What is Einstein's Moon?

With my last post I spoke of Francis Bacon and the mark he left on modern science with his method. I also pointed out, how this proposed method was later championed by none other than Isaac Newton. Further, it was indicated that the base premise of the method, is that there was not to be taken anything that could be considered as a preconceived truth or foreknowledge as a premise. In so that, the only things that could be used as such, where those that had been established by inductive reasoning suggested and confirmed through methods of experimental observation. What I also demonstrated was that this method denies that man has the capacity to know anything that is simply a given despite what I had shown earlier, that science truly could not function without such notions. At the conclusion, I stated there were those, that have denied this program to some extent to contest there are things that we simply know which can be used within the context of “why”, to further our understanding of the world. One such person was René Descartes (1596-1650)

René Descartes was a philosopher, mathematician and physicist. His obvious and best known contribution to mathematics and thereby science is in the founding and development of what is referred to as analytical geometry. This of course is the considering of geometry in the back drop of algebra. It also in turn lends algebra spacial qualities. What many of us, are most familiar with in this regard, is the plotting of algebraic formulas in as to represent space plotted in relation to defining number lines. These are of course known as Cartesian coordinates, named in his honour. This also formed the foundation from which Newton and Leibniz later created calculus. Now if this were not enough, Descartes is also considered the founder of modern philosophy. On the subject of Descartes and philosophy, I will speak in more depth in future posts. For now though, I would like to focus on his thoughts of what the expansion of knowledge should be in terms of science and the method it should follow.

Descartes, as Bacon, was suspect and concerned about what could be considered true. However, in contrast to Bacon, Descartes insisted that deductive rather than inductive reasoning should serve as the base logic for the scientific method. Now this deductive process wasn’t that of the then common type, where one could declare just about anything as the base premise or axiom in terms of what is then to be considered and thus deduced. To illustrate more clearly what form this took, I quote here from his paper entitled, Discourse on The Method: of Rightly Conducting The Reason, and Seeking Truth in the Sciences (1637)

“Among the branches of philosophy, I had, at an earlier period, given some attention to logic, and among those of the mathematics to geometrical analysis and algebra, -- three arts or sciences which ought, as I conceived, to contribute something to my design. But, on examination, I found that, as for logic, its syllogisms and the majority of its other precepts are of avail- rather in the communication of what we already know, or even as the art of Lully, in speaking without judgment of things of which we are ignorant, than in the investigation of the unknown; and although this science contains indeed a number of correct and very excellent precepts, there are, nevertheless, so many others, and these either injurious or superfluous, mingled with the former, that it is almost quite as difficult to effect a severance of the true from the false as it is to extract a Diana or a Minerva from a rough block of marble.”

Here we discover that Descartes, much like Bacon, was concerned with what could be considered true. In the next quote he states that he was in search of a method for science that would contain reliability and precision for he says:

“I was induced to seek some other method which would comprise the advantages of the three and be exempt from their defects.”

So what Descartes has said is that although there is much that is true in what he considered the somewhat unreliable sciences, he needed to find a method by which the reliability and thus the utility of science could be improved. To begin he lays out his method in four parts, the first being as follows:

“The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.”

Here as Bacon had stated, all should be considered with the element of doubt, where nothing can be simply taken as a given. However, unlike Bacon, Descartes has already suggested, that there are some things that by there very nature can be taken as true. He also suggests that this judgement is to be found within ones self and not externally. Something that I would view as almost considered instinctive reason, for lack of a better term. The next step he states as:

“The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.”

Here again, just as Bacon had insisted, things must be first broken down into all things that might be considered. Now Descartes next step is explained in the following.

“The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.”

Still from what has been said, the methodology of Bacon and Descartes are looking pretty much the same as Descartes says that not only should ideas be broken down into the smallest parts possible. He futher suggests they be assigned order, whether or not they at first appear to have priority of importance or that of connectivity of structure. He is talking about acending in small steps, which would normally relate to a bottom up approach, which on the face of it looks like a inductive process. He completes his four steps with the following:

“And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.”

Now at this point you may be confused, as to why I consider there is a distinction to be made between Bacon and Descartes in terms of their methods. From what has been revealed up to now, it appears that Descartes is just restating what Bacon said some 17 years prior, without perhaps the mention of observation, although it has not been excluded. It also seems to be shaping up to be performed within a inductive frame work, that would be satisfied as in Bacons method, only through exhaustion. But now in the following we find that the system of reasoning that Descartes insists to be primary in its execution, is not induction at all, for he now states;

“The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another.”

Despite the similarity in the preamble, we now discover, that what Descartes has in mind as the principle method of reasoning, is that of deduction and not of induction. It's not hard to imagine why Descartes feels this way, for as I mentioned before and he himself here eludes, that he was also a great mathematician. Mathematics in the main is a deductive process, building from what are referred to as axioms, that are used as premises, to deduce further truths. Bacon on the other hand, avoids for the most part this method and not surprisingly so, for he was not a mathematician as was Descartes. Bacons primary training and occupation, was that of a lawyer. In the few scientific explorations he did conduct, he excluded the use of mathematics almost entirely. I must also relate, that he had little success. Now that Descartes has set up this program of discovery, he finds himself with a bit of a dilemma, as now, what is he going to use as his axiom(s), to begin this step by step deductive process? After all, he has, as Bacon did earlier, dismissed all prior known truths. What then is he going to utilize as his foundation on which to build his deductive method? Here we now witness Descartes in his eureka moment, for he states;

“But immediately upon this I observed that, whilst I thus wished to think that all was false, it was absolutely necessary that I, who thus thought, should be somewhat; and as I observed that this truth, I think, therefore I am (COGITO ERGO SUM), was so certain and of such evidence that no ground of doubt, however extravagant, could be alleged by the sceptics capable of shaking it, I concluded that I might, without scruple, accept it as the first principle of the philosophy of which I was in search.”

