The aim of this essay is to give a preliminary statement about what induction is, and to present reasons why we should be interested in figuring out the answer.
Three Meanings of “Induction”
The term “induction” has several senses, all of them heavily related to one another, and I think that all of them have to be explained in any viable theory of induction.
Induction as Process
The first sense refers to the process of induction, by which our minds reason from particulars to universal generalizations about particulars, as Aristotle was the first to point out (Topics, Book I, Ch. 12; Rhetoric, Book I, Chapter 2, 1356b1). For instance, we reason from the fact that some individuals have eyes and can see (especially our own first-person visual of this fact), to the generalization that beings with eyes possess the ability of sight. The process involves an element of abstraction, a selective separation and contemplation of something in the world by our minds, which really can only be separated mentally; you can’t, for instance, physically take "durability" from the car that has that feature in order to further study it, but you can think about the property of durability without also having to consider that particular car, or wall, or any given object. This abstraction is how we change our cognitive focus from the particulars we were considering to a general feature or fact that is common to those particulars (and possibly other kinds of particulars as well).
The end result of this process leads to several different kinds of conceptual products, with two of the more familiar ones being individual concepts and causal explanations. For instance, we see White Shepherds and Black Labradors, and notice what they have in common (along with other kinds of dogs), and we abstract from the particular animals we see in order to form a concept “dog,” a general term which applies to a plethora of individual dogs, including unobserved and future referents of the concept. Also, we can observe people fighting angrily, breaking things, or cutting people off on the freeway and generalize from that that “people can experience rage,” that a certain emotion of ours can cause us to do certain violent or drastic things that wouldn’t happen otherwise.
Induction as Generalization
The second sense refers to the generalization itself that results from reasoning from particulars to the general. Generalizations like “all men are mortal,” “the human body resists disease,” and “all chocolate cake is food” can be inductions from our observations and scientific reasoning, such as the realization that microscopic germs can cause diseases in human beings. (Generalizations can also be reached deductively, for instance, since all men are mortal, all farmers must perforce be mortal. Due to this, I’ll speak specifically of inductive generalizations.) Definitions are probably the most familiar inductions that people know, as they state something general and essential to a class of things that differentiate them from other objects.
Induction as a Method
The third sense refers to induction as a method, which differs in its specifics depending on the theorist or philosopher you consult. The method of induction, for Aristotle (and presumably for Socrates as well, given what Aristotle said in his Metaphysics), is a comparison of things which leads to a recognition of similarity, resulting in an identification of an essential nature of the class of objects being thought about. It begins with our particular perceptions and memories of things, and ends with a general, universal identification of what makes something the kind of thing it is, which applies to an unlimited number of things which possess this similarity (Topics; Posterior Analytics, book 2, chapter 19).
A method of induction refers to the descriptive elements of this conceptual activity, the mental process of abstraction, and the end-products of this process--the completed concepts and generalizations which come to exist. More importantly, the method (1) fleshes out what these descriptive elements are in more detail, and (2) provides a normative approach for forming correct inductions and practicing generalized thinking. Bacon’s theory of induction, while saying little on the process of abstraction itself, discusses the steps we should employ in forming inductions and concepts in much detail. (See Book 2 of Bacon’s Novum Organum for his distinctive method.)
Now that I’ve explained these meanings of “induction,” I’ll explain why we need the method of induction, as in a specific theory.
Induction: Why Bother?
The components needed to make inductions are with us at birth: sense organs, the faculties of memory and reason, and the world around us. We habitually make inductive conclusions and generalizations, and try to define things and form new concepts. Sometimes, we reach sound inductive conclusions (“all men are mortal,” “man is the rational animal,” “lightning is a kind of electricity”), and sometimes we don’t (“all swans are white,” “universals are independently-existing Forms”). This might simply be an aspect of the human condition: to generalize, right or wrong.
Whence, then, is the significance of a theory of induction?
A theory of induction is needed because the human way of life is about volition--it’s about our choices. We’re given the biological equipment to make choices, but have to determine for ourselves in what way our minds are supposed to operate; we have to learn how to properly utilize our reason. Forming valid inductions is not pre-programmed into us; if it were, there would be no need to discuss a method of induction, just as there’s no need to discuss a “method” of perception.
