so before we go on, I would like to tell you a few words about what we did last time, during our first meeting I defined my goal, it's a purpose of these lectures, which I will summarize here in a few words.

I think these can be useful for you, my job is to understand make you understand this of course is to understand the road played by fictions in the rational work, I’m not talking about novels and so on.

the law of fictions in rational work of the in the rational work of the seventeenth and eighteenth century, that is early modern western philosophy, they originate to starting points. it's also the scientific revolution, in this purpose I choose to introduce gradually.

it's very important the values of dimensions that make up the concept of fiction. I didn't want to differ to define fiction and then to apply it to value states, this is not a serious missile, I want to introduce the values dimensions of the concept of fiction.

I distinguished three dimensions as you knew, fiction as an abstraction, fiction as a figuration of what is possible, and of possibility lastly. we will come to history two the connections between fiction and history, the first thing one must acknowledge, it's very important is that this notion of fiction and you have to remember, this notion plays an essential part in the development of classical rational mechanics.

the invention of moderns mechanics in the seventeenth century, from Galileo to Newton, always refer to fiction, in so far too old authors, it points what does it mean, they released first of all very easily, it points to the relations that must be abstracted from experience, in order to formulate a mathematical law.

one abstract certain properties, one consider only those properties and the relations, those described are considered as fictions, and of course these works by eliminating all the properties, for instance concerning falling buildings the resistance of the air, which always happens, second point, we saw the model of these relations is to be found in the hypothesis of the astronauts.

I guess you remember this model of such relations is to be found in the hypothesis of the astronauts, laws hepatitis, are explicitly described as fictions from.

they are always described as fictions, values astronomical hypothesis are described as fictions, what does it mean?

the most and this few words quite important in the history of philosophy, in modern times the most saves the phenomena, they must save the phenomena, these are strange sentence, but a very important one in western philosophy.

strangers classical calculator rheostat a me a laws for a prediction of the movements of celestial bodies, predictions of the moment of movements of cities notice while, and this is the important point, the hypothetical support of the law does not express in any manner, the reality or their productive causes, the new describes the movements of the cellars bodies, but it does not reach in any manner.

they have true causes, the causes of juice movements, so we came to this point next time, I would like before we go on, I would like to add something, because one of you I think it was you, I don't remember the guy who asked me an interesting questions. so if those laws are fictions, how do they reach experience, we understood their abstracted from the experience from the phenomena, but how do they reach experience again.

that's a difficult point, and I would like to tell you a few words about, this is important, where we're going to Leibniz, it's now in order to answer this question, I would like to tell you a few words about Leibniz, I gave you Descartes last week I guess you remember, he died in seventeen sixty.

I show you the dates of Leibniz, it was the first important German philosopher, the very beginning Leibniz, he wrote this philosopher, wrote an incredible number of texts, they are not all published today, and just to tell you something funny.

you can't imagine how many pages are unpublished, are not published yet, one hundred thousand pages are not published yet, so Leibniz it gives us very important indications on the problem. I’m here considering you must understand my problem now, it does not concern the discovery of the law, we talk about it last time as for instance, now is considering here, this is not my problem, my problem is to understand the application of the law to the experience.

how to justification this application of a fiction two experience of the fiftieth relation to the experience, it is of course at Descartes, that supposition are cleared observe suspicion of merely being fictional ids, those fifty relations are not merely fictional ids.

positions in discussions are not in fact are fictional ideas, but not fictions, the problem is calculations abstract calculation cannot achieve the detail of empirical determinations, but according to Leibniz this does not carry the risk of error in the predictions.

we draw from it there is no risk of error, why?

because Leibniz is considering a very important principle of continuity, he invented this, he invented the principle of continuity. I have to present you that, this principle justifies the approximation of the positions by the compatibility of similar effects, that may produce more nuances hypothesis, that is the main point.

so I’m going to tell you a few words, don't worry there will be the only words in late, but I think that for scientists as you are, it's important to know about the first formulation of these important principles, increase the principle of continuity, so perhaps you might write this, your first words in Leibniz, I guess as perhaps you know late in was scientific and philosophical language of Europe, during a seventeen centuries.

