On Infinite (1675-1699)

"Only geometry can hand us the thread [which will lead us through] the labyrinth of the continuum's composition, the maximum and the minimum, the infinitesimal and the infinite; and no one will arrive at a truly solid metaphysics except he who has passed through this [labyrinth]." (Gottfried W Leibniz, "Dissertatio Exoterica De Statu Praesenti et Incrementis Novissimis Deque Usu Geometriae", 1676)

"Where, by the way, we may observe a great difference between the proportion of Infinite to Finite, and, of Finite to Nothing. For 1/∞, that which is a part infinitely small, may, by infinite Multiplication, equal the whole: But 0/1 , that which is Nothing can by no Multiplication become equal to Something." (John Wallis, "Treatise of Algebra", 1685)

"There is an actual infinite in the mode of a distributive whole, not of a collective whole.

Thus something can be enunciated concerning all numbers, but not collectively. So it can

be said that to every even number correspond its odd number, and vice versa; but it cannot

be accurately said that the multiplicities of odd and even numbers are equal." (Gottfried W Leibniz, cca. 1686-1687) 

"Infinities and infinitely small quantities could be taken as fictions, similar to imaginary roots, except that it would make our calculations wrong, these fictions being useful and based in reality." (Gottfried W Leibniz, [letter to Johann Bernoulli] 1689)

"To measure motion, space is as necessary to be considered as time....[They] are made use of to denote the position of finite: real beings, in respect one to another, in those infinite uniform oceans of duration and space." (John Locke, "An Essay Concerning Human Understanding", 1689)