Key Arguments

• Locke observes that 'number ... is that which the mind makes use of in measuring all things that by us are measurable, which principally are expansion and duration', making number the universal measure.
• He proposes that 'our idea of infinity, even when applied to those, seems to be nothing but the infinity of number', asking 'For what else are our ideas of Eternity and Immensity, but the repeated additions of certain ideas of imagined parts of duration and expansion, with the infinity of number; in which we can come to no end of addition?'
• He argues that number uniquely furnishes us with an 'inexhaustible stock' for such additions: however large a sum a man collects, 'this multitude, how great soever, lessens not one jot the power of adding to it, or brings him any nearer the end of the inexhaustible stock of number.'
• He concludes that 'this endless addition or addibility ... of numbers, so apparent to the mind, is that, I think, which gives' us the idea of the infinite in these domains.

Source Quotes

Number measures all measureables. This further is observable in number, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are expansion and duration; and our idea of infinity, even when applied to those, seems to be nothing but the infinity of number. For what else are our ideas of Eternity and Immensity, but the repeated additions of certain ideas of imagined parts of duration and expansion, with the infinity of number; in which we can come to no end of addition?

This further is observable in number, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are expansion and duration; and our idea of infinity, even when applied to those, seems to be nothing but the infinity of number. For what else are our ideas of Eternity and Immensity, but the repeated additions of certain ideas of imagined parts of duration and expansion, with the infinity of number; in which we can come to no end of addition? For such an inexhaustible stock, number (of all other our ideas) most clearly furnishes us with, as is obvious to every one.

For such an inexhaustible stock, number (of all other our ideas) most clearly furnishes us with, as is obvious to every one. For let a man collect into one sum as great a number as he pleases, this multitude, how great soever, lessens not one jot the power of adding to it, or brings him any nearer the end of the inexhaustible stock of number; where still there remains as much to be added, as if none were taken out. And this endless addition or addibility (if any one like the word better) of numbers, so apparent to the mind, is that, I think, which gives

For let a man collect into one sum as great a number as he pleases, this multitude, how great soever, lessens not one jot the power of adding to it, or brings him any nearer the end of the inexhaustible stock of number; where still there remains as much to be added, as if none were taken out. And this endless addition or addibility (if any one like the word better) of numbers, so apparent to the mind, is that, I think, which gives

Key Concepts

• This further is observable in number, that it is that which the mind makes use of in measuring all things that by us are measurable, which principally are expansion and duration;
• and our idea of infinity, even when applied to those, seems to be nothing but the infinity of number.
• For what else are our ideas of Eternity and Immensity, but the repeated additions of certain ideas of imagined parts of duration and expansion, with the infinity of number; in which we can come to no end of addition?
• For let a man collect into one sum as great a number as he pleases, this multitude, how great soever, lessens not one jot the power of adding to it, or brings him any nearer the end of the inexhaustible stock of number; where still there remains as much to be added, as if none were taken out.
• And this endless addition or addibility (if any one like the word better) of numbers, so apparent to the mind, is that, I think, which gives

Context

Book II, chapter XVI, section 8, where Locke connects his theory of number to measurement, and to our ideas of infinity, eternity, and immensity.