Part 1
Part 2
Unit-Economy, Words, and Definitions
In part 1, I said that concepts are typically represented or symbolized by words in a language. In addition, we typically have definitions for the words we use, or seek definitions when we don’t understand or need clarity on some idea or word.
But why is this? Do words and definitions serve some important purpose in our quest for knowledge? Or could we do without them? To answer these questions, we must understand an important fact about concepts, and about the human mind.
The concept-formation process is truly multifaceted and complex. It involves observation of particulars, noting of features, differences, and similarities; it specifically is about thinking of certain particulars as members or units of a class (group) one is trying to form, abstracting certain distinctive features by omitting particular measurements, and finally integrating all of this knowledge into a single mental unit or thing, a basic unit or block of thought (or perhaps several units). The product is a kind of awareness that extends beyond what a given person could observe in his lifetime, and thus grants him a wealth of knowledge he otherwise could never achieve.
On this point, Rand states that “[c]onceptualization is a method of expanding man’s consciousness by reducing the number of its content’s units--a systematic means to an unlimited integration of cognitive data.” [Ayn Rand Lexicon: Unit Economy]
These facts about concepts and their purpose can be summed up as a guiding principle of thought: “unit-economy.”
Our minds are limited in what they can be aware of at any given time--the human mind cannot perceive everything with its sense organs; it cannot focus on everything it has learned in considering its concepts. Not even the power of memory has the ability to hold all of our knowledge and keep particular units of knowledge (like the concept job) firmly separated in our awareness from others (such as drive or door).
“Words” are the solution to this dilemma, and are the reason why concepts can perform their role as “unit-economizers” or unit-reducers.
Words are perceptual symbols for our concepts. Except for proper nouns (such as my name Roderick Fitts), all of our words represent our mental concepts. We need them because they complete the concept-formation process. Without them (or some other symbol for our thoughts, like pictures), we would have no way of retaining and subsequently using the information we’ve gained, information that’s relevant for forming a given concept, and this problem would only worsen when trying to think about other subjects which one wants to form into a concept. If this were to continue, we would more likely than not lose the conceptual information we were trying to integrate, and be completely unable to deal with even more difficult, higher-level conceptual material.
They facilitate the concept-forming process by allowing us to retain the conceptual information we’ve put together by merely perceiving the concrete symbol. The symbol (and thereby the concept) is stored into our memory and subconscious, making the information it contains instantly available whenever we choose to focus on it, and allows us to pursue other, more complex knowledge which would be impossible without the more basic conceptual knowledge already gained. It perceptually separates the concept it symbolizes from other things that exist and from our other concepts, allowing us to focus on particular concepts in our minds at will. To put it another way, perhaps in words Aristotle would use, “words” make forming concepts “second nature.”
The same sorts of problems present themselves when we consider why we need definitions.
Definitions are statements that identify the nature of the units included under concepts. We need them because we need a way to retain and recognize the characteristics that are both distinctive only to the particular units of a concept (the individual dogs of the concept dog) and the characteristics shared by them and a larger group of things (such as mammals in general, or animals). They explicitly point to the distinctive characteristic(s) of a group of similars, and identify the characteristics relating them to a larger group. By doing this, they allow us to hold in mind the relationships of our other concepts to each other. For instance, the concepts human, dog, and camel are related because their constituent units (the particular men, dogs, and camels) have characteristics which allow us to group them together as animals in our animal concept (such as mobility in environments, metabolic processes, and sensory organs).
But a definition does not merely state any given characteristic of a concept’s units, and neither does it state every single one. Merely stating a characteristic, while presumably factual in relation to the units, is not helpful for differentiating the concept from other concepts. One could say humans are “rational” (the characteristic), but this alone isn’t helpful for understanding how humans are related to other objects, like lamps, planets, and other animals. On the other hand, stating all the characteristics of a concept’s units would defeat the purpose of a definition, since it’s supposed to facilitate an immediate understanding of the nature of a concept’s units in the form of a few concepts, a single statement, not in the form of a catalog of everything one knows about the units. Definitions then, like words and concepts, are designed by us to achieve “unit-economy,” this time in relating concepts to other concepts (in terms of higher-level, more abstract concepts and lower-level, less abstract ones), and in relating a distinctive characteristic (a differentia) to a characteristic distinctive of a larger, more generalized group (a genus).
They do so by stating the essential characteristic(s) of the concept’s units, those features that make the units the kind of things they are. This characteristic both causes the greatest number of other characteristics shared by the units to even be possible, and explains the greatest number of characteristics, why they exist as aspects of the units. Consider the concept human and particular men and women: we do many, many things, among which are building functional airplanes, theorize about weather and climate, consider our mortality and free will, employ strategies in war, and laugh at ironic situations. If we were to pick any one of the above as a “defining characteristic,” we would be unable to understand why we can do any of the others, which is because they stand in a logical relationship to another feature of humans, their rationality, the capacity of reason. We can build viable airplanes, for instance, because we can use our faculty of reason to understand things like gravity, thrust, and drag, the scientific principles of electricity and magnetism, and the properties of materials which make some materials better suited as aircraft parts than others.
