Jump to content
Objectivism Online Forum

SpookyKitty

Regulars
  • Content Count

    432
  • Joined

  • Last visited

  • Days Won

    7

SpookyKitty last won the day on April 24 2018

SpookyKitty had the most liked content!

1 Follower

About SpookyKitty

  • Rank
    Member

Previous Fields

  • Country
    United States
  • Interested in meeting
    No
  • Relationship status
    Single
  • Sexual orientation
    Straight
  • Experience with Objectivism
    Atlas Shrugged, Fountainhead, ITOE, Objectivism The Philosophy of Ayn Rand and various articles

Profile Information

  • Gender
    Female

Recent Profile Visitors

2411 profile views
  1. The word "unit" is NOT a synonym of the word "particular". The word "particular" is an antonym of "universal", both of which are metaphysical notions. Units are epistemological. If I wanted to talk about units, I would have used the word "unit".
  2. Ummm... yeah... cuz that's totally a thing that normal, sane people do... Here: unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit unit Does that make you feel better?
  3. I don't remember saying anything about units.
  4. Ok, see this is what I have a problem with. Strictly speaking, there are no "quantities" in reality since every thing that actually exists is a particular. So one cannot literally have "two" (or more) of any particular thing. Therefore, quantities are abstractions, and cannot be used in the process of concept formation without concept-stealing. What I was saying earlier was that the first step of concept formation (the one where we move beyond concrete representations of concrete entities), is not the passive process of measurement omission, but the active process of interpolation (the explicit, conscious, mental construction of entities that we have never actually observed from the mental representations of entities that we have actually observed). For example, whenever I have read about Rand's description of the formation of the concept "length", in my mind, I visualize two "long" objects (pencils, say), laid next to each other and then I mentally construct a third pencil that is longer than both, and a pencil longer than that, and so on. But I still don't fully feel as though I have grasped the concept of "length", but rather, only the length of pencils. When, however, I grasp the spatial relationships among the lengths of the pencils, only then do I feel like I have grasped "length" as an abstraction. Because now that I have an awareness of the spatial relationships involved alone, I can apply the concept of length to things other than pencils, such as football fields, cars, and so forth. Note that this happens entirely without any sort of quantitative reasoning, not even implicitly. My claim is that spatial reasoning is fundamental because, while I can imagine thinking without numbers, I cannot, no matter how hard I try, think without space. Even when comparing numbers I tend to think things like : "Oh, 2 is less than 3 because 2 is to the left of 3 on the number line". And this ties back into the discussion about quantiative vs. qualitative. That a given length x is longer than some other length y is a qualitative distinction. On the other hand, that a given length x is longer than some other length y by 2.3 inches is a quantitative distinction. And I would disagree with Eiuol that length is a quantity. Length can be measured by a quantity, but it is not itself a quantity.
  5. We assumed that "P(g) or not P(g)". We then derived "P(u) or not P(u)" by excluded middle. Since we assumed one and then derived the other, we can use implication introduction to infer "If P(g) or not P(g), then P(u) or not P(u)".
  6. Recognizing a pattern you've already seen would be an instance of induction. But figuring out a totally new pattern you've never seen before would be an instance of concept formation.
  7. Abstraction from abstraction isn't relevant here because what I described is an abstraction from concretes. Not at all. My point was that what patterns someone can recognize in data is a function of the concepts they have and not simply perception.
  8. This is a contradiction. There is always some property that some thing has from which we can deduce that another thing has it too. Proof: Let g be "God" and let u be "universe". Let P be any property. First, suppose that "P(g) or not P(g)". Then, by the law of excluded middle we have, "P(u) or not P(u)". By implication introduction this gives, "if 'P(g) or not P(g)', then 'P(u) or not P(u)'". Now, let the property Q(x) be defined as "P(x) or not P(x)". We now derive, "if Q(g), then Q(u)". The proof of the converse is left as an exercise to the reader.
  9. I agree, but that's not all that they are for. To be fair, I misspoke here. The central component of Rand's theory is that you can extrapolate values of characteristics from the range of the "crow epistemology" (measurements whose values you can directly perceive) to the conceptual level (measurements you can't directly perceive, such as distances in the light years and such). Rand's theory allows you to do this. My problem with it is that, since it only allows for the total abstraction of one characteristic at a time, the resulting concepts cannot encode complicated interdependencies among characteristics. Rand did try to mitigate this issue to some extent by allowing for some unspecified functional relationship between a single characteristic (an independent variable) and all the rest (dependent variables) by using the notion of an "essential" characteristic. But