Proof and Probability

(can be applied to arguments for the existence of God)

What is a proof?

“An argument which starts from one or more premises, which are propositions taken for granted for the purpose of the argument, and argues to a conclusion.” (Swinburne, 1979)

Cannot be false; must be a logically necessary truth.

What is a probability?

The conclusion drawn from the premises in this case is not conclusive It may be the most likely conclusion, but an alternative conclusion could be made.Relies on a judgment to be made and evidence to be considered.

Direct or Indirect Proof?

Direct proof involves empirical experience on the part of the individual; it happens to them.

Indirect proof usually relies on logic, reason and/or other people’s experiences

A priori or a posteriori?

A priori: A type of proof where the premises

and conclusion are not based on any external evidence or experience; based on logic

A posteriori: A type of proof where the premises

and conclusion are based on external empirical evidence and experiences.

Deductive or Inductive?

Deductive: If you accept the premises, you must accept

the conclusion (the conclusion is logically necessary). Moves from particular instances to general conclusions.

Inductive: Premises move to a conclusion that is

probable rather than necessary. May contain an ‘if’ statement. Moves from general to specific.

Analytic or Synthetic?

An analytic statement is one where the predicate is included in the subject, e.g. a triangle has 3 angles, all bachelors are male, etc.A synthetic statement is one where the predicate adds something to the subject that would not otherwise be apparent, e.g. all bachelors are happy.

In summary…

All proofs are either:

A posteriori, synthetic and inductive(e.g. cosmological)

OrA priori, analytic and deductive(e.g. ontological)

Criteria for a Successful Indirect Proof

T. Penelhum (based on GE Moore)To prove a realist God

1. Premises must be different from conclusion.

2. Premises must be true.3. Premises must be known to be true by the

hearer.4. Conclusion follows logically on from the

premises (or is overwhelmingly probable).

Problems with Proofs

Dependent on limited experience and resources (can humans understand God?)They are dependent on empirical evidenceBelievers do not allow anything to count against proofs (e.g. Parable of Gardener)Atheist and Theist reach different conclusions from same data.If existence of God was self-evident, there would be no need for proofs.

Eschatological Verification

Some philosophers, like Hick, believe that the existence of God will only be proved at the end of time (eschatology = study of the end of time). Hick uses a parable of two travellers on a journey to the Celestial City.