This statement of the essential characteristic is the means by which a definition identifies the nature of a concept’s units. A definition of humans as the “rational animal,” as the essential characteristics of humans, points to the facts which make us what we are, as opposed to other animals, other living things, other existents. In turn, this is how definitions bring clarity to our ideas and concepts: it identifies the nature of units in a concept, thus establishing its connection to other elements in one’s knowledge (other conceptual material), bringing up the context by which we can recall what the concept meant in the first place.
Thus, words and definitions serve an important role in the concept-formation process identified in Objectivism: in their own ways, they complete the process and finally establish the “mental integration” or “retained unitary cognition” that is characteristic of concepts.
Conclusion, and a Comment about Induction
Many philosophers have discussed the relationship between concepts and the method of induction, if only indirectly. Aristotle once pointed out that if someone doesn’t yet possess a term or word for an inductive generalization he’s trying to make, then he should go ahead and coin a new term (a unit of thought, a concept) for it. Karl Popper famously denied the validity of induction entirely, and consequently denied the validity of concept-formation on similar grounds. Francis Bacon passionately stated that our very concepts would be worthless and corrupted (mere “idols”) without a viable method of induction.
Ayn Rand, though not possessing a theory on induction, noticed the significance of concepts in relation to them. She stated that:
Perhaps the way to reach sound inductions can be discovered by drawing out the method of induction's relationship to concepts.
Part 2
Unit-Economy, Words, and Definitions
In part 1, I said that concepts are typically represented or symbolized by words in a language. In addition, we typically have definitions for the words we use, or seek definitions when we don’t understand or need clarity on some idea or word.
But why is this? Do words and definitions serve some important purpose in our quest for knowledge? Or could we do without them? To answer these questions, we must understand an important fact about concepts, and about the human mind.
The concept-formation process is truly multifaceted and complex. It involves observation of particulars, noting of features, differences, and similarities; it specifically is about thinking of certain particulars as members or units of a class (group) one is trying to form, abstracting certain distinctive features by omitting particular measurements, and finally integrating all of this knowledge into a single mental unit or thing, a basic unit or block of thought (or perhaps several units). The product is a kind of awareness that extends beyond what a given person could observe in his lifetime, and thus grants him a wealth of knowledge he otherwise could never achieve.
On this point, Rand states that “[c]onceptualization is a method of expanding man’s consciousness by reducing the number of its content’s units--a systematic means to an unlimited integration of cognitive data.” [Ayn Rand Lexicon: Unit Economy]
These facts about concepts and their purpose can be summed up as a guiding principle of thought: “unit-economy.”
Our minds are limited in what they can be aware of at any given time--the human mind cannot perceive everything with its sense organs; it cannot focus on everything it has learned in considering its concepts. Not even the power of memory has the ability to hold all of our knowledge and keep particular units of knowledge (like the concept job) firmly separated in our awareness from others (such as drive or door).
“Words” are the solution to this dilemma, and are the reason why concepts can perform their role as “unit-economizers” or unit-reducers.
Words are perceptual symbols for our concepts. Except for proper nouns (such as my name Roderick Fitts), all of our words represent our mental concepts. We need them because they complete the concept-formation process. Without them (or some other symbol for our thoughts, like pictures), we would have no way of retaining and subsequently using the information we’ve gained, information that’s relevant for forming a given concept, and this problem would only worsen when trying to think about other subjects which one wants to form into a concept. If this were to continue, we would more likely than not lose the conceptual information we were trying to integrate, and be completely unable to deal with even more difficult, higher-level conceptual material.
They facilitate the concept-forming process by allowing us to retain the conceptual information we’ve put together by merely perceiving the concrete symbol. The symbol (and thereby the concept) is stored into our memory and subconscious, making the information it contains instantly available whenever we choose to focus on it, and allows us to pursue other, more complex knowledge which would be impossible without the more basic conceptual knowledge already gained. It perceptually separates the concept it symbolizes from other things that exist and from our other concepts, allowing us to focus on particular concepts in our minds at will. To put it another way, perhaps in words Aristotle would use, “words” make forming concepts “second nature.”
The same sorts of problems present themselves when we consider why we need definitions.
Definitions are statements that identify the nature of the units included under concepts. We need them because we need a way to retain and recognize the characteristics that are both distinctive only to the particular units of a concept (the individual dogs of the concept dog) and the characteristics shared by them and a larger group of things (such as mammals in general, or animals). They explicitly point to the distinctive characteristic(s) of a group of similars, and identify the characteristics relating them to a larger group. By doing this, they allow us to hold in mind the relationships of our other concepts to each other. For instance, the concepts human, dog, and camel are related because their constituent units (the particular men, dogs, and camels) have characteristics which allow us to group them together as animals in our animal concept (such as mobility in environments, metabolic processes, and sensory organs).