during seventeenth centuries, all is written in Latina, so this is the first formulation of the principle of continuity, that is better all the nineties so date us are ordinate, it's young crazy top in the same way in a similar where in the same way, it's younger is that soon because they are or dinner to that is ordinate, soon all the net this is very important, this is the first formulation of the principle of continuity, what does it mean concerning my problem.

it means that the results predicted by an abstract or effective supposition are not fundamentally different from laws based or on a genuine here hypothesis on the true, if you like genuine hypothesis you understand, so if you consider laws that have been eliminated, they do not fundamentally change the result, if you add use that data, the abstract law, you won't come to a completely different result, and this is very important principle is used by Leibniz in order to justification the application of an abstract law to the experience.

if it's that clear, if you have an equation as now on the principle of continuity, please.

I can't understand it would mean the first level data, the order of data is similar to the order of the results, but what do you mean by the order of data?

all the different things the values effects that are the order of data.

for instance tell you an example, it will be easier, if from the abstract you are predicting a certain effect, this effect will show the same kind of differences, that assuring the data as if there are only small differences in the data, as there will be only small differences in the predicted effects, so there is a very easy way to make you understand this.

I don't know how to you know the French, expression for it the effect of butterfly, you know but this is quite the opposite ， small difference， indeed at us makes a small difference in the effects.

not the butterfly, there are more different data?

yes it's not the same, it's quite the opposite, but this principle of continuity is required to understand how the philosophic and scientists in the seventeenth century, justification to apply an abstract little two phenomena, you understand this is history of science.

the consequence would be continuous, that's it you understood, but it is a very important principle in the birth of classical mechanics.

we're talking here about classical mechanics is that clear, I can't hear.

you don't know I guess you are the authors, can't hear you either, you have said something like a function that is coherent, what about that's just a much better and you will not have data and you can predict the concept and what about the function is period, the results and watch people.

well this is a very hard question.

their first of all they do not consider many phenomena as which or cure like this way, the way you said, but concerning these phenomena as because they do not abandon this principle never, the justification the give is not taken in physics, they take it in metaphysics, so I will tell you later about this, this is a very good question, but the first point is so they do not justification it inside mechanics, they use all the reasons which are philosophical or well indeed metaphysical reasons.

so I tell you later about it, but concerning classical mechanics the results they are considering are coherent, so if there is no other question I told you a few words, I did not intend to speak about last time and we have to go on at the end of my last lecture.

I came to a text of the Descartes on the idea of the sun perhaps you remember, did you receive the polar point the PowerPoint presentation, so you may also get this presentation and so you will be able to read all the texts I mentioned, but I didn't say everything I wanted on this text, so we have to ready to get？

together this text interests me for a very simple reason big out is referring a certain precise general kind of values three values, three different kinds of ids, according to take out, see it again and one kind is referred by the Descartes to the secure positions fictions of the astronomers.

that is to say that's use fictions are important enough, and generally north to understand one general kind of the human mind, so let's read it again I have observed in a number of second of instance, here was a great difference between the objects, and it's ids for instance for example, I find in my mind to wholly diverse ideas of the sun, the one by which it appears to me extremely small rose.

its origin from the senses, and should be placed in the place, in the class of adventitious ids, what are adventitious ids, very easy to understand those ids, you're because of the circumstances, I perceive something and I form that kind of advantage as according to the Descartes, I won't speak of those ids, it is very interesting indeed as fields of heat, but this is not my problem first, the author and that is very interesting, by which it seems to be, many times the sun seems to be many times larger than to hold earth.

he's sticking up on astronomical grounds, that is educated from certain notions born with me, or he is shamed by myself in some author manner these two else, I wrote the text because of the word they got is using in Latina played by myself, in some of the manner who are you model or the manner army factor.

these two ids cannot certainly both resemble the same sun and reason, teaches me that the one which seems to have immediately emanated from it, so the adventitious id is not easy most unlike the idea, when I see the sun does not look like this is not formed like a sun it's not related to know what the same ease to start with.

this i've got when I perceive it, let's go on, so I told you this last during the last class and one two we start from.