Truth and Rationality

Uses of Language

• Three main types of sentences:

  • Interrogative

  • Imperative

  • Declarative

Truth and Correspondence

• Correspondence Principle (CP):

  • A declarative sentence S is true when it corresponds to the way the world is.

  • A declarative sentence S is false when it fails to correspond to the way the world is.

Improving Upon CP

• Different sentence-tokens can belong to the same sentence-type.

• Different sentence-tokens of the same type can express different propositions.

• Different sentence-tokens of the same type can express the same proposition.

• Sentence-tokens of different types can express the same proposition.

Revised Correspondence Principle (RCP)

• A proposition p is true when it corresponds to the way the world is.

• A proposition p is false when it does not correspond to the way the world is.

• Each proposition must be either true or false.

One Truth-Value Principle (OTV)

• Every proposition bears exactly one truth-value:

  • Either the value true or the value false.

Rational Belief

Belief Principle (BP)

• For any proposition p:

  • You must either believe p, disbelieve p, or suspend judgment regarding p (not believing or disbelieving).

Principle of Rational Belief (RB)

• For any proposition p:

  • If total evidence supports p, then it is rational to believe p.

  • If total evidence goes against p, then it is rational to disbelieve p.

  • If total evidence neither supports nor opposes p, then it is rational to suspend judgment.

Principle of Proportional Belief (PB)

• It is rational to align the strength of your belief to the strength of your evidence:

  • If your evidence for p is strong, your corresponding belief should be strong.

  • If your evidence for p is weak, your corresponding belief in p should be weak.

Lecture Notes

• Correspondence Principle (CP) defined again:

  • A declarative sentence S is true when it corresponds to the way the world is, and false when it does not.

Declarative Sentence Types

• Declarative Sentence Token:

  • A specific verbal utterance or physical inscription (e.g., in a textbook or on a chalkboard).

• Declarative Sentence Type:

  • The general pattern that two or more sentence-tokens follow.

Proposition

• The meaning of a sentence token; a crucial concept linking language to truth.

Revised Correspondence Principle (RCP)

• A proposition p must be either true (corresponds to the world) or false (does not correspond to the world).

• Reinforces that every proposition must have exactly one truth-value.

Recap of One Truth-Value Principle (OTV)

• Restates that each proposition has one truth-value:

  • Either true or false.

Belief Principles Recap

Belief Principle (BP)

• Reiterates the need to choose between believing, disbelieving, or suspending judgment on proposition p.

Principle of Rational Belief (RB)

• Discusses the rationality of belief based on evidence.

Fallibilism

• The idea that a proposition can be rationally believed yet still be false.

Principle of Proportional Belief (PB)

• Reaffirms that the strength of belief should correlate with the strength of the evidence provided.