KA

Summary of Logical Arguments and Validity in Philosophy

Chapter Outline

  • Arguments

  • Good Arguments

  • Deductive Validity Defined

  • "Validity" Is a Technical Term

  • Logical Form

  • Invalidity

  • Testing for Invalidity

  • Circularity, or Begging the Question

  • Truth

  • "True for Me"

  • Wishful Thinking

  • Self-Fulfilling Prophesies

  • Review Questions

  • Problems for Further Thought

  • Recommended Readings, Video, and Audio

Philosophy and Arguments

  • Philosophy involves constructing and evaluating arguments, similar to rational activities in mathematics, economics, and everyday life.

  • The unique aspect of philosophy lies in the types of questions these arguments aim to answer.

  • The aim of this chapter is to develop techniques to differentiate between a good and bad argument.

Arguments

  • Arguments consist of two parts: premises and a conclusion.

    • Premises: Statements intended as support for the conclusion, expressed in declarative sentences, which can be either true or false.

    • Conclusion: The statement that the argument seeks to establish based on the premises.

  • Example from high school geometry: Axioms as premises and theorems as conclusions. Axioms don't require proof, unlike premises in philosophical arguments, which must be plausible and related to the conclusion.

  • The two central questions to assess an argument:

    • Are the premises plausible?

    • If the premises are true, do they support the conclusion?

Good Arguments

  • Definition of a good argument: An argument that is rationally persuasive and provides substantial reasons to consider the conclusion true.

  • Good arguments should have:

    • True premises

    • Relevant premises that provide a valid reason for the conclusion.

  • Example of irrelevance:

    • Premises: "Grass is green. Roses are red."

    • Conclusion: This lacks a connection between premises and conclusion.

  • Good arguments can be classified into:

    • Deductively Valid

    • Inductively Strong

    • Abductively Strong

Deductive Validity Defined

  • A deductively valid argument has the critical property that if its premises are true, then the conclusion must also be true.

  • Important emphasis on the conditional “IF” in validity: “A deductively valid argument is one that has the property: IF its premises were true, its conclusion would have to be true.”

  • Deductive validity requires examining logical structure rather than the actual truth of the premises.

  • Validity can exist even with false premises, provided the logical form remains consistent.

"Validity" Is a Technical Term

  • The philosophical definition of validity differs from lay understanding:

    • Validity pertains solely to the structure of arguments, not statements.

    • An argument can be valid even with implausible statements.

  • Example of a valid yet apparently false argument:

    • All plants have minds. (Premise 1)

    • All ladders are plants. (Premise 2)

    • All ladders have minds. (Conclusion)

Logical Form

  • Logical form is the property enabling an argument’s deductive validity, independent of its subject matter.

  • The structure of validity applies across various topics:

    • Form Example: All Bs are Cs; All As are Bs; Therefore, All As are Cs.

  • Arguments only achieve validity based upon their relational structure, not content.

Invalidity

  • A valid argument possesses premises that guarantee the conclusion's truth. If there is any chance that the conclusion could be false when the premises are true: deductively invalid.

  • Even true premises can lead to an invalid argument if they fail to guarantee the conclusion.

  • Example of invalid argument with true premises but false conclusion:

    • Emeralds are green. (Premise)

    • Lemons are yellow. (Conclusion) - No guarantee provided- invalid.

Testing for Invalidity

  • To test for invalidity, determine the argument's logical form, then find an example where premises are true but the conclusion is false.

    • A single example of this form being false invalidates all arguments of that form.

  • If the premises don't ensure the truth of the conclusion, the argument's validity is compromised.

Soundness

  • A term derived when both questions yield yes: Is the argument deductively valid? Are all premises true? If so, the conclusion must also be true.

Conditionals

  • Conditionals (If/then statements): Components of two declarative statements.

    • P (antecedent) and Q (consequent).

  • Conditional: "If P, then Q" does not claim P is true.

  • Contrapositive: "If not Q, then not P" is equivalent and holds the same truth value.

  • Converse: "If Q, then P" is not guaranteed to be equivalent.

Circularity, or Begging the Question

  • Begging the question involves using premises that assume the conclusion is already true, failing to convince someone who does not already hold the belief.

    • Example: Crediting the Bible for the existence of God does not persuade the doubtful.

Truth

  • Truth as an objective concept, distinct from belief or opinion.

  • A statement's truth reflects a reality irrespective of belief or perception.

  • Example illustrating subjective views of truth:

    • "It is true for me" may mislead as it conflates belief with truth.

Self-Fulfilling Prophecies

  • Situations where belief can cause reality: Believing “I cannot hit” influences performance negatively.

    • Causal chain: Thought → Action → Truth.

Review Questions

  1. Explore validity in statements and what makes arguments deductively valid.

  2. Create examples illustrating valid and invalid arguments with varied truths and conclusions.

  3. Distinguish validity from truth and consider implications of subjective belief.

Problems for Further Thought

  • Reflections on arguments (validity, logical forms, and truth) to deepen understanding.

Recommended Readings, Videos, and Audio

  • Refer to eResource for supplementary materials related to argument evaluation and types of reasoning further, including inductive and abductive contexts.

Chapter 3: Inductive and Abductive Arguments

  • Overview of various reasoning strategies, limitations of deductive reasoning, factors influencing inductive strength, and processes involved in abductive reasoning.