First.

...also: of what, and of which premises it is composed. And such a Demonstration our people call from the prior original: "A priori"; this refers to reasoning from cause to effect: or truly demonstration on account of the 'why' original: "Propter quid". And this is different from the Demonstration that is called from the posterior original: "A posteriori"; reasoning from effect back to cause and of the 'that' original: "Quia": which is that which is taken from signs and from universal causes, just as I declared above in the second way of Knowing.

FRAN. These are things that can be understood; therefore, do not let it bother you to continue.

GIOS. I will therefore put before you two definitions of Demonstration: one will be from the final cause the purpose for which something exists, and the other from the material cause the "stuff" it is made of. You must then notice: that just as we say, wanting to define a House from its end [purpose], which moves us to build: that it is a thing that covers and defends us from the cold, from the rain, from the snow, and from the heat: since it is for this end we build it. Or rather, taking the definition from the matter of which it is composed, we come to say: that it is a thing composed of stones, of lime, of wood, and other similar things: so, taking the definition of Demonstration from its end, we will say: that Demonstration (as Aristotle declares in the first book of the Posterior Analytics original: "posteriora") is a scientific syllogism Syllogism a logical argument where a conclusion is drawn from two premises: or rather it is a Syllogism of science: as it is more convenient for us to say: which truly causes in us, or gives birth to, Science, or Knowing, which we defined above.

CLAV. This I understand very well; nor have I need of other explanation: so continue, for if I learn everything you say as easily as I have learned what you have said until now, things will go well.

GIOS. The definition of Demonstration taken from its matter, Master Claudio, will be given in this way. Demonstration is a Syllogism, which is composed of premises that are true, first, immediate (or without any middle), and causes more known; and more importantly first, and better known than the conclusion. And although all these things are required: it is also necessary that such premises be before, or precede the conclusion: and be its cause: so that from both of these two definitions you can understand what enters into Demonstration, and the end for which it was found.

FRAN. Truly the first definition is clear to me: but the second makes me somewhat doubtful: for not remembering so well what is meant by True premises: first: immediate: and causes more known, and more importantly first than the conclusion. Therefore I pray you to declare these terms to us: for I believe this is the place.

GIOS. Therefore, so that you may have good knowledge of these things, listen to me. I said above that the Premises must be true: because having to make the conclusion known in such a way that it is impossible for it to arise from any other place than from the cause contained in them: it is highly necessary that such Premises be true: and consequently the cause of the conclusion.

ADRI. In what manner the cause of the conclusion?

GIOS. I say cause, not only of the consequence: as happens in other Syllogisms due to their form In formal logic, a conclusion can follow "correctly" from the structure of the argument even if the facts are wrong; Gioseffo is arguing that a true "Demonstration" must be factually true as well, which requires it to occur: but the cause of the true being of the conclusion: which is proper to the demonstrative Syllogism, of which we now speak.

CLAV. This is understood very well.

GIOS. The premises must also be more known than the conclusion: and also must precede it.

FRAN. What do you mean by this "precede": and by "more known"?

GIOS. That they are not such in relation to us: but in relation to Nature herself: whose knowledge does not always concur with ours.

FRAN. Please make us understand you better.

GIOS. Note then, that with respect to Nature we have to say, that the causes with which she works effects are more known to her than those effects are, and consequently, that those effects in her knowledge go before the causes: just as they also precede in the act itself: since without any doubt she produces all effects by means of them. Whence having respect to us, who do not work said effects: by means of the sense [perception] that shows them to us: those most of the time offer themselves to our knowledge before the causes do: which, we—reasoning by means of such effects—know in the last place. So that the order of our knowledge is most of the time found to be contrary to that of Nature, which Nature, working from that which she produces to that which follows: similarly through the intelligence she has within her: knows by means of the said order. But we from that which follows, often proceed to that which goes before, for the reason...