Jake

Rand's view of essence is epistemological. Gotthelf doesn't state that unit-economy alone achieves objectivity. As you can see, objectivity is achieved through adherence to reality, including adherence to the requirements of cognition. Unit-economy falls into the "requirements of cognition" category; it is not the sole requirement of objectivity. The principle of unit-economy tells us that we should define concepts using an essential characteristic. Reality (causal relationships) determines what that essential characteristic is. Gotthelf is saying here that definition via essentials accomplishes unit-economy, not that unit-economy determines the essence. Determination of the essence is described earlier: I don't understand your differentiation of "essence" and "fundamentality" in the context of Gotthelf's paper. A characteristic’s "fundamentality" is the nature of its causal relationship to other characteristics which makes it the proper choice as the "essence" in the process of definition. (Note: “essential characteristic” and “essence” have been used interchangeably for syntactic ease.)

Do you agree that unit-economy is the purpose of concepts? I need to read Gotthelf's paper before commenting more, but as I see it, fundamental characterstics apply to the process of defining a concept which is already formed. Man is the "rational animal", because his rational capacity is responible for the greatest number or most important characteristics that separate him from other animals and therefore "rationality" serves as the proper defining characteristic. However, as described in ItOE, a child does not need to understand rationality in order to understand the concept "man" nor to be able to identify its referents (men). Definitions may change with time, because the context of knowledge about a given set of units may change, thus changing the fundamentality of a given characteristic. The meaning of the concept (its referents) doesn't change. That unit-economy is the purpose of concepts is why I agree with Don Watkins' (DPW) old thread in which he shows that brainless babies are still babies (i.e. young instances of the concept "man"), even though they lack a rational faculty.

I perform basic arithmetic in a very similar way. I add large numbers the way you described, and I sometimes multiply pairs of 2-digit numbers by multiplying all 4 combinations of single digits and adding the results. For the brief time that I was a Math major, I used to race friends in arithmetic. There's an aspect of my job in which I have to multiply 2 percentages. The first number is usually 110-120%, and the second is always 91-100%. I'm the only one who does this regularly in my head, and I almost got the call sign "Rainman" because people think it's odd, but as you describe above, it's simple. For example, multiplying 116% by 97% directly would take some time, so I instead multiply 116% by 3% (1 - 97%) and subtract the result 3.48% from 116% to get 112.52%. In practice, I only care about whole percentages, and I round down as a safety precaution, so the calcuation is even easier, because I know 116% x 3% is more than 3% and less than 4%, so I just subtract 4%. Everyone else uses a full-page table to lookup the result or scrambles for a calculator/cell phone to punch it in. (For those interested, the first number is torque available from an engine based on environmental conditions, and the second is the engine's efficiency relative to a standard engine.) To me, the interesting question to answer is, does one do Math this way because they have a better grasp of numerical relationships, or does using such methods increase one's understanding of numerical relationships? I suspect it's both, the method and the understanding reinforce one another. I think what a lot of people don't realize is that you can often spend a small bit of your time figuring out how to solve a problem faster and with significantly fewer numbers to juggle. This initial time spent is like an investment: it may cost a few seconds to plan, but it often saves you 10 seconds or more in solving. You can be a smart, motivated person without doing math this way. Unfortunately, when I try to show my peers how they can do the same, I usually run into the anti-conceptual laziness/fear w.r.t. new methods. "That's too hard for me.", "I'd screw it up.", "I'll just stick to what I know.", "Nerd!", etc.

I concur, and would add that a transparent attempt by the woman to appear into it would be even worse. I like nude women, but I hate strip clubs...

I just want to clarify that neither Einstein nor his equations reify space. Later interpreters and people trying to dumb it down for laymen (Brian Greene, et al.) have reified space. Here's a relevant quote: Italics original I think that's the third time I've posted that quote to this forum, but it's a point I like to make. The math is solid, even if some attempts at physical intrepretation are faulty.

I read "special" as referring to the symmetric placement; I would expect a Mathematics site to use the term "unique" if that is an essential feature. In this sense, "special" is as opposed to "arbitrary." You're right, I should have said that the sum of all vectors starting at the chosen point is zero, since each vector will have a symmetric partner (equal in magnitude and opposite in direction).

Maybe another definition-pull will help here (this time from Wolfram's MathWorld) The standard "center" of a circle/sphere is right where you think it is, and it defines the circle/sphere. Alfred Centauri was discussing the curve of the circle / surface of the sphere. The definition above does not say the center must be unique, so any point on the circle's curve or sphere's surface can be considered a center, since every point has "symmetric placement" with respect to the metric on the curve/surface (i.e. the sum of the distances from the chosen point to all other points is zero).

