PHI1090

Question 1

Deductive Argumentation

Answer 1

Definition: Deductive argumentation is a type of reasoning where the conclusion is guaranteed to follow from the premises; if the premises are true, the conclusion must also be true. A deductive argument is valid if the conclusion logically follows from the premises, and it is sound if it is both valid and the premises are actually true.

Example:
Premise 1: All humans are mortal.
Premise 2: Socrates is a human.
Conclusion: Socrates is mortal.

Premise: If it rains, the ground will be wet.
Premise: It is raining.
Conclusion: Therefore, the ground is wet.

Question 2

Inductive Argumentation

Answer 2

Definition: A reasoning process that moves from specific observations to form a general conclusion. It predicts patterns or trends based on collected data but does not guarantee the conclusion. Unlike deductive reasoning, the conclusion in inductive arguments is not guaranteed to be true, but it is likely or probable based on the evidence.

Example:
Premise: The sun has risen every day so far.
Conclusion: The sun will rise tomorrow.

Observation: Water boils at 100°C at sea level.
Conclusion: All water boils at 100°C at sea level (until tested at higher altitudes).

The conclusion is most likely to be true based on the evidence.
“Induction Introduces Ideas” — Induction starts with examples and introduces broader conclusions.

Question 3

Abductive Argumentation

Answer 3

Definition: Abductive argumentation is a type of reasoning that starts with an observation or set of facts and seeks the most likely explanation for them. Unlike deductive reasoning, the conclusion in abductive reasoning is not guaranteed to be true but is instead the best possible theory based on the available evidence.

Example:
Observation: My lawn is wet.
Conclusion: It probably rained last night.
Strengths: Useful for forming hypotheses and explanations.
Weaknesses: The explanation could be wrong (e.g., the lawn could have been watered).

guessing the best explanation: You observe something and reason backward to the most likely cause.

Question 4

Tautology

Answer 4

Definition: A statement that is always true regardless of circumstances. A tautology is a logical statement or formula that is always true, regardless of the truth values of its components. It occurs when a statement is structured in such a way that it cannot be false, making it logically valid in all possible situations.

Example: “It will either rain tomorrow or it will not rain tomorrow.”
Explanation: This is true because it covers all possibilities.
“All bachelors are unmarried men.”

Tautology is “True on All Terms.”

Question 5

Contradiction

Answer 5

Definition: A contradiction is a logical statement or set of statements that cannot be true simultaneously because they directly oppose each other. In other words, a contradiction occurs when one statement denies or negates the other, making it impossible for both to be true at the same time.

Example: “It is raining and not raining at the same time.”
Explanation: This cannot happen; it violates the law of non-contradiction.

Everyday Example:
Statement A: “I always tell the truth.”
Statement B: “I just lied to you.”
Simple Contradiction:
Statement A: “All cats are mammals.”
Statement B: “Not all cats are mammals.”

Question 6

Paradox

Answer 6

A paradox is a statement or idea that seems to make no sense because it contradicts itself Definition: A statement that seems self-contradictory or absurd but may reveal a deeper truth or remain unresolved.often highlight gaps or inconsistencies in our understanding of a concept.

Example: “This statement is false.”

Explanation: If the statement is true, then it is false, but if it is false, it must be true—a logical conflict.
puzzle.

Question 7

Set of Consistent Propositions:

Answer 7

A set of consistent propositions consists of statements that are logically compatible. They can all be true at the same time without contradiction.

There is no confusion or tension—they fit together smoothly within logical rules.

Example: “It is raining.” and “The ground is wet.” These statements logically align.

Question 8

The difference between a paradox and a set of consistent propositions

Answer 8

lies in their logical relationship and clarity:

Key Difference:
Paradox: Appears to break logical rules but might still hold meaning.

A paradox is a statement or situation that seems self-contradictory or illogical at first but often reveals a deeper truth or insight upon closer examination. Paradoxes challenge our assumptions and force us to think critically about logic, language, or reality.
Consistent Propositions: Follow logical rules without breaking them.
———-
A set of consistent propositions is a group of statements that can all be true at the same time without any logical contradictions.

Question 9

Subcontrary

Answer 9

Definition: Two propositions are subcontraries if they cannot both be false at the same time, but they can both be true.
__________
I I
Example: I< ——– >I

Proposition A: “Some sails are painted.”
Proposition B: “Some sails are not painted.”
Both can be true, but they cannot both be false.

Subcontrary = Some overlap: Both can be true, but not both false.

Question 10

Contradictory

Answer 10

Two propositions is one must be true and the other must be false they cannot be true at the same time.

Two propositions are contradictory if one must be true and the other must be false; they cannot both be true or false at the same time.

Example: |X|
Proposition A: “All sails are painted.”
Proposition B: “Some sails are not painted.”
If one is true, the other is false.

Contradictory = Complete clash: One true, one false.

Question 11

Subaltern

Answer 11

Definition: A relationship between two propositions where the truth of the universal (general) proposition guarantees the truth of the particular (specific) one, but not vice versa.
________
I I
Example: V _______V

Universal: “All sails are painted.”
Particular: “Some sails are painted.”
If the universal is true, the particular is true. But if the particular is true, the universal may or may not be true.

Subaltern = One supports the other: Universal implies particular.

Question 12

Contrary

Answer 12

Definition: Two propositions are contraries if they cannot both be true at the same time, but they can both be false.

                 I< ----- >I
                 I \_\_\_\_\_\_ I Example: Proposition A: "All sails are painted." Proposition B: "No sails are painted." Both cannot be true, but it’s possible that neither is true (e.g., some sails are painted, and some are not).

Contrary = Total disagreement: Both can’t be true but can both be false.

Question 13

Universal Affirmative

Answer 13

“All A are B.” S a P

Definition: A statement asserting that every member of set A belongs to set B.

Key Features:
Applies universally to all members of the subject category (A).
Does not allow exceptions.

Example:
“All dogs are mammals.”
Every dog is a mammal, with no exceptions.

Question 14

Universal Negative

Answer 14

“No A is B.” S e P

Definition: A statement asserting that no member of set A belongs to set B.

Key Features:
Applies universally to all members of the subject category (A).
States that A and B are entirely separate categories.

Example:
“No birds are reptiles.”
There is no overlap between birds and reptiles.

Question 15

Particular Affirmative

Answer 15

“Some A are B.” S i P

Definition: A statement asserting that at least one member of set A belongs to set B.

Key Features:
Does not claim that all members of A are in B, only that there is at least one overlap.

Example:
“Some cats are friendly.”
There are at least a few cats that are friendly, but not necessarily all.

Question 16

Particular Negative

Answer 16

“Some A are not B.” S o P

Definition: A statement asserting that at least one member of set A does not belong to set B.

Key Features:
Indicates there is at least one exception where a member of A is not part of B.

“Some fruits are not sweet.”
This statement asserts that at least one member of the category “fruits” does not belong to the category “sweet.”

Question 17

What is a Simple Converse?

Answer 17

The simple converse of a statement is formed by reversing the subject and predicate of the original statement while keeping the same logical form (e.g., keeping the quantifiers intact).

If the original statement is “All A are B,” the simple converse is “All B are A.”
Validity Depends on Logical Form:

Not all statements have valid simple converses.
For instance, some logical forms (like Universal Affirmative statements) may not allow for a valid simple converse.
Applies Mainly to Certain Types of Statements:

Statements like Universal Negatives (E) (“No A is B”) and Particular Affirmatives (I) (“Some A are B”) often have valid simple converses.
For Universal Affirmatives (A) (“All A are B”), the simple converse is not always valid.

Simple Converse = Simple Swap:
Just swap the subject and predicate without overthinking quantifiers or meaning.

Question 18

What is an Accidental Converse?

Answer 18

The accidental converse of a statement is formed by reversing the subject and predicate and changing the quantifier from universal to particular. This weakens the original statement while maintaining some logical connection.

Reverses Subject and Predicate:
Like the simple converse, the accidental converse swaps the roles of the subject and predicate.

Examples
Universal Affirmative (A): “All cats are animals.”
Accidental Converse: “Some animals are cats.”
Is it valid? Yes. If all cats are animals, then it must be true that at least some animals are cats.

1. Start with the original statement.
2. Swap the subject and predicate.
3. Change the quantifier from universal (all/no) to particular (some/some not).

Question 19

Slippery Slope

Answer 19

informal: Definition: Claiming that one action will inevitably lead to a series of negative events without sufficient evidence.

Example: “If we allow students to use calculators, soon they won’t learn basic math, and eventually, they won’t even know how to count.”