Without a method of induction, we risk coming no closer to understanding the world than Socrates did, a man who made it his business to tell people that he held no genuine knowledge. What Socrates needed (and implicitly searched for) was a methodical way to reach definite concepts and definitions, to note genuine similarities and properly abstract from things to reach sound generalizations, bringing about genuine knowledge from which he could then deduce.
The consequences of not explicitly practicing a method of induction (of reaching generalizations) have already become apparent. Ignoring the generalizations that could be formed relating totalitarian/socialistic regimes to economic collapse, Venezuela is quickly becoming the latest experiment in socialism. (Generalizations formed by economist Ludwig von Mises in his work Socialism, for instance.) Despite all evidence to the contrary, there are still people who believe that the configurations of the stars influence and even determine human behavior. And there are people who make generalizations without any sensible attempt at proof and scarce evidence, such as racists, sexists, and religionists.
The reaching of such genuine knowledge is perhaps the most difficult of human endeavors, evidenced by the fact that, over two thousand years after philosophy’s inception, we still aren’t clear on how we actually reach general, universal knowledge that is true.
Our only hope, then, is to determine a definite method or theory of induction. This is what I think is the significance of inductive theory.
Three Meanings of “Induction”
The term “induction” has several senses, all of them heavily related to one another, and I think that all of them have to be explained in any viable theory of induction.
Induction as Process
The first sense refers to the process of induction, by which our minds reason from particulars to universal generalizations about particulars, as Aristotle was the first to point out (Topics, Book I, Ch. 12; Rhetoric, Book I, Chapter 2, 1356b1). For instance, we reason from the fact that some individuals have eyes and can see (especially our own first-person visual of this fact), to the generalization that beings with eyes possess the ability of sight. The process involves an element of abstraction, a selective separation and contemplation of something in the world by our minds, which really can only be separated mentally; you can’t, for instance, physically take "durability" from the car that has that feature in order to further study it, but you can think about the property of durability without also having to consider that particular car, or wall, or any given object. This abstraction is how we change our cognitive focus from the particulars we were considering to a general feature or fact that is common to those particulars (and possibly other kinds of particulars as well).
The end result of this process leads to several different kinds of conceptual products, with two of the more familiar ones being individual concepts and causal explanations. For instance, we see White Shepherds and Black Labradors, and notice what they have in common (along with other kinds of dogs), and we abstract from the particular animals we see in order to form a concept “dog,” a general term which applies to a plethora of individual dogs, including unobserved and future referents of the concept. Also, we can observe people fighting angrily, breaking things, or cutting people off on the freeway and generalize from that that “people can experience rage,” that a certain emotion of ours can cause us to do certain violent or drastic things that wouldn’t happen otherwise.
Induction as Generalization
The second sense refers to the generalization itself that results from reasoning from particulars to the general. Generalizations like “all men are mortal,” “the human body resists disease,” and “all chocolate cake is food” can be inductions from our observations and scientific reasoning, such as the realization that microscopic germs can cause diseases in human beings. (Generalizations can also be reached deductively, for instance, since all men are mortal, all farmers must perforce be mortal. Due to this, I’ll speak specifically of inductive generalizations.) Definitions are probably the most familiar inductions that people know, as they state something general and essential to a class of things that differentiate them from other objects.
Induction as a Method
The third sense refers to induction as a method, which differs in its specifics depending on the theorist or philosopher you consult. The method of induction, for Aristotle (and presumably for Socrates as well, given what Aristotle said in his Metaphysics), is a comparison of things which leads to a recognition of similarity, resulting in an identification of an essential nature of the class of objects being thought about. It begins with our particular perceptions and memories of things, and ends with a general, universal identification of what makes something the kind of thing it is, which applies to an unlimited number of things which possess this similarity (Topics; Posterior Analytics, book 2, chapter 19).
A method of induction refers to the descriptive elements of this conceptual activity, the mental process of abstraction, and the end-products of this process--the completed concepts and generalizations which come to exist. More importantly, the method (1) fleshes out what these descriptive elements are in more detail, and (2) provides a normative approach for forming correct inductions and practicing generalized thinking. Bacon’s theory of induction, while saying little on the process of abstraction itself, discusses the steps we should employ in forming inductions and concepts in much detail. (See Book 2 of Bacon’s Novum Organum for his distinctive method.)
