Summary: An Essay Concerning Human Understanding (page 6)

To sum up: it is the name that establishes and consolidates, within mixed ideas, a union of multiple ideas that has no foundation in nature.

Genus and species, therefore, have no real existence in things or in nature; they are mental constructs, devised to express various collections of simple ideas under a single general term.

Book IV: Of Knowledge

Knowledge concerns our ideas, since these are the only immediate objects of the mind in all its thoughts and reasonings.

Knowledge is the perception of the agreement or connection—or of the discord and contradiction—between two ideas.

When we say "white is not black," for instance, we perceive the discord between these two ideas.

Four types of agreement and disagreement can be identified:

- Identity or difference: an idea agrees with itself and differs from others.
- Relation: an idea is either related to or opposed to another.
- Coexistence: one idea coexists with another, for example in forming a more complex idea.
- Actual existence: an idea corresponds to real existence.

Within these four sorts of Agreement or Disagreement, is, I suppose contained all the Knowledge we have, or are capable of ¹.

For every possible inquiry falls within the following: That it is, or it not the same with some other; that it does, or does not always co-exist with some other Idea in the same Subject; that it has this or that Relation to some other Idea; or that it has a real existence without the Mind ².

Locke identifies three degrees of knowledge.

Intuitive knowledge consists in immediately grasping the agreement between two ideas. It is the clearest and most certain form of knowledge, leaving no room for doubt: it is on this Intuition that depends all the Certainty and Evidence of all our Knowledge ³.

Demonstrative knowledge, by contrast, is mediate: the mind does not immediately grasp the agreement between two ideas, and requires the mediation of other ideas, brought to bear through reasoning.

In sound reasoning, each step must be intuitively validated—one must intuitively grasp the correct agreement between the intermediate ideas at every stage, all the way to the conclusion.

The third degree of knowledge is sensitive knowledge.

This raises a problem: if all knowledge concerns our ideas rather than things themselves, how can we ascertain whether real things exist as the foundation of those ideas?

Locke's answer is illustrated by an example: the pain we feel when touching fire proves that fire is not merely an idea.

Our knowledge is limited because each of these three degrees is limited: we do not possess intuitive knowledge of all ideas; we cannot always identify the intermediate ideas required in reasoning; and sensitive knowledge is confined to things directly perceived by the senses.

Two examples of questions that resist any answer: Can matter think? What is the soul?

For Locke, algebra demonstrates that ideas of quantity can be rigorously proved. He further argues that ideas of quality are equally amenable to demonstration.

Thus, for Locke, morality is demonstrable. Such a demonstration would rest on the ideas of an existing God and of man as a rational being. Once developed, these ideas should serve as the foundations for our duties and rules of action, from which the principles of right and wrong could be derived through necessary deductions, as incontrovertible as those of mathematics:

Our moral ideas, as well as mathematical, being adequate, and complete Ideas, all the Agreement, or Disagreement, which we shall find in them, will produce real Knowledge, as well as in mathematical Figures ⁴.

In short:

Moral Knowledge is as capable of real Certainty, as Mathematics ⁵.

Locke offers a example of a universal moral law: where there is no property, there is no injustice.

¹ IV, 1, §7, p.527
² ibid.
³ IV, II, §1, p.531
⁴ IV, 4, §7, p.565
⁵ ibid.