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Critical Thinking > Module 4A > Flashcards

Module 4A Flashcards

1
Q

What is the general form of conditionals, and how are they typically expressed?

A

Conditionals are statements of the form ‘If (antecedent), then (consequent)’.

They express a logical relationship between the antecedent and consequent without directly asserting either.

In symbolic representation, ‘If P, then Q’ is often expressed as ‘P ⊃ Q’.

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2
Q

Do conditionals themselves contain arguments?

A

No, conditionals do not contain arguments.

THEY STATE A LOGICAL RELATIONSHIP BETWEEN THE ANTECEDENTS AND CONSEQUENT WITHOUT ASSERTING EITHER.

The antecedent and consequent are components of the conditional.

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3
Q

Influence of Background Assumptions

A

Conditionals can be challenging due to our tendency to assume they imply background information.

Example: “If a ball is white, it is made in Singapore,” implies the background assumption that other colors are not made in Singapore.

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4
Q

Implications of background Assumptions..

A

In everyday conversations, background assumptions are often TAKEN FOR GRANTED

Example: It would be a joke to say all cricket balls are made in Singapore because a white ball is.

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5
Q

Background assumption CHALLENGES

A

Background assumptions CANNOT ALWAYS BE MADE; e.g., if you only know white balls are made in Singapore.

In certain circumstances, such as EVIDENCE ASSESSMENT, BACKGROUND ASSUMPTIONS MUST BE SUSPENDED.

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6
Q

Not Explicitly stated Background information…

A
  1. Background assumptions are not explicitly part of what is said.

Example: Saying white balls are made in Singapore doesn’t explicitly provide information about red balls.

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7
Q

Logical approach of Background assumptions..

A

Logicians analyze CONDITIONALS IN ISOLATION from background assumptions.

They focus on the MINIMUM EXPLICITLY STATED INFORMATION.

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8
Q

OVERVIEW OF BACKGROUND INFORMATION:

A

Background assumptions are not always applicable, especially in situations requiring careful evidence assessment.

Logicians play safe by considering conditionals independently from the typical background that contributes to their point

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9
Q

Transposed (Contraposed) Conditional

A

Form: “If P, then Q” is equivalent to “If not-Q, then not-P” (contrapositive form).

Also expressed as “P only if Q” or “Not-P unless Q.”

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10
Q

What is Tense Complexity:

A
  1. Equivalence holds in the present tense; complexities arise with other tenses.
  2. Logic books often oversimplify, and a detailed treatment becomes complex and controversial with different tenses.
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11
Q

Validity of Transformation:

A
  1. A move from “If P, then Q” to the contrapositive form is deductively valid.
  2. Antecedent and consequent are swapped, and both are negated (if not already negative).
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12
Q

Converse Conditional:

A

The move from “If P, then Q” to the converse form “If Q, then P” is invalid.

Converse: Swap antecedent and consequent without negation.

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13
Q

Contraposed (Contrapositive) Process:

A

To get the contraposed conditional, swap antecedent and consequent, and negate both.

If either is already negative, add a further negation.

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14
Q

the contraposed transformation is deductively valid……

A

The contraposed transformation is deductively valid, ……while the converse transformation is not.

Converse: Only swap antecedent and consequent without negation

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15
Q

What is Double Negation?

A

Rule stating that a statement ‘S’ is logically equivalent to ‘not-not-S’.

Applies to negate statements (‘not-S’ is equivalent to ‘not-not-not-S’).

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16
Q

Repetition of Transpositions:

A

Transpositions, such as moving from ‘If P, then Q’ to its contrapositive, can be repeated without loss of validity.

Example: ‘If not-Q, then not-P’ → ‘If not-not-P, then not-not-Q’ → ‘If not-not-not-Q, then not-not-not-P’, and so on ad infinitu

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17
Q

Infinite Development Collapse:

A

The infinite development collapses into two cases: the original conditional and its contrapositive.

Achieved through the application of the Double Negation rule.

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18
Q

Rule of Double Negation:

A

States that even numbers of negations cancel out to zero; odd numbers reduce to one.

Example: ‘not-not-not-S’ reduces to ‘not-S’, and ‘not-not-S’ reduces to ‘S’.

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19
Q

Application of Rule: double negation

A

Double Negation allows simplification of statements through negation.

