Sunday, July 12, 2009

Bacon's "More Certain and Guarded Method" of Induction

"[...]our determination is that of trying, whether we can lay a firmer foundation, and extend to a greater distance the boundaries of human power and dignity."[Bacon, New Instrument, Book 1, Aphorism 116]
"Our only hope, then, is in genuine induction."[ibid., Aphorism 14. See here: The Ideas that Have Influenced Civilization, in the Original Documents]
Francis Bacon (1561-1626) was the first modern philosopher of science, and was instrumental in the development of what we now call the “scientific method.” Here are the essentials of his method of induction, which unfortunately was never completed.

(The incompleteness was due to his bronchitis-induced death—in turn caused by being outside in frigid weather while testing his theory on the preservative and insulating properties of snow through experimentation: the experiment involved stuffing a chicken full of said snow. As should become clear later, this practice of experiment was Bacon putting his method of induction into practice.)

Tables of Induction and Research

Bacon thought that induction (1) begins with sensory experiences (the five senses, feelings of pain and pleasure, for example), and (2) also involves detailed observations of similarities and differences among everything that happens in nature (including human inventions), in reference to a subject that one wants to investigate further (the nature of tides, insects walking on vertical surfaces, etc.). He gives ample examples of (1) and (2) in his two-book work, Novum Organum (“New Instrument”), while investigating the nature of heat; one example being the differences in heat between insects and other animals, noting that the heat in insects cannot be felt by our sense of touch (attributing this to their small size). (The "New Instrument" is available free on the internet to read.)

This observation of similarities and differences among existents is crucial for Bacon, as it lays the groundwork for true inductions. In Bacon’s words, “…we must first prepare as a foundation for the whole, a complete and accurate natural and experimental history.” In effect, he argued that a research program of some sort was needed to compile the data and observations needed for a sound induction, deliberately carried out by many individual natural philosophers (scientists). Coextensive with this research, we should organize the empirical data into a certain order of tables, so as to avoid being confounded by the abundance of (seemingly) disparate and varied information. These tables, which Bacon calls “a review of instances to the understanding [a.k.a. the faculty of reason, in Objectivist language],” are essentially what Steffen Ducheyne describes them as in his essay, “Bacon’s Idea and Newton’s Practice of Induction” (page 118 in the pdf):

(1) The table of essence and presence, which enumerates all situations in which the nature under consideration is present (cf. “all instances that agree in their Nature, though by different matters”[…]).
(2) The table of deviation or absence of degrees, which lists all situations which are as similar as possible to the first table, but where the nature under consideration is absent.
(3) The table of counter-instances [comparative instances], which suggests experiments in order to search possible counter-examples.
Bacon’s elaboration on these tables, including the examples he describes while discussing them, gives us two insights into his method: negative inductive inferences, and the importance of experimentation.

Experimentation and Negative Induction (Eliminative Reasoning)

Regarding experiment: he didn’t believe that we should simply observe nature and its effects, even though, occasionally, interesting things happen naturally which could expand our knowledge; one example could be our knowledge of "heat" when we consider the existence of lightning (being observably different from the heat generated in fire or animals for instance). Rather, he thought that we should actively intervene into natural events, deliberately controlling certain factors while manipulating others to discover previously unobservable, latent processes (or at least gain more data on which to hypothesize such processes).

He is also original here in thinking that there is no significant difference between natural occurrences and events produced through human intervention into nature (man-made events), and as a result, he concluded that man-made experiments are just as reliable and necessary for sound inductions as events which occur without any deliberate human actions, if not more so. (For early examples of experimental method, see James Lind’s experiment on treating scurvy, and Jan Baptist van Helmont’s experiment on willow trees, both of which are on Wikipedia.)

Experimentation was crucial for Bacon’s method of induction, as it served three functions (to my knowledge):

(1) Experiments greatly assisted in the collection of data on which to base a theory (instead of simply relying on observations of nature, which cannot give us an opportunity to penetrate into the more complex causes of phenomena). More precisely, they led to stronger samples or evidence from which one could generalize, as the experiment(s) would potentially rule out other plausible hypotheses.

(2) Experiments could be derived from low-level generalizations or hypotheses (“living” or “lesser” axioms in Bacon’s terms), and were instrumental in validating the hypotheses within a certain range (and eventually, a certain domain) of facts. And this in turn would be required to widen the hypothesis’s domain and potentially discover the latent, unobservable processes of nature, leading to even more universal generalizations or theories (“medial” or middle axioms, and lastly the general and “universal” axioms).

(3) Experiments and deductive reasoning could be employed in order to demonstrate that the cause discovered and described in a universal axiom or theory is the true cause of the effects one investigates and studies (the actual “form” of nature, as Bacon would put it). Experiments are integral in showing that no other purported cause can explain the nature under investigation, as experiments with negative results epistemologically justify “ruling out” alternative theories and causes proposed. As summarized by Antonio PĂ©rez-Ramos (and quoted in Ducheyne’s paper I linked to): “The capacity of (re)producing Nature’s ‘effects’ was perceived as the epistemological guarantee of man’s knowledge of natural processes in the external world.” (I will comment that Bacon believed his method of experimental-induction could be applied to all fields of study, including our minds, the “internal world," if you will, not only the external world.)

