Objectivism doesn't provide official definitions for concepts like 'straight' and 'line', per se. The Objectivist theory of concept-formation discusses the process by which people form concepts in general (such as 'straight' and 'line'), providing an account of the fundamental relationship between concepts and their referents in reality, as well as broad guidance for proper vs. improper concept-formation that is based in our epistemological needs and capacities. A part of this involves understanding the objective need for definitions and basic guidance in the proper vs. improper definition of concepts.
The links I have included above should provide a bit of an orientation, but I recommend reading the seminal Objectivist treatment of all of this in Rand's monograph, Introduction to Objectivist Epistemology and in the first five chapters of Peikoff's Objectivism: The Philosophy of Ayn Rand.
I can offer the brief (and therefore mostly useless :^) comment that one would not define a 'straight line' by reference to a concrete existent like a ray of light. That would only be giving an instance of the concept, which would be the wrong kind of thing altogether, because a definition in this case would be an abstract statement composed of words.
This is not to say that concepts are divorced from reality, of course. Quite the contrary: all concepts are (ultimately) formed by reference to things we observe in reality via our senses, and all (proper) concepts give us an abstract perspective on things in reality that is genuinely rooted in the real, concrete attributes of those things. But again, these brief comments are likely of little use other than to perhaps spark enough interest to explore the above links and books.
answered Jul 06 '11 at 15:59
Greg Perkins ♦♦
For completeness and future reference by others who may be interested, I would like to elaborate a little on some of the points that I hinted at in my comments.
First, as Greg already noted, it is not normally the task of a rational philosophy to define all terms that people might use. A rational philosophy defines the terms that are essential to the philosophy, and identifies the rules of proper definition. The topic of "Definitions" in The Ayn Rand Lexicon (linked in Greg's answer) provides four pages of helpful excerpts, all from Ayn Rand's Introduction to Objectivist Epistemology (aka ITOE). The second excerpt introduces the principle of definitions as consisting of a genus (wider category) and differentia (distinguishing characteristic or characteristics within the wider category). There are additional principles regarding how the genus and differentia are to be chosen, i.e., not just any wider category, and not just any distinguishing characteristics.
The expression "straight line" is a compound expression comprised of two concepts: line and straight. A "straight line" is simply a line that is straight. Lines can be curved or bent instead of straight. The genus is "line," and the differentia is "straight."
This raises the question of how to define "line" and "straight." Since these are non-philosophical terms, an ordinary dictionary is likely to be useful (though not necessarily always, and older dictionaries are often better). One of my dictionaries, Webster's New World Dictionary, paperback edition from 1959 (priced at 50 cents), gives twenty different meanings of "line," including: "1. a cord, rope, wire, etc. ... 3. a thin, threadlike mark.... 20. in math., the path of a moving point."
I don't see much room for philosophy to improve on that. (These are all noun usages, by the way. There are also multiple verb usaages.) Actually, one might attempt to refine the first definition as follows: a line (of this type) is an object that is far longer than it is thick, typically round in shape, uniform in thickness, made of flexible material that can withstand substantial pulling force, designed for pulling, lifting, tying things together, marking area boundaries, and similar uses." Similarly, #20 might be made more technically formal by using the expression "continuous locus of points" instead of "path of a moving point," although the latter formulation suffices perfectly well for a general reader. (In case anyone wants a definition of "point," my dictionary lists 13 noun usages and 7 verb usages. As always, the context makes clear, or ought to, which usage is intended.)
Terms like "substantial" might raise questions about whether or not the definition should state definite limits of measurement. This issue is discussed further in ITOE. If the context requires the specification of measurement limits, then they should be included. But a definition in ordinary usage most often can serve its cognitive purpose adequately without burdening the formulation with explicitly stated measurement ranges.
"Straight" might seem a little harder to define at first glance, but my dictionary defines it as follows: "1. having the same direction throughout its length; not crooked, bent, etc. 2. direct, undeviating. ..." (There are three additional adjective usages, some adverb usages, and even a noun usage [from poker].)
"Direction," in turn, is defined in the same dictionary as follows (among a total of six different meanings): "5. the point toward which one is moving or facing...."
It might be asked: how does one know what direction one is facing or moving? One knows mainly through vision (or a combination of other senses if one is blind). But vision depends on light. Doesn't the concept of direction, then, depend on the assumption that light rays travel in straight lines, with "line" and "straight" thereby being more fundamental than light or "direction" so that one can identify when light travels in a straight line and when it doesn't (as when light passes through transparent media such as water or glass, or passes near a large planet or star while traveling through space)?
The answer, in my understanding, is that the "dependence" is indirect and scientific, not conceptually hierarchical. Furthermore, light does, in fact, travel in straight lines in most everyday human experience. The occasional exceptions and illusions are readily recognizable by man as precisely that -- exceptions and special cases. Furthermore, one can usually check the path of a light beam using other methods of achieving straightness, such as stretching a physical line (i.e., a cord or rope, etc.) to the point of maximum separation between its endpoints without permanently damaging the line's material. But the knowledge of light and its properties, and the dependence of vision on light, are separate discoveries. One needs only the sense of sight to be able to grasp the idea of facing something or turning away from it, or of moving toward it or away from it.
The dictionary definitions of "line," "straight," and "direction" thus provide ample identifications of what a "straight line" is. One might say that the dictionary definitions in this case "pass the philosophical test" -- meaning the philosophical standards (according to Objectivism) of proper definitions. But that clearly doesn't mean that philosophy originates the definitions of non-philosophical terms.
answered Jul 08 '11 at 15:46
Ideas for Life ♦
It's an abstract concept.
No. In the mathematical sense, a straight line doesn't exist in the physical world. It's one-dimensional, perfectly smooth, and infinitely long (otherwise it's a line segment).
However, Objectivist epistemology says that valid concepts are ultimately anchored in reality -- so we have things that are close to being straight, or close to being lines -- and we can then abstract those into a more idealized form. Concepts that are not ultimately anchored in reality are arbitrary.
answered Aug 03 '11 at 10:15