Tuesday, February 16, 2010

Bacon on the "Helps" of Induction

Introduction: Some Context

In the 17th Century, Francis Bacon wrote a two-book work, the Novum Organum (New Instrument). Its aims were extraordinarily vast, covering both theoretical and practical goals. Bacon proposed a new epistemology, a new way to reach knowledge, to form concepts or notions, and to know the true causes of natural events—induction, as Bacon proposed it, would be the "new instrument" which would bring us to a greater understanding of things. Practically, induction, properly carried out, would lead to a full control of nature by mankind, and thus to a general improvement of our condition in the world.

His theory of induction is a bit technical, to say the least. To fully understand it, one would need to know a little bit about the general aims of the natural magic tradition (such as alchemy), a great deal of Aristotle's philosophy, particularly its metaphysics, physics, and epistemology (especially the treatises on logic collectively known as the "Organon"), and the Scholastic philosophy which revamped Aristotle's.

Instead of discussing all that, I'll save it all for another time, and focus now on nine things that Bacon said are helps in our ability to properly inductively reason.

The Aids and Supports of Induction

In book two of his Novum Organum, he presents an illustrative case of his method of induction in action, by investigating and discovering what he takes to be the essence, or true cause (or Bacon's term "form") of heat. Afterward, he mentions that there are additional things which assist in this inductive process:
I propose to treat, then, in the first place, of Prerogative Instances; secondly, of the Supports of Induction; thirdly, of the Rectification of Induction; fourthly, of Varying the Investigation according to the nature of the Subject; fifthly, of Prerogative Natures with respect to Investigation, or of what should be inquired first and what last; sixthly, of the Limits of Investigation, or a synopsis of all natures in the universe; seventhly, of the Application to Practice, or of things in their relation to man; eighthly, of Preparations for Investigation; and lastly, of the Ascending and Descending Scale of Axioms. (Novum Organum, Book 2, Aphorism 21)
I'll offer some general (and a few particular) comments on these nine additions to his inductive method, though only the first (Prerogative, or Privileged, Instances) is exhaustively discussed by Bacon himself.

Privileged (Prerogative) Instances

The inductive investigation of the causes in nature are saturated with observations of phenomena, of natural instances, of recordings of natural events. But not all events or things in nature are equal in terms of the interest we should pay to them; some are clearly more important for induction than others. Privileged instances are such because they assist in finding the essence of a nature and thus reach the induction's conclusive generalization quicker and with a greater degree of truth than ordinary instances.

He lists 27 different kinds of privileged instances, with some having subdivisions, so I'll only discuss a few. (I plan on writing a comprehensive account of these 27 in a later essay, to better understand this aspect of Bacon's inductive theory.) Striking instances are instances which display a nature being investigated most vividly and in great force, "standing naked," as Bacon terms it, and one of the examples is a natural magnet (lodestone) compared to other objects in relation to attractive force. Another kind are constitutive instances, which together are one species or kind of the nature being investigated, a kind of "lesser form." (In Bacon's view, the essence or form is invariably present when the nature is present, so he's saying that this "lesser form" wouldn't always exist in every manifestation of the nature in question.) Constitutive instances are important because the discovery of forms (and thus the formation of the highest generalizations/axioms) will often result from piecemeal generalizations, or the identification of less general forms. "For whatever unites nature, even imperfectly, opens the way to the discovery of the form," Bacon points out (Bk 2, Aphorism 26).

(I've discussed what I think Bacon's term "form" means in my essay, "The Importance of Concepts for Bacon." As for the idea of piecemeal generalizations leading to the highest axioms and knowledge of forms, see Ducheyne's essay "Bacon's Idea and Newton's Practice of Induction".)

The most famous of these prerogative instances are crucial instances, instances which are decisive in determining which of several theories (if any) have correctly identified the cause of a given nature. Instances of this kind have emerged many times in the history of science, perhaps first occurring with Newton's theory of optics and the nature of white light, as his experiment with lights and prisms devastated the long-standing opposing theory, that white light was pure and unmixed.

