@Dean Young;
Let me note firstly, that some members tire of me forever referring to Spinoza. If it were not for the fact that he offers the most challenging responses to the major questions pervading the History of Philosophy, my 'proselytizing' would be out of place. My apologies for this necessity.
As for definition and the questioners request for some method of defining which could circumvent the difficulty in applying 'ambiguous' terminology which leaves the defined object beyond reach, this is how Spinoza characterized the problem with words:
[88] (1) Again, since words are a part of the imagination - that is, since we form many conceptions in accordance with confused arrangements of words in the memory, dependent on particular bodily conditions, - there is no doubt that words may, equally with the imagination, be the cause of many and great errors, unless we strictly on our guard.
[89] (1) "Moreover, words are formed according to popular fancy and intelligence, and are, therefore, signs of things as existing in the imagination, not as existing in the understanding. (2) This is evident from the fact that to all such things as exist only in the understanding, not in the imagination, negative names are often given, such as incorporeal, infinite, &c. (3) So, also, many conceptions really affirmative are expressed negatively, and vice versa, such as uncreate, independent, infinite, immortal, &c., inasmuch as their contraries are much more easily imagined, and, therefore, occurred first to men, and usurped positive names. (89:4) Many things we affirm and deny, because the nature of words allows us to do so, though the nature of things does not. (5) While we remain unaware of this fact, we may easily mistake falsehood for truth."
What Spinoza is expressing here is his observation that the idea of any object or person which we form in our minds is not comprised of words. And so in trying to capture an accurate definition of a circle, using words, we must be careful to only describe its essential feature plus the motion which depicts how it is formed as an adequate idea in the mind.
Thus, he offers this definition of a circle; "A line with one end fixed and the other free."
This is devilishly difficult to conceive at first go. But if you can picture a line with one end fixed and the other end moving freely on its axis, you will 'see' the line moving in an endless arc which covers an infinite number of 360 degree arcs. And so, this definition has captured the 'essence' of the circle, describes how it is formed plus all of its properties can be deduced from the definition; circumference, radius, etc.
It is impossible to introduce this without noting the difficulty. Here is one example which I formed recently. I have no idea if it conforms to Spinoza's requirements. For me it's merely a thought experiment.
Gravity- Perpetual centripetal force, a constant within a planetary atmosphere.
This is both what the questioner asked for and what Spinoza recognized and offered a solution for.
"If instead we wish for a definition to refer to something "outside of the page", so to speak- to be more than just symbol manipulation and to refer to aspects about the world around us- then we cannot demand that all words be expressed in terms of other words."
Here is some more information on Spinoza's conception of 'definition'.
On the Improvement of the Understanding by Benedictus de Spinoza
Second part of method (91-110)
Second part of method
[91] [91e] (1) "Now, in order at length to pass on to the second part of this method, I shall first set forth the object aimed at, and next the means for its attainment. (2) The object aimed at is the acquisition of clear and distinct ideas, such as are produced by the pure intellect, and not by chance physical motions. (3) In order that all ideas may be reduced to unity, we shall endeavor so to associate and arrange them that our mind may, as far as possible, reflect subjectively the reality of nature, both as a whole and as parts.
[92] (1) As for the first point, it is necessary (as we have said) for our purpose that everything should be conceived, either solely through its essence, or through its proximate cause. (2) If the thing be self-existent, or, as is commonly said, the cause of itself, it must be understood through its essence only; if it be not self-existent, but requires a cause for its existence, it must be understood through its proximate cause. (3) For, in reality, the knowledge, [92f] of an effect is nothing else than the acquisition of more perfect knowledge of its cause.
[93] (1) Therefore, we may never, while we are concerned with inquiries into actual things, draw any conclusion from abstractions; we shall be extremely careful not to confound that which is only in the understanding with that which is in the thing itself. (2) The best basis for drawing a conclusion will be either some particular affirmative essence, or a true and legitimate definition. (93:3) For the understanding cannot descend from universal axioms by themselves to particular things, since axioms are of infinite extent, and do not determine the understanding to contemplate one particular thing more than another.
[94] (1) Thus the true method of discovery is to form thoughts from some given definition. (2) This process will be the more fruitful and easy in proportion as the thing given be better defined. (3) Wherefore, the cardinal point of all this second part of method consists in the knowledge of the conditions of good definition, and the means of finding them. (4) I will first treat of the conditions of definition.
[95] (1) A definition, if it is to be called perfect, must explain the inmost essence of a thing, and must take care not to substitute for this any of its properties. (2) In order to illustrate my meaning, without taking an example which would seem to show a desire to expose other people's errors, I will choose the case of something abstract, the definition of which is of little moment. (95:3) Such is a circle. (4) If a circle be defined as a figure, such that all straight lines drawn from the center to the circumference are equal, every one can see that such a definition does not in the least explain the essence of a circle, but solely one of its properties. (5) Though, as I have said, this is of no importance in the case of figures and other abstractions, it is of great importance in the case of physical beings and realities: for the properties of things are not understood so long as their essences are unknown. (6) If the latter be passed over, there is necessarily a perversion of the succession of ideas which should reflect the succession of nature, and we go far astray from our object.
[96] In order to be free from this fault, the following rules should be observed in definition:- I. (1) If the thing in question be created, the definition must (as we have said) comprehend the proximate cause. (2) For instance, a circle should, according to this rule, be defined as follows: the figure described by any line whereof one end is fixed and the other free. (3) This definition clearly comprehends the proximate cause. II. (4) A conception or definition of a thing should be such that all the properties of that thing, in so far as it is considered by itself, and not in conjunction with other things, can be deduced from it, as may be seen in the definition given of a circle: for from that it clearly follows that all straight lines drawn from the center to the circumference are equal. (5) That this is a necessary characteristic of a definition is so clear to anyone, who reflects on the matter, that there is no need to spend time in proving it, or in showing that, owing to this second condition, every definition should be affirmative. (6) I speak of intellectual affirmation, giving little thought to verbal affirmations which, owing to the poverty of language, must sometimes, perhaps, be expressed negatively, though the idea contained is affirmative.
[97] The rules for the definition of an uncreated thing are as follows:-- I. The exclusion of all idea of cause - that is, the thing must not need explanation by Anything outside itself. II. When the definition of the thing has been given, there must be no room for doubt as to whether the thing exists or not. III. It must contain, as far as the mind is concerned, no substantives which could be put into an adjectival form; in other words, the object defined must not be explained through abstractions. IV. Lastly, though this is not absolutely necessary, it should be possible to deduce from the definition all the properties of the thing defined. All these rules become obvious to anyone giving strict attention to the matter."
