Socrates is not a Pre-Socratic philosopher because he lived and taught in the 5th century BCE, while the Pre-Socratic philosophers lived and taught in the 6th and 5th centuries BCE.

Thales of Miletus believed that water was the fundamental element of all matter because he observed that water can exist in all three states of matter (solid, liquid, and gas) and that it is essential for life.

Anaximander believed that the fundamental element of all matter was the Boundless, which he described as an infinite, indeterminate substance from which all things arise and to which all things return.

Pythagoras believed that numbers were the fundamental elements of all matter because he observed that mathematical relationships could be used to describe the natural world.

Heraclitus believed that the fundamental principle of the universe was change, which he described as the constant flux of all things.

Parmenides believed that being is the only reality because he argued that non-being cannot be thought or spoken about.

Empedocles believed that the four fundamental elements of all matter were earth, air, fire, and water because he observed that these elements could be used to explain the diversity of the natural world.

Anaxagoras believed that all things were made up of seeds, which he described as tiny, invisible particles that contained all the properties of the things they made up.

Leucippus and Democritus believed that the fundamental elements of all matter were atoms and the void, which they described as tiny, indivisible particles and the space between them.

Protagoras believed that man is the measure of all things because he argued that there is no objective truth and that all knowledge is relative to the individual.

Gorgias argued that nothing exists, that if anything exists, it cannot be known, and that if anything can be known, it cannot be communicated.

Hippias believed that the law is the measure of all things because he argued that it is the only thing that can ensure justice and order in society.

Critias believed that the universe arose from chaos because he argued that it is the only way to explain the diversity and order of the natural world.

Prodicus believed that virtue is knowledge because he argued that people only do wrong because they do not know what is right.

Thrasymachus believed that justice is the will of the stronger because he argued that the strong always get what they want, while the weak always suffer.