In her Introduction to Objectivist Epistemology (ItOE), Rand presents a theory of concepts, which describes what concepts are (as opposed to what they are not) and how they are properly formed (and how they are improperly formed). A concept, Rand maintains, is a “mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.” (ItOE, 2nd Edition, p. 13)
Monday, July 27, 2009
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]Sir 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.
Induction's Bad Reputation
[Originally posted on Facebook]
In my note "Aristotle on Induction," commenter Brian Tinker raised a good question:
Most people understand induction to be "by enumeration." Something like: "All of the enumerated cases of swans I've observed are white, therefore all swans are white," or "the sun has always risen, therefore it will rise tomorrow (and the next day, etc.)."
Philosopher Bertrand Russell (1872–1970) gives another example, through parable, of "induction by enumeration" in his book The History of Western Philosophy, page 543. The parable begins: A census officer is questioning homeowners in a village, all of whom seemed to have the same name, William Williams. Finally, the officer decides that every homeowner in the village is named William Williams (an enumerative induction), records the names, and takes a holiday. But he was mistaken: there was one man named John Jones who owned a home there, but the officer had missed him.
This means that the induction is faulty, and illustrates the problem—that inductions by enumeration are never certain; one counter-example can ruin even the strongest of inductive generalizations.
Francis Bacon, the first modern philosopher of science, points out the basic problems with enumerative induction (a criticism which I agree wholeheartedly with):
Also, I agree with Dr. Leonard Peikoff's comments on enumerative induction in a lecture course that he presented some years ago:
In my note "Aristotle on Induction," commenter Brian Tinker raised a good question:
Given what you and [Edwin] Locke [in this paper] have said about induction, why does it have such a bad reputation?I think some of its bad reputation is earned: a very small part, that is. Let me explain.
Most people understand induction to be "by enumeration." Something like: "All of the enumerated cases of swans I've observed are white, therefore all swans are white," or "the sun has always risen, therefore it will rise tomorrow (and the next day, etc.)."
Philosopher Bertrand Russell (1872–1970) gives another example, through parable, of "induction by enumeration" in his book The History of Western Philosophy, page 543. The parable begins: A census officer is questioning homeowners in a village, all of whom seemed to have the same name, William Williams. Finally, the officer decides that every homeowner in the village is named William Williams (an enumerative induction), records the names, and takes a holiday. But he was mistaken: there was one man named John Jones who owned a home there, but the officer had missed him.
This means that the induction is faulty, and illustrates the problem—that inductions by enumeration are never certain; one counter-example can ruin even the strongest of inductive generalizations.
Francis Bacon, the first modern philosopher of science, points out the basic problems with enumerative induction (a criticism which I agree wholeheartedly with):
The induction which proceeds by simple enumeration is puerile, leads to uncertain conclusions, and is exposed to danger from one contradictory instance, deciding generally from too small a number of facts, and those only the most obvious. [Bacon, Novum Organum (New Instrument), Book 1, Aphorism 105.]Bacon summarizes why most philosophers (in my opinion) denigrate induction, and why it has a bad reputation. Since what he points out about enumerative induction is true, it is my reason for thinking some of induction's bad reputation is earned.
Also, I agree with Dr. Leonard Peikoff's comments on enumerative induction in a lecture course that he presented some years ago:
Induction in my judgment is not in any sense a matter of quantity. There's a type of induction called induction by simple enumeration, which means induction simply by enumerating or counting instances. [...]Now, I regard quantity as such as insignificant. It entirely depends on what happens to that quantity, which can be a good suggestive beginning if you see something happening. What happens when you integrate it with everything else you know that's relevant? (Art of Thinking, Lecture 2)While enumerating cases can be instructive in forming ideas, noting similarities and differences, and in figuring out how rare or widespread certain phenomena may be (say, meteoroid impacts), I think it's a poor candidate for valid inductive thinking.
Aristotle on Induction
According to Aristotle, Socrates is the first person known to discuss induction and general definitions:
An example would be forming the concept "animal": we can observe with our senses the similarities among individual species (humans, dogs, mules, etc.) and how different they are from both inanimate objects and other life-forms which don't seem to be conscious (plants would largely be our data for this conclusion)--all of this could eventually lead to forming the concept "animal" through induction. (Also, it might lead to concepts such as "consciousness," "awareness" "life," "mobility" and concepts of particular animal species.)
