IB Philosophy: Proof and Logic

IB Philosophy: Proof and Logic

The topic ‘Proof and Logic’ deals with how an argument is formulated and the lines of reasoning that can lead to its success. The basic definitions that can be found in all logical arguments are as such:

A premise is a statement that supports what you argue.

A deductive argument claims that if all premises are true, the conclusion that is inferred from the premises is also truthful.

A logical fallacy refers to an invalid case of deductive reasoning where the conclusion does not follow the premises.

Syllogisms

A syllogism is a type of deductive argument where a conclusion is deduced from two (or more) distinct premises. For example, an example of a simple syllogism is:

1. Ryan is a dog.
2. All dogs are mammals.
3. Therefore, Ryan is a mammal.

This example above features two different premises (1 and 2) and a single conclusion (3).

Validity and soundness

When describing a deduced argument, the terms valid and sound can be used.

A valid argument is one where the conclusion of an argument is correctly deduced from the information provided by the premises. For example, the deduction that:

1. All woman are mothers.
2. Martha is a woman.
3. Therefore, Martha is a mother.

…illustrates a valid argument where the conclusion (3) follows the premises that are set out.

However, the example also features an untrue premise (1) as it is factually untrue for all woman to be mothers, meaning that the argument is valid but not sound.

A sound argument is one that has to be valid, meaning that the conclusion necessarily follows from the premises, and the premises are also true.

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Deductive and inductive reasoning

If deductive reasoning can be described as forming specific conclusions from general premises, the process of inductive reasoning is to form generalisations that are usually true by observing a number of specific cases.

For example, if a person travels to a pizza shop and sees a circular pizza and does so for multiple pizza shops, he can reason using inductive reasoning that ‘all pizzas are round’.

Key Terminology

Throughout the Core Theme unit, it will become necessary for a student to build a repertoire of philosophical terminology when discussing the idea of knowledge.

Here is a list of definitions that you may find helpful to refer back to when studying further into the course:

A priori – Knowledge that is rationally derived; knowledge that does not originate from experience

A posteriori – Knowledge that is derived from experience

Analytic (statements) – Describes a statement that can be verified through the meanings of the words itself. For example, the statement all dogs are animals is true by the virtue of the word animal being inclusive of the existence of dogs.

Synthetic (statements) – Describes a statement that attempts to derive meaning from concepts that do have any innate link. These statements can be denied without contradiction through empirical proof. For example, the statement sushi is delicious is synthetic as both concepts are independent in meaning of each other and the statement can only be proven through experience.

Necessary (truths) – Also known as logical truths. Describes concepts that are universally true in all possible worlds. For example, the statement speed is the rate of velocity over a period of unit time is necessarily true because the meaning is part of the definition of the very word itself; this means that necessary/logical truths does not concern with factual statements of the world.