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What the senses cannot give

'Seven and five make twelve', 'the whole is greater than the part': necessary, universal truths that no experience could establish.

Supports Rationalism

Leibniz, Descartes · New Essays on Human Understanding, II.i · 1704

1. The senses deliver only particular, contingent facts: this body here is hot, that swan is white. They tell us what is, here and now, never what must be so in every possible case.
2. Yet we possess truths of an entirely different order: that the angles of a triangle sum to two right angles, that nothing can at once be and not be. They hold necessarily, everywhere, before any verification, and no amount of observations could ground or refute them.
3. What is necessary and universal cannot come from what is contingent and particular: the source of these truths is therefore in reason, not in the senses. 'Nothing in the understanding that did not come from the senses, except the understanding itself.'

Therefore So reason possesses resources of its own, independent of experience: it is in reason, not in the senses, that the most certain knowledge is grounded.

How far does this reasoning convince you?