Relatedly, he thought that induction is part of the means of forming general concepts ("genus") and, from there, building even more generalized concepts utilizing the knowledge gained from the earlier-formed ones. An example Aristotle gives is the inductive forming of the genus "animal" from the various animal species, and this kind of reasoning is the first lead to the formation of an even wider generalization; in our present context, we can integrate plants and microscopic lifeforms with our knowledge of the "animal" genus into a wider genus "organism." Regarding induction and concept-formation, Dr. Edwin Locke summarizes Aristotle's position this way:
Lastly, as I noted earlier, Aristotle believed that induction was the basic or founding rational activity; the other main reasoning process, deductive thinking, was held to be a product of inductive thinking. Induction was thus logically antecedent to deduction, as it supplies the premises from which one can deduce.
References
On perception as validly giving knowledge/experience of reality:
On the Soul (Latin: De Anima), Book II, Chapters 6-12, and Book III, chapter 3, 427b27-428a18.
In the latter chapter, Aristotle even notes: "for perception of the special objects of sense [like "color" for the sense of sight] is always free from error, and is found in all animals..." (427b11-13) Also, his biological treatises, such as History of Animals (Historia Animalium) and Parts of Animals (De Partibus Animalium), are filled with evidence that he affirmed sense-perception as a means of knowing reality.
Induction as the foundational form of reasoning:
Rhetoric (Ars Rhetorica), Book II, chapter 20, 1939a25-27.
Induction as based on sense-perception, and as reasoning from "particulars" to "general":
Topics (Topica), Book I, chapter 12.
Induction and concept-formation:
Posterior Analytics (Analytica Posteriora), Book II, chapter 19, 100b1-5.
Dr. Edwin Locke, "The Case for Inductive Theory Building," Journal of Management, Vol. 33, No. 6, (2007).
Induction, as supplying premises used in deductive thinking and argument:
Posterior Analytics, Book 2, chapter 19, 100b3-5, when compared with Book I, chapter 3, 72b23-29.
On Socrates being the originator of the study of induction:
Aristotle, Metaphysics, Book XIII, Chapter 4, 1078b25-30.
P.S. Chapter 1 of McCaskey's dissertation goes in-depth into Aristotle's conception of induction, so my summary here may be expanded in the future if I learn of anything significant in this different account.
...for two things may be fairly ascribed to Socrates—inductive arguments and universal definition, both of which are concerned with the starting-point of science [knowledge])...[Aristotle, Metaphysics, Book XIII, Chapter 4, 1078b25-30]Induction is the foundational reasoning activity and is built upon sense-perception. More specifically, induction is (following Socrates's practice) reasoning from particular cases or individuals to general or universal knowledge.
An example would be forming the concept "animal": we can observe with our senses the similarities among individual species (humans, dogs, mules, etc.) and how different they are from both inanimate objects and other life-forms which don't seem to be conscious (plants would largely be our data for this conclusion)--all of this could eventually lead to forming the concept "animal" through induction. (Also, it might lead to concepts such as "consciousness," "awareness" "life," "mobility" and concepts of particular animal species.)
Relatedly, he thought that induction is part of the means of forming general concepts ("genus") and, from there, building even more generalized concepts utilizing the knowledge gained from the earlier-formed ones. An example Aristotle gives is the inductive forming of the genus "animal" from the various animal species, and this kind of reasoning is the first lead to the formation of an even wider generalization; in our present context, we can integrate plants and microscopic lifeforms with our knowledge of the "animal" genus into a wider genus "organism." Regarding induction and concept-formation, Dr. Edwin Locke summarizes Aristotle's position this way:
His view was that one groups entities according to their perceived similarities and identifies their essential characteristics, the essence of a kind ... [t]his included the formulation of definitions based on genus and differentia [a genus--integrating the concept into a wider category—and a differentia—differentiating the concept from other existents in that genus, namely, man is the rational animal—meaning he is the animal who has the capacity to reason].[Dr. Edwin Locke, The Case for Inductive Theory Building, Journal of Management, Vol. 33, No. 6, page 870 and 881 in brackets (2007)]
Lastly, as I noted earlier, Aristotle believed that induction was the basic or founding rational activity; the other main reasoning process, deductive thinking, was held to be a product of inductive thinking. Induction was thus logically antecedent to deduction, as it supplies the premises from which one can deduce.
References
On perception as validly giving knowledge/experience of reality:
On the Soul (Latin: De Anima), Book II, Chapters 6-12, and Book III, chapter 3, 427b27-428a18.
In the latter chapter, Aristotle even notes: "for perception of the special objects of sense [like "color" for the sense of sight] is always free from error, and is found in all animals..." (427b11-13) Also, his biological treatises, such as History of Animals (Historia Animalium) and Parts of Animals (De Partibus Animalium), are filled with evidence that he affirmed sense-perception as a means of knowing reality.
Induction as the foundational form of reasoning:
Rhetoric (Ars Rhetorica), Book II, chapter 20, 1939a25-27.
Induction as based on sense-perception, and as reasoning from "particulars" to "general":
Topics (Topica), Book I, chapter 12.
