Locke holds that there are three, and only three, degrees of human knowledge—intuitive, demonstrativ… — John Locke

Locke holds that there are three, and only three, degrees of human knowledge—intuitive, demonstrative, and sensitive—and that whatever falls short of intuition or demonstration, at least in general truths, is mere faith or opinion rather than knowledge.

By John Locke, from An Essay Concerning Human Understanding

Key Arguments

He first reaffirms that 'These two, viz. intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of these, with what assurance soever embraced, is but faith or opinion, but not knowledge, at least in all general truths.'
He then explicitly adds sensitive knowledge as a third sort: 'So that, I think, we may add to the two former sorts of knowledge this also, of the existence of particular external objects ... and allow these three degrees of knowledge, viz. intuitive, demonstrative, and sensitive.'
He notes that 'in each of which there are different degrees and ways of evidence and certainty', recognizing an internal gradation of evidential strength within each of the three degrees while still sharply distinguishing them from mere belief.
By reserving the name 'knowledge' to these three modes of perceiving agreement or disagreement of ideas (including with existence), he maintains the boundary set earlier in Book IV, Chapter I, between knowledge and 'fancy, guess, or believe'.

Source Quotes

Sensitive knowledge of the particular existence of finite beings without us. These two, viz. intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of these, with what assurance soever embraced, is but faith or opinion, but not knowledge, at least in all general truths. There is, indeed, another perception of the mind, employed about the particular existence of finite beings without us, which, going beyond bare probability, and yet not reaching perfectly to either of the foregoing degrees of certainty, passes under the name of knowledge.

But yet if he be resolved to appear so sceptical as to maintain, that what I call being actually in the fire is nothing but a dream; and that we cannot thereby certainly know, that any such thing as fire actually exists without us: I answer, That we certainly finding that pleasure or pain follows upon the application of certain objects to us, whose existence we perceive, or dream that we perceive, by our senses; this certainty is as great as our happiness or misery, beyond which we have no concernment to know or to be. So that, I think, we may add to the two former sorts of knowledge this also, of the existence of particular external objects, by that perception and consciousness we have of the actual entrance of ideas from them, and allow these three degrees of knowledge, viz. intuitive, demonstrative, and sensitive: in each of which there are different degrees and ways of evidence and certainty. 15.

Key Concepts

These two, viz. intuition and demonstration, are the degrees of our knowledge; whatever comes short of one of these, with what assurance soever embraced, is but faith or opinion, but not knowledge, at least in all general truths.
So that, I think, we may add to the two former sorts of knowledge this also, of the existence of particular external objects, by that perception and consciousness we have of the actual entrance of ideas from them, and allow these three degrees of knowledge, viz. intuitive, demonstrative, and sensitive:
in each of which there are different degrees and ways of evidence and certainty.

Context

Book IV, Chapter II, §14, summing up Locke’s taxonomy of the 'degrees of our knowledge' and distinguishing all three from mere opinion, with a special restriction of the 'faith or opinion' verdict to general truths.