this still wouldn't be enough, since actual phenomena may not have any essential characteristic in the Randian sense. This happens all the time when you have feedback loops. When this occurs, engineers and scientists are forced to describe the behavior of such systems by using differential equations and characterizing those systems by their solution sets. And these solution sets are abstract spaces! These spaces are then understood to be the essential defining features by which systems are classified. Note that in these cases, the systems are not classified by any one nor any combination of their measurements. Indeed, they cannot be. No, it has everything to do with Rand's theory of concepts, because it is precisely the concepts we have that make some data-sets easily recognizable. A layman and a physicist may have the exact same perceptual apparatus, but data that is meaningful to the physicist might seem completely random to the layman. The difference is in the physicist's far superior integration of lots and lots of physics and math concepts. Exactly. Which is precisely why Rand's theory of measurement omission cannot possibly be complete.
  10. @Eiuol I agree with a lot of what you said. I also think qualitative distinctions are more fundamental than quantitative ones. @Grames @Easy Truth I will write out some rough thoughts I've been having and some research I've been doing on this subject. Hopefully it will make things clearer. Imagine that you have two entities where the measurements of the first entity with respect to some characteristics (that we care about) are (1.0,1.0,1.0) and the measurements of the second entity are (2.0,1.0,1.0). Now, at the end of the day, Objectivism allows you to form exactly one "big" concept from this data set: A = (x,1.0,1.0) where the use of the variable "x" means that the entities belonging to this concept must have some measurement value for the first characteristic, but may have any measurement value. But also, we can use differentia to get many more "small" concepts by specifying ranges that the variable is allowed to take. For example: B = ([1.0, 12.0], 1.0, 1.0) means that the value of the first characteristic can be anything between 1.0 and 12.0, but the values of the other two characteristics must be exactly 1.0 and 1.0, respectively. So B is a sub-concept of A. You can take concepts like these and make further restrictions to get sub-concepts of sub-concepts, for instance C = ([2.3, 4.6], 1.0, 1.0). And, I don't think it would be too much of a stretch to say that you can do disjunctive sums of intervals to get even more complex concepts such as: D = ([1.0, 12.0] + [26.5, 123.4], 1.0, 1.0) where the notation "+" means that the entity is allowed to have values either in the interval [1.0, 12.0] or in the interval [26.5, 123,4]. Furthermore, by using these two entities in combination with others, again, I don't think it would be an unreasonable interpretation of Objectivism to say that you can have concepts that look like this: E = ([1.0, 12.0] + [26.5, 123.4], y, [0.1, 2.6]) or even ones that allow for infinite collections of allowed intervals like this: F = ( [1,0, 2.0] + [4.0, 5.0] + [7.0, 8.0] + ..., y, z). If you spend some time graphing these examples, you will notice that all of the concepts formed by these methods look like rectangular prisms arranged in rectangular prisms arranged in rectangular prisms, etc., all of which have edges that are parallel to at least one of the axes. Furthermore, these are the only kinds of shapes that concepts in Objectivism are allowed to have. I hope that this will make clear what I meant when I said that Rand's theory of concepts is "merely classifying things". The problem with her theory is that there will always be real-world collections of entities that completely confound this sort of scheme. That is, when you plot the measurements of all the entities in the collection, they might form a shape which is very simple but which cannot be a combination of rectangular prisms. For instance, consider the collection of entities: {(0,2),(1,1),(2,0),(3,1.1)(4,2.1),(3.1,3),(2.1,4),(1.1,3)} Any combination of measurement omissions and restrictions to intervals will result in just two kinds of interpretations of the data. On the one hand, you will have very simple interpretations which underfit the data. And on the other hand, you will have very complicated and counter-intuitive interpretations which overfit the data. And in no case whatsoever will you obtain a system of concepts which notices the super-simple underlying pattern you would have gotten had you simply plotted some points and used your spatial intuition to play connect-the-dots. Even though none of the entities in the above example have any measurements in common, by using your spatial intuition, you can form a simple network of similarities: (0,2) ~ (1,1) ~ (2,0) ~ (3,1.1) ~ ... ~ (1.1,3) ~ (0,2) which your brain would immediately recognize as a one-dimensional loop. A one-dimensional loop is a notion that: 1) Is highly abstract, and can be applied to just about any data whatsoever to yield tons of non-trivial information about that data. 2) Is super easy to understand. It's almost concrete in how easy it is to understand. 