Now that I’ve explained these meanings of “induction,” I’ll explain why we need the method of induction, as in a specific theory.
Induction: Why Bother?
The components needed to make inductions are with us at birth: sense organs, the faculties of memory and reason, and the world around us. We habitually make inductive conclusions and generalizations, and try to define things and form new concepts. Sometimes, we reach sound inductive conclusions (“all men are mortal,” “man is the rational animal,” “lightning is a kind of electricity”), and sometimes we don’t (“all swans are white,” “universals are independently-existing Forms”). This might simply be an aspect of the human condition: to generalize, right or wrong.
Whence, then, is the significance of a theory of induction?
A theory of induction is needed because the human way of life is about volition--it’s about our choices. We’re given the biological equipment to make choices, but have to determine for ourselves in what way our minds are supposed to operate; we have to learn how to properly utilize our reason. Forming valid inductions is not pre-programmed into us; if it were, there would be no need to discuss a method of induction, just as there’s no need to discuss a “method” of perception.
Without a method of induction, we risk coming no closer to understanding the world than Socrates did, a man who made it his business to tell people that he held no genuine knowledge. What Socrates needed (and implicitly searched for) was a methodical way to reach definite concepts and definitions, to note genuine similarities and properly abstract from things to reach sound generalizations, bringing about genuine knowledge from which he could then deduce.
The consequences of not explicitly practicing a method of induction (of reaching generalizations) have already become apparent. Ignoring the generalizations that could be formed relating totalitarian/socialistic regimes to economic collapse, Venezuela is quickly becoming the latest experiment in socialism. (Generalizations formed by economist Ludwig von Mises in his work Socialism, for instance.) Despite all evidence to the contrary, there are still people who believe that the configurations of the stars influence and even determine human behavior. And there are people who make generalizations without any sensible attempt at proof and scarce evidence, such as racists, sexists, and religionists.
The reaching of such genuine knowledge is perhaps the most difficult of human endeavors, evidenced by the fact that, over two thousand years after philosophy’s inception, we still aren’t clear on how we actually reach general, universal knowledge that is true.
Our only hope, then, is to determine a definite method or theory of induction. This is what I think is the significance of inductive theory.
Roderick Fitts noted many crucial facts about the meanings of induction and its importance, but there are important ideas that were only briefly mentioned or implicit that need to be made explicit.
ReplyDeleteTHE MEANING OF INDUCTION
In order to be perfectly clear about the subject we are discussing, we really ought to have a formal, genus and differentia, definition of induction.
The genus, as Roderick indicates in his first and third senses are a process or method, both of which involve actions of consciousness. The second sense is the product of an action of consciousness. Let us agree that the genus of induction is an action of consciousness, but what is the differentia?
What differentiates induction from other actions of consciousness like deduction, perception, hallucination, identification, etc.? It is not that its goal is the creation or validation of generalizations because, as Roderick pointed out in his "All farmers are mortal" example, you can also create and validate generalizations via deduction.
Roderick noted that induction involves reasoning from particulars to universal generalizations about particulars. This is true, but so does concept formation. How does induction differ from concept formation?
INDUCTION: WHY BOTHER?
Finding the differentia of induction requires answering Roderick's second question: Induction: Why Bother? Whatever induction is, we do it for a REASON, and that can provide us with a differentia.
WHY do men do this? Does induction meet an essential human need or is it just a recreational intellectual activity like telling jokes or playing chess? What do we GET from doing induction?
Roderick nailed it when he wrote: "The end result of this process [of going from particulars to universal generalizations about particulars] leads to several different kinds of conceptual products, with two of the more familiar ones being individual concepts [that is concept formation] and causal explanations [that is induction]."
Observe that ALL generalizations can be expressed as causal statements. "All men are mortal" means there is something about all men that causes them to die. "Acorns grow into oak trees" means there is something about an acorn than can cause it to change into an oak.
Finding causes -- correct causes -- is essential to human life. To gain and keep values, we need to know how to enact the causes of those values. All the "whys" and "hows" of life require finding and validating causes.
Therefore, I would define induction as the process of finding and validating causes.