James Still

My understanding of the term "stipulated object" is one in which a proxy term that may or may not have anything to do with the object being stipulated, nevertheless stands in for that object anyway. So if I were to define Ierrellus' series of dashes as a "Frookie" my introduced term is a stipulated definition for the series of dashes that Ierrellus typed in his message. So far so good?

That is an extremely interesting question (one fraught with philosophical danger). For how is legitimacy conferred? Is there a metaphysical "place" in which there is a real sign corresponding to its signifier such that two people can measure the correctness of their stipulated definitions against that standard? I do not think that there is such a place. Legitimacy is conferred by agreement in language and not because of something "out there" in reality.

Suppose you draw a certain object and call it a line segment. You show it to me and I say that it is a circle. Our language reveals that we either do not see the same thing or that we are not yet aware that the signs we use are different but reduce to the same thing. (I don't think anyone wants to say that we do not see the same thing *and* our signs for it do indeed signify different objects; that way madness lies.) But suppose instead that I agree with you and say that the object is a line segment. Here we have agreement in language. This agreement is the "criterion of correctness" (per Wittgenstein) or the yardstick by which we can say that the object is a line segment.

When you say that our linguistic agreement risks "losing all its original perceived meaning" you assume that there is some objective real definition that lies prior to the linguistic exchange between us. I resist this sort of realism. Is there an object there in front of us? Certainly. Does it have a real definition rather than a stipulated definition? Certainly not. This is what Shakespeare meant when he said that "a rose by any other name would smell just as sweet." The property of "sweetness" is an empirical matter but the sign itself is totally arbitrary. Those are my thoughts on the matter.

Ierrellus

Owleye, you got it!

If I had simply asked, as phaedrus suggests, "What is this design?", I would never have gotten a variety of interpretive responses. The nature of the responses has exemplified something of the nature of those responding, at least, to some extent, how each approaches interpretation of a given object. From that vantage point, we can discuss subject/object relationships.

Ierrellus

Wafel

Take the equation f(x) = 45 / (x-5)

In this case you would have a division by 0 (vertical asymptote) where x = 5.

Let's say that a division is simply counting how many times you can put the numerator fits into the denominator. (5 goes 2 times into 10, thus 10/5=2)

How many times does 0 fit into 45? Or in other words, if you start with 0, how many times could you add the denominator (0) to that until you reach 45?

Infinte times.


That's one of the situations in which infinity contributes to math.

snatchbalance

<a href="http://www.alleydog.com/glossary/definition.cfm?term=Gestalt" target="_blank">gestalt</a>

Ierrellus

wafel:

A simpler example of infinity in mathematics is two-thirds stated as the decimal .6666666. . . .
Is this decimal form more accurately expressed to the 100th place than it could be to the 10th? If so, does that make mathematical computations using decimals to any degree inaccurate?

Jim and owleye:

On the computer a circle is expressed as pixels (dashes). Current research into visual perception of curved objects seems to suggest that layers of neurons break down the circular form to, you guessed it, dashes!

Ierrellus

Wafel

Ahh right, now why didn't I think of that? <img src="graemlins/banghead.gif" border="0" alt="[Bang Head]" />

owleye

James....

I'm not sure you captured the significance of what I was saying about constructed objects. A constructed object can be considered aesthetically or symbolically. Ierellius's post, it seems to me, has nothing to do with what it symbolizes. We must take the dashed line not as a symbol (e.g., what it might mean if we found ourselves driving adjacent to one) but rather as a dashed line (or however Ierrelius wants us to consider it).

Consider how figures are used in geometry. When we draw a triangle, intending a certain geometrical object, it will have three sides, probably unequal in length and angled in some neutral fashion, notwithstanding that some of the drawing might be conventional (e.g., the "bottom" side might be horizontal). We would object if it had four sides, or could never be recognized as a triangle at all.

