Philosophy Concordance - online philosophical quotations

Expressions which are usable to the same effect have equal values, they are equivalent; and synonymy is primarily just this kind of equivalence.

This, as well as all the following equations, is to be understood in the extended sense, such as stating that the equated values are either equal or are both undefined.

And, in the first place, I observed, that the great certitude which by common consent is accorded to these demonstrations, is founded solely upon this, that they are clearly conceived in accordance with the rules I have already laid down In the next place, I perceived that there was nothing at all in these demonstrations which could assure me of the existence of their object: thus, for example, supposing a triangle to be given, I distinctly perceived that its three angles were necessarily equal to two right angles, but I did not on that account perceive anything which could assure me that any triangle existed: while, on the contrary, recurring to the examination of the idea of a Perfect Being, I found that the existence of the Being was comprised in the idea in the same way that the equality of its three angles to two right angles is comprised in the idea of a triangle, or as in the idea of a sphere, the equidistance of all points on its surface from the center, or even still more clearly; and that consequently it is at least as certain that God, who is this Perfect Being, is, or exists, as any demonstration of geometry can be.

We may define function f with its domain equal to the set of all natural numbers by defining f(0) and giving the recipe how to compute f(x') out of f(x), or we may base the definition on a more complicated system of rules generating natural numbers, but it is impossible to define such a function directly, bypassing generating rules altogether.

Suppose the log makes a bang on passing me. We can say these bangs are separated by equal, or unequal, intervals.

Suppose that the passing logs seem to be equal distances apart.

But it is not a matter of experience that equal distributions of nuts and raisins must occur when they are swished about.

To say that if equal distribution does not occur there must be a difference in weight of the nuts and raisins, even though these have not been weighed, is to assume some other force to explain the unshuffling.

We tend to say that there must be some explanation if equal distribution does not occur.

And, of equal importance, they are endowed with a capacity for free action and collective intentionality.