be taken?

Name the fallacy committed (if multiple, only one needs to be named).