Now Descartes has discovered, his first and primary truth, from which he proposes that all the others will follow and in turn proved is to be, he “thinks” so therefore he “is”. He contends here he has found the bedrock truth that he feels that no one can dispute and that is they exist. This, like many other statements in history, have been repeated so many times, that they tend to become completely misunderstood. Some for instance imagine, that this means that only things that “think”, “are“. That is because many do not understand the deductive process, for they imagine that like a equation this suggests that (think = am). That would mean that to write (am = think) is the same. Now to compare, what if I said , I “walk” so therefore I “travel”. If this were then interchangeable, you could say, since I “travel” so therefore I “walk”. I don’t know about you, but I take the bus some times. Also, it could thus be suggested, that baseballs have legs. No, deductive reasoning is very precise, for it only holds that what is deduced from the premise is true, not that it is equal to the premise.

So now we have discovered, that Descartes has proposed a method, in which the deductive process serves as its primary system of logic. It must be also made clear that he does not entirely omit the inductive process, which in science is rooted in its observations. He however warns, that in these observations that deduction must also play a role for as he states:

“But this is certain, and an opinion commonly received among theologians, that the action by which he now sustains it is the same with that by which he originally created it; so that even although he had from the beginning given it no other form than that of chaos, provided only he had established certain laws of nature, and had lent it his concurrence to enable it to act as it is wont to do, it may be believed, without discredit to the miracle of creation, that, in this way alone, things purely material might, in course of time, have become such as we observe them at present; and their nature is much more easily conceived when they are beheld coming in this manner gradually into existence, than when they are only considered as produced at once in a finished and perfect state.”

What Descartes is pointing out with this, is that to observe something as it is and then therefore suppose it is, as it was always, is a mistake. Therefore, one must also consider it may have come from something or things simpler perhaps and to look to this also as a possible explanation of outcomes in observation. He is saying that induction is therefore vulnerable with this flaw and it is only by deduction that we may be able to avoid this. What is also interesting to note, is that this is turn would later serve as the seeds of discoveries, such as Darwin’s. In as Descartes suggests with this, that the world is not so much a place of being, but rather a place of becoming, as to what it will be. It is of no wonder with such thoughts, that shortly after his death, the Vatican put some of his writings on the forbidden reading list.

Now once again we have come to the question, so what is my point? Actually I have a few. The first, is to indicate the differences between the methods of deductive and inductive reasoning, when used as science’s base. In the inductive process, where observation plays the primary role, truth is formed by consensus or the weight of evidence rooted in a statistical background. If all the available observations support a conclusion, then it is considered to be true. In the deductive process, truth is only established with reason derived from a premise, which is a self evident truth or has been before deduced from one. Both are processes that attempt to relieve doubt. However, in the inductive process, with nothing pre-established as truth, what is proposed is only as good as the observations taken and the methods so used to consider them. In deductive reasoning, everything is derived from the premise, the only remaining doubt is that of the soundness of the initial truth and the correctness of the connections made with subsequent deductions. In deduction, we must look to the premise and only that to be sure. In induction, we have to not only trust our observations, as to their quantity, but also the quality of them. It must be also assured that the inductive statement then formed is a strong one, in the context of the data collected. In the deductive process, the demanded first requirement is to initially ask “why”. To realize this, lets look to what Descartes must have done to come up with his initial premise. He would have had to at first asked, “why” am I certain that I “am“? His answer would then have followed because I “think”. With this one may see more clearly that the function of “why”, is to lend certainty to man's understanding and thereby of nature's, so that we might have firm footing to further explore its aspects of purpose and thereafter perhaps its utility, in concert with other means presented or at our disposal. This is what Descartes so discovered and which I most certainly agree is so.

As a post script to this, I would like to address as to what happened to Descartes ideas, in the context of their current application to science. Descartes today, is viewed as primarily a philosopher and by many a great one at that. He is not however, considered much as a scientist, despite the fact that he is also acknowledged as the founder and father of analytical geometry, that science still covets and from which also Newton required in the course of discovering calculus. I would contend, that not only for his refinement and promotion of this deductive method, which I have attempted to explain, but also stressing that the “why”, plays a role in understanding, that he was then so dismissed. As evidence of this, I will make one final quote. This quote is of Voltaire, who discussed in the following, just what I have contented. Here he is to be found using Newton as the comparison in this regard upon a visit to England in the mid 1700‘s. ;

We may admire Sir Isaac Newton on this occasion, but then we must not censure Descartes.

The opinion that generally prevails in England with regard to these new philosophers is, that the latter was a dreamer, and the former a sage.

Very few people in England read Descartes, whose works indeed are now useless. On the other side, but a small number peruse those of Sir Isaac, because to do this the student must be deeply skilled in the mathematics, otherwise those works will be unintelligible to him. But notwithstanding this, these great men are the subject of everyone's discourse. Sir Isaac Newton is allowed every advantage, whilst Descartes is not indulged a single one. According to some, it is to the former that we owe the discovery of a vacuum, that the air is a heavy body, and the invention of telescopes. In a word, Sir Isaac Newton is here as the Hercules of fabulous story, to whom the ignorant ascribed all the feats of ancient heroes.

So to conclude, I would submit, that the fear Voltaire expressed as to the fate of Descartes and thereby his ideas, has come to pass. It is then not to wonder, why, lesser persons choose not to follow the route of Descartes, but rather that of Newton's, to avoid such. This then is not to say that no one has since. As there have been a few. These few in turn, have also broadened the insight of humanity and yet as Descartes, have in there own way also been made to pay the price. About these people and other related things I will continue to speak of in future posts.