67. But after all, whatsoever dependence be conceived in voluntary actions, and even though there were an absolute and mathematical necessity (which there is not) it would not follow that there would not be a sufficient degree of freedom to render rewards and punishments just and reasonable. It is true that generally we speak as though the necessity of the action put an end to all merit and all demerit, all justification for praise and blame, for reward and punishment: but it must be admitted that this conclusion is not entirely correct. I am very far from sharing the opinions of Bradwardine, Wyclif, Hobbes and Spinoza, who advocate, so it seems,[160] this entirely mathematical necessity, which I think I have adequately refuted, and perhaps more clearly than is customary. Yet one must always bear testimony to the truth and not impute to a dogma anything that does not result from it. Moreover, these arguments prove too much, since they would prove just as much against hypothetical necessity, and would justify the lazy sophism. For the absolute necessity of the sequence of causes would in this matter add nothing to the infallible certainty of a hypothetical necessity. 68. In the first place, therefore, it must be agreed that it is permitted to kill a madman when one cannot by other means defend oneself. It will be granted also that it is permitted, and often even necessary, to destroy venomous or very noxious animals, although they be not so by their own fault. 69. Secondly, one inflicts punishments upon a beast, despite its lack of reason and freedom, when one deems that this may serve to correct it: thus one punishes dogs and horses, and indeed with much success. Rewards serve us no less in the managing of animals: when an animal is hungry, the food that is given to him causes him to do what otherwise would never be obtained from him. 70. Thirdly, one would inflict even on beasts capital punishments (where it is no longer a question of correcting the beast that is punished) if this punishment could serve as an example, or inspire terror in others, to make them cease from evil doing. Rorarius, in his book on reason in beasts, says that in Africa they crucified lions, in order to drive away other lions from the towns and frequented places, and that he had observed in passing through the province of Juelich that they hanged wolves there in order to ensure greater safety for the sheepfolds. There are people in the villages also who nail birds of prey to the doors of houses, with the idea that other birds of the same kind will then not so readily appear. These measures would always be justified if they were of any avail.