Idea: “If we let this happen, it will lead to something much worse.”

Easy to remember because it’s a visual image of sliding down a hill.

Question 20

False Cause

Answer 20

informal: Definition: occurs when someone assumes that one event caused another simply because they occur together (correlation) or in sequence (post hoc), without evidence of a causal link. (one thing causing the other).

Example: “It rained right after I washed my car. Washing my car must cause rain.”

Idea: Assuming one thing caused another just because they happened together.

Easy because it’s intuitive (“correlation ≠ causation”).

Question 21

Hasty Generalization

Answer 21

informal: Definition: Drawing a conclusion based on insufficient or unrepresentative evidence. It occurs when someone jumps to a conclusion too quickly, without considering all relevant information.

Example: “My neighbor is rude, so all neighbors must be rude.”

Idea: Drawing a conclusion from too little evidence.

Easy to spot and remember because it’s about “jumping to conclusions.”

Question 22

Appeal to Authority

Answer 22

informal : Definition: Using the opinion of an authority figure as evidence, even when they are not an expert on the topic.

Example: “A famous actor recommends this diet, so it must be effective.”

Idea: Believing something is true because an “expert” said it.

Simple to recall as “because they said so.”

Question 23

Appeal to Pity

Answer 23

informal : Definition: when someone tries to gain support for their argument by exploiting their audience’s sympathy or emotions instead of presenting logical reasoning or evidence. This is an informal fallacy because it distracts from the argument’s merit.

Student to teacher: “I deserve a better grade because I’ve been going through a really tough time lately, and failing this class will ruin my life.”

Job applicant: “You should hire me because I’m a single parent struggling to make ends meet.”

Think “pity party”—the focus shifts from logic to feelings.
Imagine someone saying, “Don’t argue with me; I’m sad, so I must be right!”

Question 24

Ad Hominem (Abusive)

Answer 24

informal: Definition: Attacking the person making an argument instead of the argument itself. it shifts the focus from the issue being discussed to irrelevant personal traits or circumstances of the individual. Example: “You can’t trust his opinion on climate change; he’s not even a scientist.”

Idea: Attacking the person instead of the argument.

Easy because people often argue this way in debates or online.

Question 25

Poisoning the Well

Answer 25

informal : Definition: Presenting negative information about someone to discredit their argument before they even speak. Example: “Don’t listen to her argument; she’s always been unreliable.”

Idea: Preemptively discrediting someone to bias others.

Easy because of the vivid metaphor (polluting the water).

Question 26

Affirming the Consequent

Answer 26

formal : Definition: Assuming that if the conclusion is true, the premise must also be true. The mistake lies in reversing the logical direction of the conditional statement. Form:
If A, then B.
B is true.
Therefore, A is true. (Invalid reasoning) Example:
If it rains, the ground is wet.
The ground is wet.
Therefore, it must have rained. (Not necessarily; sprinklers could have been used.)

Memory Trick:
“Just because the ground is wet doesn’t mean it rained!” Think of sprinklers or other possibilities.

Question 27

Denying the Antecedent

Answer 27

formal : Definition: It occurs when someone assumes that if the antecedent (“if” part) of a conditional statement is false, then the consequent (“then” part) must also be false. Form:
If A, then B.
Not A.
Therefore, not B. (Invalid reasoning)
Example:
If it rains, the ground is wet.
It did not rain.
Therefore, the ground is not wet. (Again, sprinklers could make the ground wet.)

Memory Trick:
“There are many ways to get wet!” Don’t assume one reason explains everything.

Question 28

False Dilemma (Bifurcation)

Answer 28

informal : Definition: Presenting only two options when more options exist. It forces a choice between extremes and ignores the possibility of middle ground or additional choices. Example:
“You’re either with us or against us!”
(In reality, one could be neutral or partially supportive.)

Memory Trick:
“Life isn’t black and white—there’s a rainbow of choices!”

Question 29

Circular Reasoning (Begging the Question)

Answer 29

Formal : Definition: Using the conclusion as a premise without providing evidence. the argument simply restates the conclusion in different words or assumes it is true without proof. Example:
“Why is this book good? Because it’s the best book ever!”
Structure:
Premise: X is true because Y is true.
Conclusion: Y is true because X is true.
This creates a loop without offering actual evidence.

Memory Trick:
“You’re going in circles—give me proof!”