 But it is not at all clear that Heyting would want to make that distinction. If the notion of proposition is understood in such a way that a proposition is true or false independently of our knowledge of this fact, then Heyting would readily agree with Kolmogorov that a proposition is different from a problem; but as soon as one adopts the view that propositions express intentions that are fulfilled (and the proposition made true) or disappointed (and the proposition made false) by our mathematical constructions, which is the view that Heyting actually held, then there would seem to be no essential difference between propositions and problems. Kolmogorov himself had already indicated that a problem may consist in finding the proof of a proposition; exploiting this, one can argue that the following two notions of proposition coincide: