Wednesday, May 28, 2008
Woo hoo!
I got into the OAC! Also, in a week and a half I'm off to the "Moral Foundations of Capitalism" conference. AND, I have a shipment coming in from the Ayn Rand Bookstore soon, too! So I'm just chock-full of Objectivism, ain't I?
Saturday, May 24, 2008
Thoughts on "The Cogito"
This post was motivated by a recent google search which lead to my blog: "arguments against cogito." Unless I am mistaken, and much more popular than I suspected, this googler was looking for a response to a famous statement in philosophical history, not for a response to my brilliant and witty argumentation. Before I start this post in earnest, I want to clear up some confusion relevant to this post. My nickname, "Cogito" has nothing whatsoever to do with the (in)famous declaration by Renee Descartes, cogito ergo sum. Cogito simply means "I Think" in Latin, and for many reasons the meaning of the word and its language apply particularly well to me.
That being said, I do want to discuss Descartes's declaration here. I should note that my knowledge of the statement and its context stems on one side from general philosophy discussions/classes and on the other side from discussion by Objectivists, not from reading Descartes's work myself. The literal English meaning of the term is "I think therefore I am." Most Objectivists who have spoken on this issue have taken this to mean "the act of thinking, of being conscious, causes my existence", i.e. that consciousness is more fundamental than existence. While this is a valid possible interpretation, from my overall understanding, and perhaps from my general optimism, I'd like to suggest another interpretation: "the fact that I am thinking, am conscious, is evidence that I exist." In other words, nothing which doesn't exist could be conscious, and therefore the fact of my consciousness implies my existence, which is a primacy-of-existence viewpoint.
I want to make it clear that I do not, in any way, support Descartes's rationalistic castle-making, nor do I think that those claiming that the primacy-of-consciousness interpretation is correct are wrong. I'm just offering an alternative, one which, if viewed in the right light, is very similar to the axiom of consciousness. That being said, Descartes as a whole has never particularly interested me, so this is probably the last you'll hear about him from me.
That being said, I do want to discuss Descartes's declaration here. I should note that my knowledge of the statement and its context stems on one side from general philosophy discussions/classes and on the other side from discussion by Objectivists, not from reading Descartes's work myself. The literal English meaning of the term is "I think therefore I am." Most Objectivists who have spoken on this issue have taken this to mean "the act of thinking, of being conscious, causes my existence", i.e. that consciousness is more fundamental than existence. While this is a valid possible interpretation, from my overall understanding, and perhaps from my general optimism, I'd like to suggest another interpretation: "the fact that I am thinking, am conscious, is evidence that I exist." In other words, nothing which doesn't exist could be conscious, and therefore the fact of my consciousness implies my existence, which is a primacy-of-existence viewpoint.
I want to make it clear that I do not, in any way, support Descartes's rationalistic castle-making, nor do I think that those claiming that the primacy-of-consciousness interpretation is correct are wrong. I'm just offering an alternative, one which, if viewed in the right light, is very similar to the axiom of consciousness. That being said, Descartes as a whole has never particularly interested me, so this is probably the last you'll hear about him from me.
Wednesday, May 21, 2008
Fiddling with Geohashing
Today's xkcd gives an interesting algorithm for randomly generating a meeting spot:
Image copyrighted by Randall Munroe under the Creative Commons Attribution-Noncommercial 2.5 Generic License
While this algorithm is fun in its own right, for some people and some places it can create unreasonable destinations (for instance, more than half of the locations for most Manhattanites
end up in the ocean, and most of the locations for the rest of the Manhattanites end up in Jersey). With this problem in mind, I've generalized the algorithm to give a random destination within any given parallelogram of any size. Follow xkcd's algorithm until you get to the point where you have two decimals, 0.xxxxxx... and 0.yyyyyy..., which we'll call n and m, respectively . Now, if A is the south-western point of the parallelogram, B is the north-western point, and C is the south-eastern point, then your latitude is given by (latitude of A + n(latitude of B - latitude of A) + m(latitude of C - latitude of A)), and your longitude is given by (longitude of A + n(longitude of B - longitude of A) + m(longitude of C - longitude of A)). Happy Hashing!
P.S. xkcd's algorithm is a special case of my algorithm, where the parallelogram is a square whose sides are 1 degree long and whose corners are at integer degrees.
While this algorithm is fun in its own right, for some people and some places it can create unreasonable destinations (for instance, more than half of the locations for most Manhattanites
end up in the ocean, and most of the locations for the rest of the Manhattanites end up in Jersey). With this problem in mind, I've generalized the algorithm to give a random destination within any given parallelogram of any size. Follow xkcd's algorithm until you get to the point where you have two decimals, 0.xxxxxx... and 0.yyyyyy..., which we'll call n and m, respectively . Now, if A is the south-western point of the parallelogram, B is the north-western point, and C is the south-eastern point, then your latitude is given by (latitude of A + n(latitude of B - latitude of A) + m(latitude of C - latitude of A)), and your longitude is given by (longitude of A + n(longitude of B - longitude of A) + m(longitude of C - longitude of A)). Happy Hashing!
P.S. xkcd's algorithm is a special case of my algorithm, where the parallelogram is a square whose sides are 1 degree long and whose corners are at integer degrees.
Monday, May 19, 2008
Light Posting This Week
It's finals week, so I'll be spending most of my time studying. You can look forward to a review of Pat Corvini's "Two, Three, Four and All That" lecture which she gave at last year's OCON and is now available from the Ayn Rand Bookstore.
Sunday, May 18, 2008
The Problem with Debating
When two people disagree on any issue, it can be very beneficial for both parties to explain the method by which they arrived at their conclusions, in an attempt to ensure that both parties know as much about the issue and the nature of the disagreement as possible. Unfortunately, with a few refreshing exceptions, the source of disagreement on any issue is much more fundamental than the issue itself (especially in the realm of philosophy, but also in other realms). For example, it is impossible to discuss politics reasonably without a common base of metaphysics, epistemology, ethics, and some knowledge about history and the nature of man that is not included in these fields (contrary to what some believe, capitalism is more than just the deductive application of egoism to social interactions; some knowledge about the nature of force, freedom, etc, which is outside of egoism per se, must be brought to the table).
I used to try to debate issues at the highest level possible, ignoring any possible fundamental disagreements. Within the past few years, however, whenever I find myself disagreeing with someone (and whenever I think it's worth trying to convince him), I try to find the most fundamental disagreement so that the debate can proceed properly. In many cases, especially when debating with people who disagree with me on the epistemological or even metaphysical levels, the other person decides that the discussion is simply not worth that kind of effort, and the issue is dropped. Sometimes, however, the debate will continue on the more fundamental level.
This is where it gets frustrating. The person is clearly interested in figuring out the truth (people who simply want to win the argument typically don't like it when the "battleground" changes), but the issues are so complex and fundamental that they are both difficult to describe explicitly (even if they are understood perfectly well implicitly) and difficult to change (or even convince the other person that your alternative is possible). The high involvement of the topics combined with the fact that two opposing wills are involved often leads to long, possibly necessary, tangents, and after a few hours of debate only moderate ground, if any, has been established.
I don't find this kind of discussion completely useless (so long as you don't fall into a loop or concede any ground without reason), but it's a lot of work for what seems like very little progress and there's the ever-present fear of saying something the wrong way and turning someone off to an idea (even though it's not your responsibility to make sure others are rational, it's reasonable to want to "serve" the truth in the best way possible). I'm not really sure where I'm going with this, I just needed to vent a bit after a very long discussion that still isn't really over.
I used to try to debate issues at the highest level possible, ignoring any possible fundamental disagreements. Within the past few years, however, whenever I find myself disagreeing with someone (and whenever I think it's worth trying to convince him), I try to find the most fundamental disagreement so that the debate can proceed properly. In many cases, especially when debating with people who disagree with me on the epistemological or even metaphysical levels, the other person decides that the discussion is simply not worth that kind of effort, and the issue is dropped. Sometimes, however, the debate will continue on the more fundamental level.
This is where it gets frustrating. The person is clearly interested in figuring out the truth (people who simply want to win the argument typically don't like it when the "battleground" changes), but the issues are so complex and fundamental that they are both difficult to describe explicitly (even if they are understood perfectly well implicitly) and difficult to change (or even convince the other person that your alternative is possible). The high involvement of the topics combined with the fact that two opposing wills are involved often leads to long, possibly necessary, tangents, and after a few hours of debate only moderate ground, if any, has been established.
I don't find this kind of discussion completely useless (so long as you don't fall into a loop or concede any ground without reason), but it's a lot of work for what seems like very little progress and there's the ever-present fear of saying something the wrong way and turning someone off to an idea (even though it's not your responsibility to make sure others are rational, it's reasonable to want to "serve" the truth in the best way possible). I'm not really sure where I'm going with this, I just needed to vent a bit after a very long discussion that still isn't really over.
Saturday, May 17, 2008
Selected Topics in the Philosophy of Science, Part III: Philosophical Vacua
In the physics part of his lecture, Dr. Binswanger excludes two forms of "empty space" based on metaphysical arguments. The first form, "space outside the universe", is not an issue if, as I argue is metaphysically permissible in the previous post, space is finite but unlimited (and if it is not, I agree with Dr. Binswanger's argument). My disagreement is with his metaphysical argument against vacua within the universe itself.
Before I go into detail, I want to clearly delimit the scope of this post. I intend to argue that vacua are metaphysically permissible. That being said, given my understanding of the current knowledge of physics, I do not think vacua actually exist. In this sense I agree with Dr. Binswanger, and the only practical upshot of my disagreement is that if scientists do find evidence for an actual vacuum, I would not dismiss him out of hand (while Dr. Binswanger, at least according to this lecture, would).
Dr. Binswanger's defines a vacuum as a region where there is nothing, and for the sake of this discussion I will use that definition, though I think a better definition would be a region with no entities, as Dr. Binswanger's definition could lead to the reification of "nothing" (complete side note: Firefox's spell-check suggests "deification" in place of "reification". I find that humorously appropriate). Dr. Binswanger attacks this definition by saying there is no "region" to have the nothing. He first points out that you can't distinguish two separate points within the vacuum because there are no two things in the vacuum to distinguish. To separate point A from point B, he argues, there has to be something at A and something at B.
He goes on to recognize that you could possibly distinguish portions of a vacuum by means of a potential: the potential to put a ruler between two objects outside the vacuum without having to move the objects apart. He states that any potential has to be a potential of something (which is correct), and then claims that such a potential would have to be a potential of the vacuum, which is nothing. But why can't the potential be a potential of the entities surrounding the vacuum?
Dr. Binswanger tries to attack that possibility by saying that the potential would disappear by moving the entities together, but that very argument shows that it is in fact a potential of the entities, specifically a potential resulting from the relative locations of the entities. The fact (which Dr. Binswanger acknowledges) that moving the entities removes the potential demonstrates that the potential is dependent on the location of the entities. To put it in terms of identity, one aspect of the natures of the entities (specifically, their relative positions) gives rise to the potential of putting a ruler between them without moving the entities. Nowhere in that formulation is any attribute given to the vacuum itself, and therefore the potential rests on solid ground.
This concludes my critique of Dr. Binswanger's course. To sum up, I disagreed with the ideas that Gödel's Theorem is invalid, that space and the number of entities must necessarily be limited, and that vacua can not exist on metaphysical grounds. Despite these disagreements, I still greatly enjoyed the lecture and strongly recommend it to anyone interested in science.
Before I go into detail, I want to clearly delimit the scope of this post. I intend to argue that vacua are metaphysically permissible. That being said, given my understanding of the current knowledge of physics, I do not think vacua actually exist. In this sense I agree with Dr. Binswanger, and the only practical upshot of my disagreement is that if scientists do find evidence for an actual vacuum, I would not dismiss him out of hand (while Dr. Binswanger, at least according to this lecture, would).
Dr. Binswanger's defines a vacuum as a region where there is nothing, and for the sake of this discussion I will use that definition, though I think a better definition would be a region with no entities, as Dr. Binswanger's definition could lead to the reification of "nothing" (complete side note: Firefox's spell-check suggests "deification" in place of "reification". I find that humorously appropriate). Dr. Binswanger attacks this definition by saying there is no "region" to have the nothing. He first points out that you can't distinguish two separate points within the vacuum because there are no two things in the vacuum to distinguish. To separate point A from point B, he argues, there has to be something at A and something at B.
He goes on to recognize that you could possibly distinguish portions of a vacuum by means of a potential: the potential to put a ruler between two objects outside the vacuum without having to move the objects apart. He states that any potential has to be a potential of something (which is correct), and then claims that such a potential would have to be a potential of the vacuum, which is nothing. But why can't the potential be a potential of the entities surrounding the vacuum?
Dr. Binswanger tries to attack that possibility by saying that the potential would disappear by moving the entities together, but that very argument shows that it is in fact a potential of the entities, specifically a potential resulting from the relative locations of the entities. The fact (which Dr. Binswanger acknowledges) that moving the entities removes the potential demonstrates that the potential is dependent on the location of the entities. To put it in terms of identity, one aspect of the natures of the entities (specifically, their relative positions) gives rise to the potential of putting a ruler between them without moving the entities. Nowhere in that formulation is any attribute given to the vacuum itself, and therefore the potential rests on solid ground.
This concludes my critique of Dr. Binswanger's course. To sum up, I disagreed with the ideas that Gödel's Theorem is invalid, that space and the number of entities must necessarily be limited, and that vacua can not exist on metaphysical grounds. Despite these disagreements, I still greatly enjoyed the lecture and strongly recommend it to anyone interested in science.
Friday, May 16, 2008
Fall Semester Scheduling, Try II
After putting some thought into my previous schedule and speaking to an adviser, I've redesigned my ideal schedule. Like before, course descriptions follow, and, like before, click the down arrow and then the + to zoom in.
Course Descriptions:
BME 101 Introduction to Biomedical Engineering:
Course Descriptions:
BME 101 Introduction to Biomedical Engineering:
"An introductory overview of the multidisciplinary field of biomedical engineering. Application of elementary engineering principles to the analysis of physiological systems. Includes basic introduction to the use of computers as tools for solving engineering problems. Course topics include biomechanics, cell and tissue engineering, biosignals and bio-instrumentation, medical imaging, medical optics, and bioethics[sic!]. Includes some guest lectures by biomedical engineering faculty"ECE 111 Introduction to Signals and Circuits:
"Analysis techniques for DC and AC circuits"MTH 173Q Honors Linear Algebra with Differential Equations:
"An honors [course] covering the material of MTH [165] in greater depth from the standpoint of both theory and applications. Students completing this [course] successfully will have met the requirements of MTH 235 and can begin taking upper-level courses immediately"BIO 112 Biology Perspectives I:
"The first semester of a two-course introductory sequence for students with a strong background in science. Topics include biochemistry, molecular and cellular evolution, cell reproduction, fundamentals of genetics, and molecular biology. This course differs from BIO 110 in that there is greater emphasis on experimental approaches, data analysis, and quantitative methods, and may include reading original papers. A significant writing component includes preparation of a book review (from selected titles, such as The Selfish Gene). Note, both BIO 110 and BIO 112 are designed to prepare students who intend to major in biology."CHM 203 Organic Chemistry I:
"An introduction to organic chemistry that focuses on chemical bonding, structure and stereochemistry, reactions and reaction mechanisms of organic compounds."CHM 207 Organic Chemistry I Laboratory:
"One lab lecture and lab session per week provide an introduction to the characterization and reactivity of organic molecules. The course provides an introduction to modern laboratory techniques used in organic chemistry."BCS 110 Neural Foundations of Behavio(u)r:
"Introduces the structure and organization of the brain, and its role in perception, movement, thinking, and other behavio[u]r. Topics include the brain as a special kind of computer [ed: That could end badly], localization of function, effects of brain damage and disorders, differences between human and animal brains, sex differences, perception and control of movement, sleep, regulation of body stages and emotions, and development and aging."
You Mean the Bible isn't Enjoyable?
Via Randex:
Favorite book: "Being a Christian, I love the Bible. For enjoyable reading, I loved 'Advice and Consent' and 'Atlas Shrugged.' "
Selected Topics in the Philosophy of Science, Part II: Limited Space, Limited Entities, Infinity
In the lecture on mathematics, Dr. Binswanger considers the concept of infinity and asks whether it is valid, even as a concept of method or potentiality. He answers (tentatively) in the negative, for two essential reasons, the metaphysical and the psycho-epistemological.
The metaphysical argument hinges on the idea that there are a finite number of entities and thus a finite number of things to which we can assign a number, and therefore the concept of infinity as "always being able to add one more" isn't true: we reach a point (albeit a very large point) where our next number doesn't stand for anything.
The psycho-epistemological argument also depends on the finitude of entities: making a symbol to represent the next number takes up space, and even though the human consciousness can make mental condensations, those condensations themselves take up space and therefore there will be a point, even with a computer-augmented mind, where we can no longer hold the next symbol in our head as anything relevant.
In the Q&A period of the mathematics lecture, Dr. Binswanger is asked a question about whether there has been an infinite amount of time, and he answers this to the effect of "infinite time between now and... when? Between now and the beginning of the Universe? Well, there was no beginning. Between now and any actual point in the past? Well, no, that's a finite amount of time."
Dr. Binswanger's response indirectly invalidates the finitude of space and, therefore, the finitude of entities (and therefore the metaphysical and psycho-epistemological arguments as well). Consider the question "Isn't there an infinite amount of space?" Well, we could just say "no, it's finite and limited", or, following Dr. Binswanger's argument in regard to time, we could respond "space between here and... where? Between here and the edge of the universe? Well, there is no edge. Space between here and any given entity? Well, no, that's a finite amount of space."
In this way, there is a metaphysical possibility (Possibility here meaning that the idea does not contradict anything in metaphysics. It is not a claim to any amount of evidence supporting that it's actually correct) of unlimited space which is nevertheless always finite. With the possibility of unlimited space comes the possibility of unlimited entities, by the same argument: withing any given amount of space, there is a finite number of entities, but the size of that given amount of space can increase without limit, and with that the number of entities in that space.
If there is no limit to the number of entities, then any number we come up with has something to refer to, and thus the metaphysical argument is invalidated. Similarly, if there is no limit to the number of entities and if we augmented our brains with computers, it is possible that we would always be able to find enough raw material to continue to increase the number of symbols we can store in our computer-brains, thus invalidating the psycho-epistemological argument against infinity. Infinity is thus restored as a valid term.
The primary issue in this discussion is the idea of applying properties to the universe as a whole that do not apply. To apply "time" to something, you need to have two endpoints, so unless you postulate a beginning and/or an end of the universe, you cannot apply time to the universe as a whole. To apply "distance" to something, you need two endpoints, so unless you postulate an edge of the universe you cannot apply distance to the universe as a whole. To count the number of anything, you must know the limits of the space you're counting. You ask "how many books are there on that shelf," or "how much water is there in this glass," etc. Thus, unless you postulate a limited space, you cannot apply amount of anything to the universe as a whole.