Induction and concept-formation:
Posterior Analytics (Analytica Posteriora), Book II, chapter 19, 100b1-5.
Dr. Edwin Locke, "The Case for Inductive Theory Building," Journal of Management, Vol. 33, No. 6, (2007).
Induction, as supplying premises used in deductive thinking and argument:
Posterior Analytics, Book 2, chapter 19, 100b3-5, when compared with Book I, chapter 3, 72b23-29.
On Socrates being the originator of the study of induction:
Aristotle, Metaphysics, Book XIII, Chapter 4, 1078b25-30.
P.S. Chapter 1 of McCaskey's dissertation goes in-depth into Aristotle's conception of induction, so my summary here may be expanded in the future if I learn of anything significant in this different account.
First Suggestion for Induction
In a dissertation by Dr. John McCaskey that I'm currently reading, it is noted that Aristotle appears to know exactly what induction is whenever he discusses it in his works. Aristotle,
One day, I would like to have that level of confidence in my understanding of induction, even if it will probably differ from that of Aristotle's. In fact, we should all strive to achieve his level of understanding.
My first suggestion then for induction is to gain some basic knowledge of it from everyday life, and use this knowledge to become more familiar with its basic method, to make it more obvious. Taking an alternative approach, such as immersing oneself in the heated philosophical controversies over the issues of induction, might leave one bewildered by--and unprepared for--the many variants of the method that now exist.
To conclude, I suppose I'll give a rough definition of what induction basically is, the very one that Aristotle thought was obvious: a kind of reasoning that moves from particular cases or instances to general or universal knowledge about those kinds of particulars.
Next, I offer what I think Aristotle says on induction.
never suggests that his theory of induction is problematic, complicated, or controversial. He never presents a catalog of competing theories of induction (as he frequently does for other matters), never says there are multiple ways of understanding induction, never says he will consider a kind of induction different from that usually discussed, never even explains fully what induction is." (Page 17 of "Regula Socratis: The Rediscovery of Ancient Induction in Early Modern England.")In short, Aristotle was neither confounded by induction nor ignorant as to what its practice consisted of. On the contrary, readers of Aristotle are told in his work Topics that "[w]hat sort of thing induction is, is obvious."
One day, I would like to have that level of confidence in my understanding of induction, even if it will probably differ from that of Aristotle's. In fact, we should all strive to achieve his level of understanding.
My first suggestion then for induction is to gain some basic knowledge of it from everyday life, and use this knowledge to become more familiar with its basic method, to make it more obvious. Taking an alternative approach, such as immersing oneself in the heated philosophical controversies over the issues of induction, might leave one bewildered by--and unprepared for--the many variants of the method that now exist.
To conclude, I suppose I'll give a rough definition of what induction basically is, the very one that Aristotle thought was obvious: a kind of reasoning that moves from particular cases or instances to general or universal knowledge about those kinds of particulars.
Next, I offer what I think Aristotle says on induction.
First Post
Hello!
I'm Roderick Fitts, and this is my blog, Inductive Quest.
Personal Information
I'm an Airman First Class (E-3) in the U.S. Air Force, and before that, I attended (and dropped out of) the University of Michigan. I was formerly a philosophy major and am still very interested in the field; in fact, philosophy is my main motivation for creating this blog.
I consider myself an Objectivist, meaning that I understand and agree with the principles articulated in Ayn Rand's philosophy. My other philosophical influences are Aristotle, Francis Bacon, and John Locke.
I've studied philosophy for about 3 years now, and I'm a sophomore student of the Objectivist Academic Center (currently on hiatus). The OAC has been a great place to enhance my understanding of the philosophy, and I highly recommend it for others who would like to learn about it (and other philosophies) from highly-trained professors.
Why the title "Inductive Quest"
I named my blog "Inductive Quest" because I'm determined to understand induction, both its proper and improper forms, as much as possible—even to the point of developing my own theory. I have two misgivings about whether or not a theory of induction can successfully be presented, which I plan to discuss sometime in a future post.
For now, I want to know the features of induction. This has led me to read several philosophers in ways I haven't done previously, and I think most of my posts will be my reflections on what I've learned.
Also, expect posts about the philosophy of Objectivism, since I'm still learning about the philosophy (though I do consider myself somewhat advanced) and will want to discuss some elements of it every once in a while. I'll also write about the philosophy because understanding it regularly involves implementing inductive thinking; though I haven't listened to it yet, this seems to be the main point of Dr. Leonard Peikoff's "Objectivism Through Induction" series of lectures.
Lastly, I'll probably post anything I have in mind about rationalism and empiricism, and other topics in epistemology, as I've been more interested in that branch of philosophy than any other field.
I hope you, the reader, enjoy!
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