3) Captures the essence of how the entities in the example are related in a very simple and accurate way, even though they are all different from each other. I say "accurate" in the above because saying that the data is described by a one-dimensional loop also implies a network of dissimilarities among the given entities. For instance, we can say that (0,2) is dissimilar to (2,0), because, on the one-dimensional loop, there is no shortcut from (0,2) to (2,0) which allows you to skip the entity (1,1). The process of fitting a manifold to a set of data-points is studied in the field of Persistent Homology: In my opinion, I think that Rand was trying to do something like this when she formulated her theory of concept formation. Rand's theory also suffers from another problem which I've been trying to address. Basically, it smuggles huge portions of mathematics (at the very least the non-zero rational numbers), which themselves have highly non-trivial spatial structure, into the notion of measurement. This, in addition to the above, is why I don't find Grames' account of how concepts of space can be derived from measurement omission at all convincing. I believe that this problem can be remedied by claiming that the human brain comes equipped with a very small number of simple spatial ideas and operations which can be used to form any mathematical concept including the concepts of logic. All this has lead me to investigating the theory of simplicial sets. These are very simple and very interesting mathematical gizmos that can encode combinatorial and topological information simultaneously. Furthermore, they constitute what is called a "topos" in category theory, which means that they are capable of serving as a foundation for all of mathematics. Additionally, every topos has its own internal logic, (and these logics are, in general, higher-order intuitionistic type theories). So there is a conception of logic out there somewhere which can be derived entirely from spatial concepts. The main problem is that the standard theory of simplicial sets allows for simplices of arbitrarily high finite dimension, and the human brain can handle only 3. However, as it turns out, it's very easy to prove that simplicial sets restricted to at most 3 dimensions also constitute a topos. I am currently trying to figure out the ins-and-outs of all of this stuff, but I think that Rand's dream of a mathematical epistemology is on the horizon.
  11. This is an important question that I've been thinking about as well. The more I introspect, the more I realize that my brain just doesn't work the way that Rand describes. For me, if I merely know how to classify a thing, I don't feel like I understand it. But if I can see its structure and the structures it forms in relation to other things and how that structure might be changed and so on, only then do I feel like I truly understand it, and only then can one come up with truly non-arbitrary classification schemes. As an example from algebra, if you were to just tell me that a group is just a monoid where every element has an inverse, I wouldn't understand the concept of "group". But if you were to then show me a rotating triangle and how those rotations relate to the group operation, then I would easily understand the concept of a group. Even the concept of "concept" (the one that Rand describes) I currently understand primarily in terms of space. For instance, when thinking about the relationship of dogs to all other animals, I see a big circle in my mind labeled "animals", and within that circle, a smaller circle labeled "mammals", and within that circle, a smaller circle labeled "dogs". So I think that all of the concepts in my mind are spatial ones. Therefore, I strongly suspect that the process of concept formation is some kind of operation on spaces. At the very least, this is true in my case. other people's brains might work differently. Some people can't see anything in their mind's eye. Others don't hear an internal monologue. And some think only in terms of pictures of things they've actually seen. It's too simplistic to think that everyone's brain works just like yours does. EDIT: I should probably mention some of the research on this topic that I've been doing. I've been studying category theory, and I think the idea of adjunctions may hold the key to concept formaiton. By using adjunctions, one can "mechanically" derive significant mathematical concepts from totally trivial ones. I just need to find an interpretation of adjunctions that makes sense.
  12. Yes, that seems like a very important distinction to keep in mind. The only thing I would change is to avoid naming this characteristic "constructible" and the values "0" and "1", and instead use the terms "hypothetical" and "actual". An entity with the value "hypothetical" denotes an entity that has merely been imagined, whereas the value "actual" denotes an entity that has actually been observed. I'm sure there's a fancy word for this kind of distinction, but I forgot what it was. Is this what you have in mind? Yeah, it would be absurdly hard, since then you would have to reproduce a human-like perceptual system. Instead, the point here is to represent entities as they are represented in conscious reasoning, and, during the course of conscious reasoning, you cannot conceive of a specific entity apart from its characteristics.
  13. Two characteriatics A and B are commensurable if and only if they are identical as types. For example, Char1 is commensurable with Char1 and nothing else. Color is commensurable with color and nothing else.
  14. Characteristics are supposed to be anything you can directly perceive. For example color, texture, shape, etc. Their terms are the values of those characteristics like red, rough, round, etc. I Will make a more detailed submission soon.
×
×
  • Create New...