Of course, the triangle as it is drawn, is not the triangle being referred to. That triangle is the concept which has general, not specific properties, and can never literally be represented by the object of the construction as it is drawn (even if we idealize it as an image which consists of its mere form). (I should let you know I'm following Kant's analysis of what is going on.) The generality associated with the drawn triangle derives from the rules of its construction in conjunction with the ability our imagination has in allowing for the variations that convey all triangles through it. We do the same sort of thing when we construct what is intended to represent the general concept of a dog. We learn the rules of constructing it so as not to give away any special features of a specific kind of dog, if we can help it. If this can be done, our imagination has to understand the generality in the concrete instances. And it does this in virtue of our ability to (imaginatively) adjust the lengths of the lines or angles of the vertices in accordance with the general concept derived from the definition of a triangle.

Stipulating that what is drawn is a triangle (or dog), if it looks nothing like a triangle (or dog), may be possible, but my guess is that what is being drawn will have lost its aesthetic meaning and instead draws only on its symbolic meaning, in which case we may be able to think its a triangle (or dog), possibly having an image of one in our mind, by thinking through it, but what is depicted by the drawing cannot be said to reflect that image.

Thus, when presented with 'triangle' as it appears in this message, one can readily see that it looks nothing like a triangle. It only symbolizes the three sided figure which can be constructed. In that case, 'triangle' is not to be understood in its aesthetic sense (though of course we can, morphologically, phonologically, orthographically, etc...) but rather in its symbolic sense.

owleye

phaedrus

Ierrellus

Consider the lowly photon, which can be viewed as a particle or a wave depending on who's looking and why. Each view of the photon yields verifiable and practical results in experiments. But it can't be both, or can it?

There is no unified definition of a photon, hence its pragmatic definitions are dual. Of course there is agreement on both sides of the issue, there is relativistic perspective on both sides of the issue , no argument there. But what is a photon?

While asking the question "what is the photon?", you are at the same time limiting the options for anyone by stating that it can be either a particle or a wave (which is fine since that is what our current scientific knowledge says). If you ask what is a photon to the uninitiated, you will get a blank stare, if you show them the photon and ask them what it is, you will get multiple interpretations...if you ask someone with scientific grounding what a photon is you will get the description above. It depends on the question and how it is asked. Questions are important, answers may be zillion.

If you really want to know whether human beings look at a particular issue or event or idea in a unified manner or dualistic manner or pluralistic manner, you cant pre-define. That is like drawing the boundary and then setting out to find whether there is a boundary. The bottomline is simple - there could be umpteen number of interpretations but in order for us to function as a society, we form a knowledge base which is subscribed to by the majority. This knowledge is formed due to a process of communication and is a result of common agreement and mutual understanding. As the hermeneutics would put it, truth is a "practical" concept, it is not sitting out there waiting for us to discover, it is made through the process of communicative rationality

JP


Edited to add...

If I had simply asked, as phaedrus suggests, "What is this design?", I would never have gotten a variety of interpretive responses.

Care to explain after going through the above?

[ May 02, 2002: Message edited by: phaedrus ]</p>

James Still

Very well put! This is exactly what I was trying to say above. Kant's Ding an sich, the "thing-in-itself," or the essence of a thing that is its true identity, is an illusion. It comes from the same philosophical confusion that said the human being was in essence an immutable soul. Idealism's habit of abstracting essences from things and removing them to some noumenal realm makes nothing more "real" -- reality is linguistic ambiguity and the multi-faceted phenomenal world in which we live. What is the essence of a thing? It is a hermeneutic; it is agreement in language; it is conformity to the "knowledge base," which is always open to interpretation.

James Still

I hear what you're saying Owl. But ask yourself this question: what does it mean for a thing to look "nothing like a triangle"? Is there a triangle in reality to which we must conform our thoughts and perceptions? Or is it the case that the ancients fashioned an abstract object with three sides which they then defined to be a triangle? If it is the latter (as I believe) then for a thing not to look like a triangle means that it fails to conform to our definition of the abstract object that has been constructed from our perceptions.