More on bacon
Since here we observed that, for what concerns deduction: (all Italians eat is pasta; Eleonora is Italian; Eleonora eats pasta); we start from a universal statement and end up to a specific statement. This is the logical syllogism. The peculiarity of deductive reasoning is that, if the premises are true, than the conclusion is also true and vice versa. In this type of reasoning, we conclude something on the middle term that is included in the major term, but how do we know the premises are true? It is a problem for Aristotle when he makes logic bare on science. How do we know all Italians eat pasta? The idea here is we acquire a wide enough number of repeated instances (induction by enumeration) and then we subdue this list to a series of condition (what Bacon tries to do) and we then feel entitled to state what we state. We are now generalizing to the universal case. All Italians eat pasta in a generalization, in an inductive approach. Then we now go from the single case/instances to the general rule/statement. The principle of induction: if a large number of objects As have been observed under a wide variety of conditions, and if all those observed As without exceptions possessed the property b, then all As have b. It will make legitimate not only how we go from the particular to the universal, but also it’ll allow us to draw conclusions on the instances that have yet to be observed. All swans are white. We can draw two conclusions: probably, the next swan I’ll see will be white, and, probably, all the other swans I’m going to see are going to be white. Induction relies on experience and on senses, for example we use induction when we expect to be attending classes day after day: we have an empirical proof to be expecting to find the teacher the following days. We are entering a slightly dangerous territory: the conclusion of deductive inference does not say much more than its premises, and if the premises is true I will be assured the conclusion is also true. Still, induction can’t make us so certain. How wide must be our number of observed facts to be certain of them, for example? The whole point in science, as reminded by Bacon, is to establish the truth of the premises, to improve and expand our knowledge. And deductive reasoning doesn’t expand our knowledge, while induction does. How justified are we in making these assumptions? We know how risky it is to follow induction, specifically from a logical point of view: in an induction, we might start from true premises but could eventually end up with a wrong conclusion. Do really all Italians eat pizza? I can even say all swans are white, even if I haven’t seen them: this is very dangerous of induction. David Hume analyzed the problem of induction. What is his strategy to face induction and to correctly use it to increase our knowledge? He faces these problems in his book “An Enquiry Concerning Human Understanding”. The first distinction is that all the objects of human reason or enquiry may naturally (02:06:00) Relations of ideas: propositions that are discoverable by the mere operation of thought; even if there were no triangles on Earth, Pitagora’s theorem would still be true. They are subject to logical contradiction as well and they can be demonstrated to be false Matters of facts: the contradiction comes out when we make a logical contradiction, but here it is not as easy as in the relations of ideas. We cannot say “the sun will rise tomorrow” if the sun doesn’t exist: the sun’s existence is not a matter of logic, so it is not possible to find out whether such a proposition is true merely by reasoning. We need to appeal to experience. If we do this, we defeat the very purpose of inference in the first place, for inference wants to arrive to conclusion before using senses to draw a conclusion.A prioriknowledge of matters of facts is impossible. Relations of ideas can be known by deductive relations. Hume wants to enquire how are we able to establish the truth of our proposition without experience, how it is possible to infer a universal generalization “the sun will always rise” from a collection fo observation of what the sun has done up until today. Hume says that only some of our factual knowledge is based on something we perceive directly. If you were to ask a man why he believes his friend his out of town, he will reply by giving another matter of fact, like he has received a letter from his friend where he says he is out of town. A man finds a watch in a desert island, therefore he concludes there must have been someone else there before him, without direct acquaintance. All matters of facts relies on a present facts and another fact which the former is inferred from. How do we reason here? Exactly in the same way in which we reason when we connect an effect to a cause: we see something and we asked ourselves what brought it about. How do we formulate this type of reasoning? Are we entitled to make this connection? Can we acquire knowledge from this connection?