Understanding Logical Arguments

• Logic trains the mind to draw correct conclusions and avoid errors
• Logic involves reasoning from given facts to new statements.

Arguments

• Arguments are structured statements
• Arguments consist of reasons and a conclusion

Logical Argument

• A group of statements with one considered the conclusion.
• The conclusion follows from reasons (premises)

Statements

• Statements have truth-value (True or False)
• Questions, wishes, exclamations, and commands do not have truth-value.
• All statements are sentences, not all sentences are statements.

Standard Argument Form

• Premises (reasons) are stated first, followed by the conclusion.
• Not all arguments follow this structure

Argument Indicators

• Certain words indicate premises and conclusions
• Premise indicators: since, as, because
• Conclusion indicators: therefore, so, hence, thus, consequently

Argument Construction

• Arguments are constructed to explain, predict, convince, and persuade.
• Context and motives aid in interpreting arguments

Deductive and Inductive Reasoning

Deductive Logic

• Deductive arguments provide conclusive evidence for the conclusion
• Deductive arguments can be valid or invalid

Validity

• A deductively valid argument guarantees that if the premises are true, the conclusion is also true.
• A deductively invalid argument does not guarantee this.

Validity and Truth

• Validity does not concern the truth of premises, but the structure of the argument.
• A sound argument is deductively valid with all true premises

Inductive Logic

• Inductive logic deals with connections allowing for graduations in strength.
• Inductive arguments can be strong or weak.

Inductive Argument Strength

• An inductively strong argument's conclusion is likely true if the premises are true.
• Inductive strength depends on how improbable a false conclusion is.
• Inductive arguments assert more than the premises alone.

Evaluating Inductive Arguments

• Probability or likelihood of the conclusion being true must be determined if premises are true.
• Weather forecasts are examples of inductive arguments.

Deductive vs Inductive

• Deductively invalid arguments can be inductively strong or weak.
• Inductive logic usually moves from experienced to unexperienced.
• Logic is the study of the strength of the evidential link between premises and conclusions.

Deductive and Inductive Arguments

• Deductive arguments proceed from general premises to specific conclusions.
• Inductive arguments proceed from specific premises to general conclusions
• Deductive and inductive arguments are not distinct types except for analytical purposes

Fallacies: Errors in Reasoning

Good and Bad Reasoning

• This is an analysis between correct or incorrect reasoning
• Logic is used in a specific context

Fallacy Definition

• A fallacy is a mistake in reasoning or inference
• Logicians use it to describe typical errors in ordinary discourse

Fallacious Arguments

• For an argument to be fallacious, it must appear valid or cogent
• Arguments are constructed to prove the conclusion's truth.

Premises and Conclusions

• Premises provide evidence or justification for the conclusion
• Inference: The step-by-step process from premises to conclusion

Argument Failure

• Arguments fail by assuming false premises or lacking a logical connection between premises and conclusion
• Every argument claims that the conclusion's truth follows from the premises

Logician's Role

• A logician evaluates logical relations between propositions
• Broadly, there are formal and informal fallacies.

Formal vs Informal Fallacies

• Formal fallacies are identified through the argument's form.
• Informal fallacies are identified through the argument's content.

Formal Fallacies

• Arise from errors in the structure or form of an argument.
• Formal fallacy is an error in deductive reasoning.

Syllogism

• A syllogism is a two-premised argument that appears valid but is not

Rules for Syllogism Validity

• In a valid categorical syllogism, the middle term must be distributed at least once
• No term may increase its distribution
• No valid categorical syllogism can have two negative premises

Negative Premises in Syllogisms

• If a premise is negative, the conclusion must be negative
• Syllogism with a conclusion cannot have two universal premises

Fallacies of Affirmation

• Affirming the consequent is a fallacy
• Denying the antecedent is a fallacy

Informal Fallacies

• Identified by analyzing the content of the argument
• Two types: fallacies of relevance/irrelevance and ambiguity

Fallacies of Relevance

• Irrelevance of the conclusion to the premises is present in these fallacies
• Appeal to the people or masses (argumentum ad populum)

Fallacies of mass appeal

• Using numbers as evidence for a position is a fallacy
• The truth of something doesn't depend on popular opinion

Fallacies of appeal to authority

• Accepting a view because an authority accepts it is a fallacy
• A statement's truth isn't based on an authority's prestige

Fallacies of appeal to force

• Assent sought via force or threat is a fallacy
• Might does not make something right or true

Fallacies of appeal to ignorance

• Arguing a view is true because it hasn't been proven false (or vice versa) is a fallacy.
• This can be treacherous reasoning

Fallacies against the person

• Rebutting the person instead of the argument's basis

Abusive Fallacy

• Fallacy consists of attacking the person's character
• Dismissing ideas due to someone's immorality involves this fallacy

Fallacy Circumstantial

• Rejecting a position due to the person's circumstances is a fallacy.
• This shifts focus from the argument

Fallacy Tu Quoque

• Making an opponent appear to argue in bad faith is still a fallacy
• Citing inconsistencies doesn't invalidate advice

Fallacy of Appeal to pity

• Invoking pity or mercy to ensure assent is a fallacy
• Fallacy of accident: Applying a general rule to an instance rendering it inapplicable

Fallacy of accident in general terms

• Fallacy of converse accident: Ascribing what holds for unique cases to general cases
• This is the converse of the fallacy of accident

Fallacies of Ambiguity:

• This consists of Fallacy of Equivocation
• This consists of Fallacy of Amphiboly

Fallacy of Equivocation

• Conclusion drawn from an argument with an ambiguous word

Fallacy of Amphibility

• Conclusion drawn from a statement with multiple interpretations.
• The divisions and categorisation of fallacies is usually never rigid