Supports and Rectifications of Induction

It's unfortunate that Bacon never gets to these parts of his theory, as they certainly would have helped expand and strengthen his account of induction. His theory on induction tentatively points to some things which he might have brought up in his presentation of "supports" for induction, and what would assist in correcting an erroneous one ("rectification"), but nothing which stands out enough to comment on here.

Varying the Investigation according to the Nature of the Subject

Again, Bacon never directly addresses this point, but does offer some leads. Typically, Bacon suggests making detailed observations of nature and experiments carried out, but admits that this is not always possible, such as the field of astronomy, which deals with incredibly far away objects. An investigation may vary depending on what prerogative instances, if any, are already available, and if they can or cannot be organized in an orderly structure.

The availability of tools or status of inventions may also change the direction of an investigation, in that it may preclude more liberal generalizing and inducing. Two examples illustrate this. Charles Darwin ended his investigation of the origin of species with conclusions pertaining to external, environmental factors, and long spans of time. He didn't have the technological means to investigate the internal workings of plants and animals and thus complete his theory. (Also, he assumed that the traits passed down to offspring were "mixed" within them, and never thought to observe several generations of a species to confirm if his idea was true; Mendel, the forerunner of genetics, famously did this very experiment within Darwin's own lifetime.) Secondly, Newton ended his theory of gravity with a mathematical description of it as a force which is pervasive within the universe, but had no means to investigate what accounts for gravity, or even why it acts on objects "at a distance," without any obvious intermediate agent.

Prerogative Natures with respect to Investigation

Prerogative natures, I would presume, are natures which expedite the discovery of forms and process of induction. When investigating the causes of things, we shouldn't study them at random, but rather what seems to be relevant and that will assist in investigating a certain subject. Things that can be readily studied should go first, because Bacon holds that we should begin our inductive investigations with what is perceptible by the senses and observed, and the last natures to be studied would presumably be the forms themselves, the general laws that objects are subject to.

Limits of Investigation

Bacon says that this is a synopsis or summary of all natures in the universe, something similar to a natural dictionary or even something as detailed as an encyclopedia for the natural world. This would be immensely helpful, as it could spark new inquiries on subjects no one has thought to look into, or to improve upon the natures we've already investigated.

Application to Practice

Bacon says that this is what relates to man, and from the import of his book, I think he's referring to practical concerns, the welfare and "estate" of man. The results of an inductive theory lead to new experiments, possible ideas for inventions, and innovations for instruments already being used. One of the major roles of induction was to allow us to have greater control over the causes in nature, to increase our power, and improve our lives, which is precisely what applying our investigations to the practical issues of our lives accomplishes.

Preparations for Investigation

Bacon notes in book 2, aphorism 32 that five of the prerogative instances which I'll address in another essay (singular, similar, deviating and bordering, and power instances, specifically) should be used as a preparative for the mind towards the path to true notions. These instances correct the mindset of those whom are affected by the habits and impressions of daily life. The whole of book 1 seems to prepare our minds for his version of induction, and hence to prepare to investigate any subject, so I'm not sure what else Bacon would have in mind here.

Ascending and Descending Scale of Axioms

Since Bacon's induction can be described as a progression from individual fact to the highest axioms and back, and this point was covered in book 2, I'm really interested in what Bacon might have said about this "ascending and descending." Perhaps it would have been a more theoretical discussion of natural laws, and how induction is involved with them? "Axiom" is one of the most important, and least discussed, concepts in Bacon's philosophy, and any more information would have been incredibly beneficial for those who study him, such as myself.

Conclusion

And so ends my comments on the "helps" of induction Bacon mentions. With the exception of prerogative instances, what I've said here are only my perspective on aspects of Bacon's philosophy, and shouldn't be interpreted as Bacon's thought. If I learn anything else pertaining to these nine points, I'll be sure to discuss them some other time, though I doubt I will.

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