Repeated transpositions collapse into original and contrapositive forms via this rule.

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20
Q

Equivalence Principle:

A

Double Negation is a principle of logical equivalence, aiding in the simplification and understanding of complex statements.

Helps establish the relationship between a statement and its double negation.

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21
Q

Expressible Statements:

A

Certain statements can be expressed as conditionals, including those involving sufficient and necessary conditions.

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22
Q

Sufficient and Necessary Conditions:

A

Example: ‘Ionisation is sufficient for conductivity’ can be expressed as ‘If something is ionised, it conducts electricity.’

A conditional asserts that the antecedent’s truth is sufficient for the consequent’s truth, and vice versa.

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23
Q

Biconditionals:

A

Joint necessity and sufficiency are expressed with ‘if and only if’ (iff, just if, just in case).

Biconditionals are often underpinned by definitions of one side in terms of the other.

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24
Q

Universal Statements:

A

Universal statements (e.g., ‘All X’s are Y’s’) can be expressed as conditionals, such as ‘If something is an X, then it is a Y.’

Quantifiers (e.g., ‘all’) are used in these statements.

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25
Q

Quantifiers in English:

A

Various quantifiers in English include ‘some,’ ‘a few,’ ‘many,’ ‘most,’ ‘at least one,’ ‘only.’

Statements with universal quantifiers (any, every, all) are expressible as conditionals.

26
Q

Examples of Expressible Forms:

A

‘Whenever’ sentences (e.g., ‘Whenever it rains, it pours’) can be expressed as conditionals (e.g., ‘If it rains, it pours’).

‘Only’ sentences (e.g., ‘Only artists are sensitive’) can be expressed as conditionals (e.g., ‘If a person is sensitive, then that person is an artist’ or ‘A person can be sensitive only if he/she is an artist’).

27
Q

Advantages of Conditional Form:

A

Rewriting sentences as conditionals can facilitate the evaluation of arguments, as they often exemplify standard forms.

28
Q

Deductive Valid Moves:

A

Three deductively valid argument forms that depend on conditionals are:

  1. Modus Ponens
  2. Modus Tollens
  3. Hypothetical Syllogism
29
Q

Modus Ponens:

A

Form: If P, then C; P; therefore, C

Deductive valid move in the argument.

30
Q

Modus Tollens:

A

Form: If P, then C; not-C; therefore, not-P

Deductive valid move in the argument.

31
Q

Hypothetical Syllogism:

A

Form: If A, then B; if B, then C; therefore, if A, then C

Deductively valid move in argument.

32
Q

Note on Deductive Validity:

A

Despite being deductively valid, using these forms with true premises does not guarantee a cogent argument.

Fallacies like begging the question may still be committed.

33
Q

Importance of Premise Quality:

A

The cogency of an argument depends not only on the deductive validity of the form but also on the truth and quality of the premises.

34
Q

Potential Pitfalls:

A

While these forms are valid, it’s crucial to ensure that the premises are not fallacious or circular, as this could weaken the overall argument.

35
Q

Deductive Validity and Cogency:

A

Deductively valid argument forms, even with true premises, don’t guarantee cogent arguments as fallacies like begging the question may still be present.

36
Q

Conditionalisation:

A

Move: From a deductively valid argument from premises P to conclusion C, infer a necessarily true conditional, ‘If P, then C’.

Importance will become apparent later.

37
Q

Invalid Forms Corresponding to Valid Ones:

Denying the Antecedent:

A

Denying the Antecedent:

Form: If A, then C; not-A; therefore, not-C

Superficially similar to modus tollens but deductively invalid.

38
Q

Invalid Forms Corresponding to Valid Ones (Cont.):

Affirming the Consequent:

A

Affirming the Consequent:

Form: If A, then C; C; therefore, A

Superficially similar to modus ponens but deductively invalid.

39
Q

Importance of Context:

A

Deductively invalid forms can, in certain circumstances, give fairly strong support to their conclusions.

It’s a mistake to label these forms as ‘fallacious’ without considering context and specific situations.

40
Q

Conditionalisation…importance of context…

A

Example: Joe (a surgeon) being a danger to patients.

Argument: If Joe is a danger to patients, their survival rate will be lower. Joe’s patients’ survival rate is lower. Hence he is a danger to his patients.