Another comment about circles/spheres... The metric on the curve of the circle / surface of the sphere is finite (bounded by R*pi in both cases). As shown by plasmatic's dictionary pull, "finite", "bounded", and "limited" are synonymous with respect to a given quantity.

This discussion seems to have been made more difficult due to: (1) confusion about the definitions of the various forms of "bound", and (2) sloppiness of context when discussing boundedness. (1) I don't have access to the OED, so you'll have to accept Merriam-Webster One can see that the boundary of an entity is the limit of its extent, regardless of whether or not another entity is at or abutting that boundary. Imagine a droplet of water floating in the emptiness of space. If you were to travel outward from the center of the droplet, you would cross the boundary when you are no longer inside the droplet and start being outside. The boundary is where the water stops and nothing (no thing) starts. (2). The surface of a sphere (or of Earth) is bounded in the sense that the entire surface can be described by a finite coordinate system (i.e. Lat/Long), and it is unbounded in the sense that the distance one can travel in a straight line is potentially infinite. One must be clear about the context of the property "bounded." Finiteness of a certain aspect most certainly entails boundedness in that same aspect. The size of a circle is bounded and the numbers required to describe a position on a circle are bounded (0 < s < 2pi). The unbounded aspect of a circle is travel along the curve, which is also potentially infinite. The meaning of "finite and boundless" may be clear to mathematicians and physicists when discussing circles/spheres, but it involves sloppy context - It's the equivalent of saying I am "brown and green," because my hair is brown and my eyes are green.

I only read the first paragraph on the site. It reminded me of L. Ron Hubbard's nonsense.

Your injective map definition assumes the natural numbers have infinite quantity, so it is circular. To say that the natural numbers are infinite is to say: - there is no largest natural number, or - the natural numbers are unbounded, or - for any natural number n, n+1 is a natural number, or - the series of natural numbers is open-ended. It does not mean that there are an infinite number of natural numbers. In fact such a statement isn't even valid. It is incorrect to smuggle in the idea of infinity as a number rather than a concept of method which denotes an open-ended iterative process or unbounded set. The concept of "quantity" refers to the amount of something, which is determined by counting the units which comprise it. This is not a "special notion." The idea of "infinite quantity" is invalid because the Law of Identity demands that whatever the final count of units is, it is that count. If the counting process is open-ended, the counting is never complete: there is no final count; there is no quantity. Infinity is not a number, or in the words of my high school math teacher: "Infinity isn't a place you can visit."

As discussed earlier (and in the other thread), "0.999..." refers to the following: What I see as a reasonable objection to the above concept of method is the invocation of an infinite process, but this is not necessary. A common description of the above limit might be, "The value of the sum of the sequence if it were to be carried out to inifinity." I would agree this is a bad description, because no sequence can actually be carried out inifinitely. However, you can describe the evaluation of the above limit in a well-defined way which corresponds to reality, as such: The evaluation of the limit is equal to the smallest real number which is greater than the sum of the sequence after n iterations, where n may be any natural number greater than or equal to 1. The value of the limit does not have to be described as something which is approached or as the evaluation of an impossibly infinite sequence. It is mathematically well-defined and conceptually valid (i.e. connected to reality). Edit: replace "is" with "may be"

I also know of people whose SSNs start with the same 3 digits as their parent(s), as opposed to the number commonly issued in their state of birth/residence. For example, a buddy of mine was born in FL and raised in AL, but has a 5xx SSN (CA/AZ areas).

If remember correctly, when Rand discussed the Bond films, she liked the first 2 or 3 and disliked the later films which were campier and seemed to poke fun at Bond.

I think the confusion and apparent circularity might be cleared up by observing that reason, purpose, and self-esteem are only values if you choose to live. Each of these are not 'values in themself' - they are subordinate to the utlimate value: life as a human. Rationality, productiveness, and pride are virtues, because they are principled means to living. In other words: while the virtue of rationality leads one to have reason, the end of rationality (the ultimate goal it serves) is life.

This is not quite correct. According to GTR (and Einstein's own words), space is not an independent entity. It is a description of the relationships between massive entities. There is not literally a curved spacetime; the behavior and relationships of massive entities are affected by the presence of other massive entities. There is no background, just entities.

I was also referring to the "liberty of action" meaning, and I agree with the last sentence above. A right is a freedom of action, but freedom from what? The answer is other people. Rights derive from our nature including the requirements of living (according to that nature) with other people.