I’ll note that while Bacon wasn’t the first person to advocate experimentation as a means of discovering knowledge about reality (for instance, see Alhazen (c. 965-1040) and his Book of Optics), he was the first to assert that identification of causal relationships through experiment was a requirement for a valid induction and had to be incorporated into a sound theory of induction.

Lastly, the “ruling out” I just discussed, in regard to experiments, is carried out by an “exclusion table”: this fourth table lists rejections of supposed causes of the phenomena being investigated, and thus further lays the foundation for a true induction by delimiting the objects one must now focus on. In this way, experiments, the tables of induction (“presence, absence, and counter-instances”) and the table of “exclusion” lead to negative inductive inferences regarding some purported causes and the phenomena which are thought to be the effects.

(One example being Woodward’s experiment on plants following Helmont’s own, and Woodward’s correct negative inductive generalization—against Helmont’s conclusion—that it is never water
alone which accounts for plant growth in soil that does not come from the soil itself. Historically, this correction of Helmont's conclusion was the beginning of the photosynthesis theory of plant growth.)

Interplay of Induction and Deduction

What I’d like to point out now is his view that forming proper inductions involves regular use of deduction grounded in piecemeal inductions (and ultimately universal inductions) and experiments. My earlier section on experimentation basically covers the induction-deduction interplay found in Bacon’s method of induction, so I’ll only add a few comments.

Deduction, reasoning from generalizations to particular cases (in contrast to induction, reasoning from particulars to generalities), appears to play a two-fold role in Bacon’s view of induction:

(1) Integrated with certain elements—namely, evidence, experiments, and a hypothesis or theory—deductions (predictions) of what the hypothesis/theory entails about reality serve to partially confirm the hypothesis if the deductions are shown to be true through further experiments, strengthening the induction’s explanatory power and opening the way to further modification, expansion of what the hypothesis is explaining, and generally to more building upon the same theory.

(2) Faulty predictions/deductions mean that either (i) the hypothesis/theory one is working on contradicts the facts and should be abandoned (or salvaged through modification, or replaced by a better theory), or that (ii) the experimental and/or research methods used in forming the hypothesis are incorrect/inaccurate.

Bacon also noted that inductive axioms (hypotheses/theories) are capable of being modified and expanded in the light of improved experiments and data gained from research, so this is another way in which deduction affects induction. And, as a result, this modified or expanded inductive theory will lead to new deductions/predictions and experiments, so it’s also a way in which induction affects deduction. For Bacon, then, the methodized use of induction is an open-ended process, in which the hypothesis is formed from evidence and checked for accuracy by experiment and deductive thinking, leading to the expansion or modification of the theory in regards to the amount of phenomena it is causally explaining, allowing individuals to do more testing and applying the working hypothesis or theory to further practical tests, and so on (until it determinates in true knowledge of the forms, Bacon would insist).

As a final comment before concluding, I’ll say that Bacon’s theory of induction does not extend much beyond what I’ve said thus far. While he notes that there are nine other elements to his theory in addition to the four tables, heavy use of experimentation, and the formation or sketching of a hypothesis/low-level axiom (which he calls a “First Vintage”), he never has the chance to elaborate on the vast majority of these elements. (He discusses the first element in lengthy detail, namely the “prerogative instances” which can allow one to decide between two competing hypotheses/theories; he also elaborates on the eighth element, “preparations for investigation [preparations for a natural history],” but they are of little help without his fully elaborated theory.)


Bacon viewed his version of induction as a valuable assistant to our very limited senses and unguided (and error-prone) reasoning capabilities. Though plagued by erroneous habits of mind that could wreck our success of discovering knowledge (and which had already done so in the past, Bacon would insist), he thought his method would help any person penetrate into the real nature of things. Along with this view, he thought it would validate our conceptual knowledge (our “notions,” as Bacon referred to them) and inductive generalizations, thus broadening the practical applications and industry of human affairs to areas never before attempted.Summarized, Bacon’s theory of induction is something along the lines of: a method of reasoning from observation of effects and experiments which gradually ascends to universal inductive generalizations and the discovery of causes through building on top of piecemeal generalizations, and regularly descends to effects (further experiments, predictions of phenomena).

Sections of “New Instrument” of Potential Interest

[As an example: “Bk 1, A23,” means: Book 1 of New Instrument, Aphorism 23. Please note that each aphorism in Bacon’s book is numbered as a section, with usually multiple paragraphs in each section.]

Tables of induction: (Bk 1, A102; Bk 2, A10-19)

Research: (Bk 1, A85, end of A98, A101, Bk 2, A14)

Experimentation: (Bk 1, A18, A50, A70, A82 (third paragraph), A88 (3rd paragraph), A98-99; in book 2, discussion of experiments is found throughout)

Interplay between induction and deduction (Bk 1, A103-105, first paragraph of A117, A118 (true inductions can rule out proposed deductions), third paragraph of A121

Applicability of induction to all fields of study (Bk 1, A127)

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