Epistemology is the study of knowledge.

• Empiricism claims that knowledge comes from sensory experience (perception), that is, empirical evidence.
• Rationalism regards reason as the chief source and test of knowledge; it claims that any reliable knowledge requires a justification.
• Skepticism questions the possibility of certainty in knowledge; it claims that it is not possible to have an adequate justification of knowledge.

For a rationalist, as all knowledge needs to be justified, the regress problem emerges: a proposition requires a justification, but any justification itself requires support (i.e., further justification), thus the justification chain goes forever. In response to the regress problem, the justification of beliefs can take very different approaches:

• Foundationalism, where a statement is inferred from a basis of unprovably sound premises (“foundations”).
• Coherentism, where a statement holds true as long as it coheres with all other justified beliefs, including itself (“coherent truth”).
• Infinitism, where a justification chain is allowed to be infinite, thus there could never be adequate justification for any statement in the chain.

Foundationalism is often related to constructivism, which claims that knowledge is a compilation of human-made constructions rather than objective truth. The corresponding approach in the philosophy of mathematics is called intuitionism.

1 Knowledge and Science

Traditionally, knowledge is defined as “justified true belief”. However, this definition has been questioned by the Gettier problem.

Based on the role of empirical evidence in reasoning, knowledge may be divided into two categories:

• A priori knowledge, which is independent of empirical evidence, e.g., mathematics, logical deductions.
• A posteriori knowledge, which is dependent of empirical evidence, e.g., statistics, statistical learning.

Science is the approach to filter out unreliable knowledge and gather together reliable knowledge (either a priori or a posteriori) as a scientific theory, by means of inference. The demarcation problem concerns what qualifies as science.

2 Hypothesis

A hypothesis is a proposed explanation or prediction method for a phenomenon. Only formally proved or statistically tested hypotheses may become reliable knowledge.

Epicurus’ principle of multiple explanations. If multiple hypotheses are consistent with the observations, one should retain them all.

Occam’s razor. Among all hypotheses consistent with the observations, choose the simplest.