14.1 Logic in Philosophical Arguments

Logic in philosophical arguments is all about structure and reasoning. It's the backbone of how we build and analyze arguments, using tools like deductive and inductive reasoning, syllogisms, and categorical propositions.

When we evaluate arguments, we look at validity and soundness. We also watch out for fallacies and use modal logic for more complex ideas. These skills help us think critically and argue effectively in philosophy and beyond.

Types of Reasoning

Deductive and Inductive Reasoning

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• Deductive reasoning draws conclusions from premises that logically follow
  • Premises assumed to be true, conclusion must be true if premises are true
  • Moves from general principles to specific instances (All men are mortal, Socrates is a man, therefore Socrates is mortal)
• Inductive reasoning draws probable conclusions from premises
  • Premises provide evidence for conclusion, but conclusion not guaranteed to be true
  • Moves from specific instances to general principles (Every raven I've seen is black, therefore all ravens are probably black)

Syllogisms

• Syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion
  • Major premise states a general principle (All mammals are warm-blooded)
  • Minor premise provides a specific instance related to the major premise (Dogs are mammals)
  • Conclusion logically follows from the premises (Therefore, dogs are warm-blooded)
• Syllogisms can be categorical or hypothetical
  • Categorical syllogisms involve categorical propositions (All A are B, No C are D)
  • Hypothetical syllogisms involve conditional statements (If P then Q, If Q then R, therefore if P then R)

Components of Arguments

Premises and Conclusions

• Premise is a statement offered as evidence or reason for accepting the conclusion
  • Premises provide support for the conclusion
  • Premises can be explicit or implicit (unstated but assumed)
• Conclusion is the main claim or point the argument is trying to establish
  • Conclusion is what the argument aims to prove or persuade the audience to accept
  • Conclusions are often indicated by words like "therefore," "thus," "hence," or "so"

Categorical Propositions

• Categorical proposition is a statement that asserts or denies something about a category or class of things
  • Consists of a subject term (S) and a predicate term (P)
  • Can be affirmative (S is P) or negative (S is not P)
  • Can be universal (All S are P, No S are P) or particular (Some S are P, Some S are not P)
• Four types of categorical propositions: A (All S are P), E (No S are P), I (Some S are P), O (Some S are not P)
  • These form the basis for categorical syllogisms (All mammals are warm-blooded, All dogs are mammals, therefore all dogs are warm-blooded)

Evaluating Arguments

Validity and Soundness

• Validity refers to the form or structure of an argument
  • Argument is valid if the conclusion logically follows from the premises
  • In a valid argument, it's impossible for the premises to be true and the conclusion false
• Soundness refers to both the form and content of an argument
  • Argument is sound if it is valid and all its premises are actually true
  • A valid argument can be unsound if one or more premises are false (All cats are dogs, All dogs are mammals, therefore all cats are mammals)

Fallacies and Modal Logic

• Fallacy is an error in reasoning that makes an argument invalid or unsound
  • Formal fallacies involve errors in the form or structure of the argument (affirming the consequent, denying the antecedent)
  • Informal fallacies involve errors in the content or reasoning of the argument (ad hominem, straw man, appeal to authority)
• Modal logic deals with concepts like possibility, necessity, and contingency
  • Introduces modal operators such as "necessarily," "possibly," "contingently"
  • Allows for more nuanced analysis of arguments involving these concepts (If necessarily P then Q, P, therefore necessarily Q)