While superficially resembling denying the antecedent, the argument provides some support to the conclusion in certain circumstances.

41
Q

Contextual Background Truths:

A

Given certain background truths that can be reasonably taken for granted in context.

42
Q

Example Context:

A

Example: Background truths about Joe, such as receiving large representative samples of patients and not exceeding the usual proportion of high-risk surgeries.

43
Q

Support for the Conclusion:

A

Conclusion not proved by the truth of premises, but with contextual background truths, it gains some support.

44
Q

Confirming Evidence:

A

The fact that the consequent (conclusion), when separately asserted, turns out to be true, provides confirming evidence.

45
Q

Evidence Strength:

A

The supporting evidence is not conclusive but adds strength to the argument.

46
Q

Importance of Separately Asserted Components:

A

Separately asserting the truth of the consequent gives supporting indications about the truth of the antecedent, considering the context and background information.

47
Q

Consideration of Background Information:

A

Contextual background information plays a crucial role in evaluating arguments and understanding the strength of the evidence provided.

48
Q

Nuanced Evaluation:

A

Arguments may not be black or white; the evaluation often involves nuanced considerations, including contextual factors

49
Q

“A normal conditional is a statement of the form ‘If P, then Q’ (where the schematic letters are place-holders for statements).”

A

true

50
Q

“In a statement of the form ‘If P, then Q’, the Q part is known as the ‘consequent’.”

A

true

51
Q

“In a statement of the form ‘P, if Q’, the P part is known as the ‘antecedent’.”

A

false
To say “P, if Q” is the same as saying “If Q, then P.”

In this conditional P is the consequent and Q is the antecedent.

52
Q

“Asserting a normal conditional of the form ‘If P, then Q’, is logically equivalent to asserting that P is true only if Q is true.”

A

true

53
Q

‘These statements are logically equivalent:
(a) “If an argument’s conclusion is false, then that argument is unsound”;
(b) “If an argument is sound, then its conclusion is not false”.’

A

true

54
Q

‘These statements are logically equivalent:
(a) “Napoleon was a great general”;
(b) “It is true that Napoleon was a great general”;
(c) “It is not true that Napoleon was not a great general”;
(d) “It is not the case that it is not true that Napoleon was a great general”.

A

true

55
Q

‘These statements are logically equivalent: (a) “Napoleon was not a great general”; (b) “It is not the case that it is not true that Napoleon was not a great general.’

A

true

56
Q

“For the purpose of assessing argument, we can treat the following statements as equivalent:
(a) ‘Whenever a cow eats grass, it produces methane’;
(b) ‘All cows which eat grass produce methane’; (c) ‘If a cow eats grass, it produces methane’; (d) ‘If something is both a cow and eats grass, then that thing produces methane’;
(e) ‘For a cow to produce methane, it is sufficient that it eat grass’;
(f) ‘Cows don’t eat grass without producing methane’
(g) ‘If something is grass, it meets the following condition: were a cow to eat it, methane would be produced’.”

A

true

57
Q

“For the purpose of assessing argument, we can treat the following statements as equivalent:
(a) ‘Only the French are chic’;
(b) ‘If someone is chic, they’re French;
(c) ‘You can be French only if you’re chic’.”

A

false

58
Q

“The expressions ‘modus tollens’ and ‘denying the consequent’ are just different names for the same kind of reasoning.”

A

true

59
Q

“The statement-form ‘If not-P then not-Q’ is the __________ form of ‘If Q then P’.”

A

TRANSPOSED

If you said contraposed, don’t despair. Govier uses the term ‘transposed’ for the treatment of conditionals in propositional logic and reserves the term ‘contraposed’ for use in categorical logic. And in this unit, we follow her.

But, as it happens, the term ‘contraposed’ is widely used in reference to transposed conditionals in propositional logic. Wikipedia, for instance, agrees.

60
Q

“This sentence expresses an argument: ‘If spiders are insects, then they have six legs, so if they don’t have six legs then they’re not insects’.”

A

TRUE

61
Q

Is the following argument form valid or invalid? “If P then Q; if not-Q then not-R; so, if R then not-P.”

A

INVALID

62
Q

Is the following reasoning valid or invalid? — “If this computer was assembled in Taiwan then it’s an Acer, so if it was assembled somewhere else then it’s another brand.”

A

INVALID

Critical Thinking (18 decks)

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