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Shiavault - a Vault of Shia Islamic Books A Guide To Locke's Essay Degrees and Types of Knowledge Locke distinguished four types of agreement or disagreement that may be perceived in human knowledge: Knowledge of identity and diversity rests solely upon our recognition of the distinctness of each idea from every other; knowledge of relation employs positive, non-identical connections among ideas; knowledge of co-existence perceives the coincident appearance of a collection of qualities; and knowledge of real existence presumes some connection between an idea and the real thing it represents.

[Essay IV i 1] He further supposed that these types of knowledge can occur in any of three degrees: Intuitive knowledge is the irresistable and indubitable perception of the agreement of any two ideas without the mediation of any other. This is the clearest and most perfectly certain of all degrees of human knowledge. It accounts for our assent to self-evident truths and serves as the foundation up-on which all other genuine knowledge must be established.

[Essay IV ii 1] Intuition is most common in our knowledge of identity and relation among clear ideas, but (following Descartes) Locke also supposed that each thinking being has an intuitive knowledge of its own existence. [Essay IV ix 3] Even when the agreement of ideas is not intuitively obvious, it may be possible to discover a series of intermediate ideas by means reason establishes a connection between them.

The resulting demonstrative knowledge of the agreement of the original ideas shares in the certainty of the intuitive steps by means of which it has been proven, yet there is some loss of assurance resulting from the length of the chain itself.

[Essay IV ii 2-7] The success of the entire process depends upon our having clear ideas at each step of the process of demonstration and upon our ability to perceive the agreements between them, and both of these conditions are specific to the nature of human intellectual abilities.

[Essay IV iii 4, 26-28] The most common area of demonstrative human knowledge is mathematics, where our possession of distinct ideas of particular quantities yields the requisite clarity, disciplined reasoning helps to uncover the intermediate links that establish knowledge of identity and relation, and a perspicuous system of symbolic representation helps us to preserve the results we have obtained.