Please define "natural right." What is a right outside of the context of human relationships (society)?

There is a reason Rand doesn't discuss bare survival or merely staying alive as the proper goal of man's life. She uses phrases like "man's survival qua man," which means to live as a man or in accordance with the nature of man (i.e. as a rational being). Tara Smith uses the term "flourishing" to emphasize the point. Perhaps I should have been more descriptive. The choice which opens the door to rational ethics is not "Do I want to stay alive?" It is: "Do I want to live, as a man, in accordance with the nature of man?" Man's nature is that of a rational animal. Like other animals, it is man's nature to eat, sleep, etc. These are required for bare survival, however, it is also man's nature to reason. In fact, reason is man's primary tool of survival. To live as a man is to reason. What actions should one take if one wants to continue thinking rationally? Objectivist ethics has the answer. Great questions, and kudos for asking them. When I first read Rand's fiction, the sense-of-life resonated with me and I read a bit of the non-fiction. I wasn't unable to immediately integrate all of the ideas into a coherent whole, and unfortunately, I let my philosophic inquiry fall to the side for a few years. Keep at it. Warning: the following is personal opinion and should not be taken as a representation of Objectivism... I've recently come to realize that I thoroughly enjoy choosing. I see conscious choice (contrasted with animals' instinctive selection between alternates) as a fundamental aspect of human nature. Not only is rationality the best way to stay alive, it is the best way to sustain my ability to choose, improve my methods of choosing, and increase the breadth of choices available to me.

1. If you have already read Objectivism: The Philosophy of Ayn Rand (OPAR), I suggest picking up Tara Smith's books on the subject: Ayn Rand's Normative Ethics: The Virtuous Egoist and Viable Values. Both of these helped me clarify and concretize my understanding of Objectivist ethics. 2. An obligation assumes an agreement or contract - so innate and/or single-party obligations are a contradiction in terms. Objectivist ethics is about the choice to live and acting in accordance with reality to fulfill that choice. "If I want to live, then I must ________." <-- Ethics fills in that blank. Edit: formatting

I saw an episode of Dexter tonight with a good quote from the main character regarding his adoptive father: The quote reminded me of why I will tell my son that Santa Claus is just a story.

I agree, though I would point out that the actions leading to that man-made fact may be immoral (e.g., even if you never kill anyone, planning or fanasizing about murder is immoral.)

You found that OPAR quote significant enough to make it bold, so my question is: If focus is the readiness to think, how can any creature be ready to think (focused), if it is not capable of thinking (i.e., having a rational faculty?) Edit: While the choice to focus is prior to rational activity, it is not prior to rational capacity. Diana clarified her use of the term "rational mind" as "rational faculty" on the first page of the thread.

I disagree. I joined the Navy at 23, and the Navy sent me to college at 26. As an Engineering major, I found plenty of mature 20-year olds with whom I could socialize, and I shared a house with graduates students who were the same age as me. Unless you're going to college married or well into your 30s, the social aspects of the age difference will be negligible. Even if one were to use friends and family as the standard for one's own life, I see no basis for this claim. I met my wife while in college and married her at 28 after graduating. I am, on average, six years older than my professional peers. Other than a few 'grandpa' jokes, it makes no difference. Some people get married and have kids before 25; some people wait until after 35. I would not let your age prevent you from joining the military. The Post-9/11 G.I. Bill pays for quite a bit. If you are interested in the military, check it out here. Sounds like you have a good plan. I was in a similar situation. I went to college at 17 with no goals and was "asked" to leave after 3 semesters with a 1.4 GPA. When I returned 7 years later, I knew why I was there and what I needed to do. It's amazing how easy it is to get straight-As when one is properly focused. U of MD has a little-known process called "academic clemency", whereby you can have up to 16 credits removed from your GPA calculation if you are returning to school after an extended absence. You might want to see if your university has something similar. It turned my 1.4 into a 2.6 and allowed me to graduate with a 3.7 overall. Also, regarding your academic past: Don't be afraid to make some phone calls and talk to a dean or two about your past, what's changed, and your current intentions. Entrance requirements are not necessarily set in stone. When I was trying to get back into school, I called the Aerospace department head and told him I was set on studying Aero at MD and nothing else. I explained my past mistakes and why it wouldn't happen again. He was impressed with the effort and fought for me get accepted to the Engineering college. Good luck.

I know that "A is A" has abandoned this thread, but I just found the authoritative quote which shows his misunderstanding of Objectivist epistemology...