Algebraic species or letters are denominations of denominations. Therefore Arithmetic to be treated of before Algebra. 2 crowns are called ten shillings. Hence may appear the value of numbers. Complex ideas are the creatures of the mind. Hence may appear the nature of numbers. This to be deeply discuss’d. I am better informed & shall know more by telling me there are 10,000 men, than by shewing me them all drawn up. I shall better be able to judge of the bargain you’d have me make wn you tell me how much (i.e. the name of ye) money lies on the table, than by offering and shewing it without naming. I regard not the idea, the looks, but the names. Hence may appear the nature of numbers. Children are unacquainted with numbers till they have made some progress in language. This could not be if they were ideas suggested by all the senses. Numbers are nothing but names—never words. Mem. Imaginary roots—to unravel that mystery. Ideas of utility are annexed to numbers. In arithmetical problems men seek not any idea of number. They only seek a denomination. This is all can be of use to them. Take away the signs from Arithmetic and Algebra, and pray wt remains? These are sciences purely verbal, and entirely useless but for practice in societies of men. No speculative knowledge, no comparing of ideas in them(162). Qu. whether Geometry may not properly be reckon’d amongst the mixt mathematics—Arithmetic & Algebra being the only abstracted pure, i.e. entirely nominal—Geometry being an application of these to points(163)? ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M225) Locke of Trifling Propositions. [b. 4. c. 8] Mem. Well to observe & con over that chapter. (M226) Existence, Extension, &c. are abstract, i.e. no ideas. They are words, unknown and useless to the vulgar. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M227) Sensual pleasure is the _summum bonum_. This the great principle of morality. This once rightly understood, all the doctrines, even the severest of the Gospels, may clearly be demonstrated. (M228) Sensual pleasure, quâ pleasure, is good & desirable by a wise man(164). But if it be contemptible, ’tis not quâ pleasure but quâ pain, or cause of pain, or (which is the same thing) of loss of greater pleasure. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ (M229) Wn I consider, the more objects we see at once the more distant they are, and that eye which beholds a great many things can see none of them near. (M230) By _idea_ I mean any sensible or imaginable thing(165). (M231) To be sure or certain of wt we do not actually perceive(166) (I say perceive, not imagine), we must not be altogether passive; there must be a disposition to act; there must be assent, wch is active. Nay, what do I talk; there must be actual volition. What do we demonstrate in Geometry but that lines are equal or unequal? i.e. may not be called by the same name(167).