But a definition does not merely state any given characteristic of a concept’s units, and neither does it state every single one. Merely stating a characteristic, while presumably factual in relation to the units, is not helpful for differentiating the concept from other concepts. One could say humans are “rational” (the characteristic), but this alone isn’t helpful for understanding how humans are related to other objects, like lamps, planets, and other animals. On the other hand, stating all the characteristics of a concept’s units would defeat the purpose of a definition, since it’s supposed to facilitate an immediate understanding of the nature of a concept’s units in the form of a few concepts, a single statement, not in the form of a catalog of everything one knows about the units. Definitions then, like words and concepts, are designed by us to achieve “unit-economy,” this time in relating concepts to other concepts (in terms of higher-level, more abstract concepts and lower-level, less abstract ones), and in relating a distinctive characteristic (a differentia) to a characteristic distinctive of a larger, more generalized group (a genus).
They do so by stating the essential characteristic(s) of the concept’s units, those features that make the units the kind of things they are. This characteristic both causes the greatest number of other characteristics shared by the units to even be possible, and explains the greatest number of characteristics, why they exist as aspects of the units. Consider the concept human and particular men and women: we do many, many things, among which are building functional airplanes, theorize about weather and climate, consider our mortality and free will, employ strategies in war, and laugh at ironic situations. If we were to pick any one of the above as a “defining characteristic,” we would be unable to understand why we can do any of the others, which is because they stand in a logical relationship to another feature of humans, their rationality, the capacity of reason. We can build viable airplanes, for instance, because we can use our faculty of reason to understand things like gravity, thrust, and drag, the scientific principles of electricity and magnetism, and the properties of materials which make some materials better suited as aircraft parts than others.
This statement of the essential characteristic is the means by which a definition identifies the nature of a concept’s units. A definition of humans as the “rational animal,” as the essential characteristics of humans, points to the facts which make us what we are, as opposed to other animals, other living things, other existents. In turn, this is how definitions bring clarity to our ideas and concepts: it identifies the nature of units in a concept, thus establishing its connection to other elements in one’s knowledge (other conceptual material), bringing up the context by which we can recall what the concept meant in the first place.
Thus, words and definitions serve an important role in the concept-formation process identified in Objectivism: in their own ways, they complete the process and finally establish the “mental integration” or “retained unitary cognition” that is characteristic of concepts.
Conclusion, and a Comment about Induction
Many philosophers have discussed the relationship between concepts and the method of induction, if only indirectly. Aristotle once pointed out that if someone doesn’t yet possess a term or word for an inductive generalization he’s trying to make, then he should go ahead and coin a new term (a unit of thought, a concept) for it. Karl Popper famously denied the validity of induction entirely, and consequently denied the validity of concept-formation on similar grounds. Francis Bacon passionately stated that our very concepts would be worthless and corrupted (mere “idols”) without a viable method of induction.
Ayn Rand, though not possessing a theory on induction, noticed the significance of concepts in relation to them. She stated that:
The process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.It was Rand who demonstrated to us the validity of concepts by drawing out the striking similarities between concept-formation and the field of mathematics.
The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.[Ayn Rand Lexicon entry: Induction and Deduction]
Perhaps the way to reach sound inductions can be discovered by drawing out the method of induction's relationship to concepts.
Induction depends on essences, on each concrete being the same essence/instance (unit) holding for each instance, not instances of other essences. Rand's warning against forming concepts by non-essentials (IOE, 2nd. Ed, hc, p.71) applies to induction. She notes the intellectual hash from defining man as "a running animal" and then attempting "to form a single higher-level concept out of 'running entities,' such as a running man, a running river..." The error compounds when the non-essence is different in each instance of the skeptical rejection of inducton. This substitutes degrees for kinds (essences). Eg, small circles are different from big circles, thus one, at least, is not a circle.
ReplyDeleteAs Peikoff says in his rules of induction (Induction in Physics and Philosophy), "Induction requires the contextual discovery of causal connections." Ie, not randomly flitting among wider and narrower causes but the same cause throughout the induction.
This seems to make the process of induction, for so long and so many a problem of induction, strangely easy to identify. Perhaps, tho, Aristotle was correct in claiming that “[what] sort of thing induction is, is obvious.” Perhaps when man's mind is used to integrate instead of to disintegrate, the essence, problem, is rejected for the essence, process.
The bizarre complexity-worship that has disintegrated science with the primacy of (arbitrary) hypothesis over observation can be avoided with Aristotle's primary concern with systematically conceptualized observations. Arbitrary description is not part of science. Measurement and experiment must be guided by rationally systematic thinking about what the scientist wants. Science is not the Pragmatism of "Let's go and see what happens." Newton was not the first to observe falling apples. His mind was prepared with a rational system of essences/instances.