Deductive Arguments - Reading

Deductive Arguments

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

Philosophy and Arguments

  • Philosophy involves constructing and evaluating arguments, similar to mathematicians, economists, physicists, and even in everyday life.

  • Distinctive element of philosophy: the kinds of questions that arguments aim to answer, as discussed in the previous chapter.

  • Objective of this chapter: develop techniques to distinguish good arguments from bad ones.

Arguments

  • An argument consists of two parts: premises and conclusion.

    • Premises: statements presented as reasons for believing the conclusion, expressed by declarative sentences that can be true or false.

    • Conclusion: the statement that is to be established based on the premises.

  • Comparison to high school geometry:

    • Axioms = assumptions (premises).

    • Theorems = conclusions derived logically from those assumptions.

  • Unlike geometry, philosophical arguments demand examination of the premises for plausibility and their relation to the conclusion.

Good Arguments

  • Definition of a good argument: a rationally persuasive case that offers substantial reason to believe the conclusion is true.

  • Good arguments provide reasons without trickery, like some advertisers or politicians may do.

  • A good argument must satisfy two criteria:

    1. Contain true premises.

    2. Premises must be relevant and support the conclusion.

Example of a Poor Argument

  • Argument:

    • Premise: "Grass is green."

    • Conclusion: "Roses are red."

    • Flaw: Irrelevance of premises to conclusion.

Categories of Good Arguments

  • Good arguments can be categorized into two main types:

    • Not Deductively Valid

    • Deductively Valid

    • Additionally, good arguments may be:

    • Abductively Strong

    • Inductively Strong

  • The three categories (deductively valid, inductively strong, abductively strong) will be treated as mutually exclusive.

Deductive Validity Defined

  • Deductively Valid Argument: If its premises are true, the conclusion must be true.

    • Important: The premises do not need to be true for the argument to be valid.

    • Expressed as:

    • "A deductively valid argument is an argument with the property: IF its premises are true, its conclusion must be true."

Example of Deductive Validity

  1. Premises:

    • All fish swim.

    • All particles have mass.

    • All sharks are fish.

    • All electrons are particles.

  2. Conclusion:

    • All sharks swim.

    • All electrons have mass.

Logic of Validity

  • Validity is a technical term, different from common usage where "valid" implies plausibility or truth.

  • Validity strictly refers to the structure of argument, not the truthfulness of its premises or conclusion.

  • Example:

    • All plants have minds.

    • All ladders are plants.

    • Therefore, all ladders have minds.

    • Valid structure; false premises.

Logical Form

  • What makes an argument deductively valid is the logical form.

  • Different content but same form leads to the same conclusions about validity.

  • General skeleton of logical form:

    • If all Bs are Cs, and all As are Bs, then all As are Cs.

Invalidity

  • Deductive invalidity defined:

    • If there's a possibility for a true premise to lead to a false conclusion, then the argument is invalid.

    • E.g.,

    • If Emeralds are green.

    • Lemons are yellow.

    • Invalidity explained: Premise doesn’t warrant conclusion.

Example of Invalid Argument

  • Argument:

  1. If Jones stands in the heavy rain without an umbrella, then he will get wet.

  2. Jones is wet.

  3. Jones was standing in the heavy rain without an umbrella.

  • Evaluation: Even if true, it doesn’t deductively lead to correct conclusion about Jones.

Testing for Invalidity

  • Isolate logical form, ignoring subject matter to see if other arguments with the same form yield a true premise and false conclusion.

  • Conclusion on valid and invalid must rely on logical relationships, not just empirical truths of the premises.

Circularity, or Begging the Question

  • An argument is circular if it assumes as a premise what it attempts to prove.

  • Uses terms or information that may not be accepted as true by those questioning the argument.

  • The phrase "begs the question" is often misunderstood in ordinary language but has a specific meaning in philosophy.

Truth

  • Discussion of truth relates closely to argument validity.

  • Truth must be distinguished from belief — A belief can be false or true regardless of consensus.

  • Utilizing Redundancy Theory of Truth: Simply attributing true properties to statements doesn't add substantial information (example: "The Rockies are in North America" just restates fact).

"True for Me"

  • Misleading because it suggests subjective reality — truth should be viewed objectively.

  • Beliefs can diverge greatly from objective truths; subjective truth is often incorrect.

    • Example: "True for me" doesn’t equate to universal truth.

Wishful Thinking

  • Mention of the difference between subjective hopes and objective facts in establishing belief.

Self-Fulfilling Prophesies

  • Discusses how certain beliefs could create actions that conform to beliefs (e.g., fear of failure leads to poor performance).

  • Laid as distinction between mere belief making a truth and belief affecting behavior to manifest a possibility.

The notes provide a comprehensive overview of the foundational aspects of deductive arguments, their structure, validity, and associated philosophical considerations, which could serve as an invaluable resource for students delving into philosophy and logic.