A question that occurred to me based upon this thought process is whether or not "universe" is a proper term at all (note that even if "universe" is proper, it is not a concept but rather an instance of the concept "collection"). The issue I'm having is that, since so many properties like "time", "space", "number of entities" do not apply to the universe, which properties do (i.e. what is its identity)? You could say "the universe is that collection which contains everything that exists", but attributes must be finite (the omitted measurements may be any quantity, but they must be some quantity). So, what exactly is the universe? I don't have an answer, and comments are greatly appreciated.
I should note here that I have been approaching this issue metaphysically. The essence of my argument is that nothing in metaphysics necessitates the existence of an edge of the universe (and therefore nothing necessitates space being limited). At the same time, however, I'm not sure that anything in metaphysics necessitates the absence of such an edge (though I would be open to such an argument). Therefore, as of now the question remains in my mind one for the physical sciences (though I do not count the current discussions of the size of the universe within the scientific community as at all valid).
That was a hefty post, so to sum up: Dr. B claims that infinity is invalid on metaphysical and psycho-epistemological grounds because the number of entities is limited, and then goes on to claim that time is finite but unlimited. I claim that Dr. B's claim of the finite-but-unlimited nature of time applies equally well to space, and therefore to the number of entities, and therefore the metaphysical and psycho-epistemological arguments are invalidated, and infinity is restored as a proper term. I end with some speculation on the propriety of the term "universe", and specify that my argument is purely metaphysical, and that the issue might have to be settled by the physical sciences.
The metaphysical argument hinges on the idea that there are a finite number of entities and thus a finite number of things to which we can assign a number, and therefore the concept of infinity as "always being able to add one more" isn't true: we reach a point (albeit a very large point) where our next number doesn't stand for anything.
The psycho-epistemological argument also depends on the finitude of entities: making a symbol to represent the next number takes up space, and even though the human consciousness can make mental condensations, those condensations themselves take up space and therefore there will be a point, even with a computer-augmented mind, where we can no longer hold the next symbol in our head as anything relevant.
In the Q&A period of the mathematics lecture, Dr. Binswanger is asked a question about whether there has been an infinite amount of time, and he answers this to the effect of "infinite time between now and... when? Between now and the beginning of the Universe? Well, there was no beginning. Between now and any actual point in the past? Well, no, that's a finite amount of time."
Dr. Binswanger's response indirectly invalidates the finitude of space and, therefore, the finitude of entities (and therefore the metaphysical and psycho-epistemological arguments as well). Consider the question "Isn't there an infinite amount of space?" Well, we could just say "no, it's finite and limited", or, following Dr. Binswanger's argument in regard to time, we could respond "space between here and... where? Between here and the edge of the universe? Well, there is no edge. Space between here and any given entity? Well, no, that's a finite amount of space."
In this way, there is a metaphysical possibility (Possibility here meaning that the idea does not contradict anything in metaphysics. It is not a claim to any amount of evidence supporting that it's actually correct) of unlimited space which is nevertheless always finite. With the possibility of unlimited space comes the possibility of unlimited entities, by the same argument: withing any given amount of space, there is a finite number of entities, but the size of that given amount of space can increase without limit, and with that the number of entities in that space.
If there is no limit to the number of entities, then any number we come up with has something to refer to, and thus the metaphysical argument is invalidated. Similarly, if there is no limit to the number of entities and if we augmented our brains with computers, it is possible that we would always be able to find enough raw material to continue to increase the number of symbols we can store in our computer-brains, thus invalidating the psycho-epistemological argument against infinity. Infinity is thus restored as a valid term.
The primary issue in this discussion is the idea of applying properties to the universe as a whole that do not apply. To apply "time" to something, you need to have two endpoints, so unless you postulate a beginning and/or an end of the universe, you cannot apply time to the universe as a whole. To apply "distance" to something, you need two endpoints, so unless you postulate an edge of the universe you cannot apply distance to the universe as a whole. To count the number of anything, you must know the limits of the space you're counting. You ask "how many books are there on that shelf," or "how much water is there in this glass," etc. Thus, unless you postulate a limited space, you cannot apply amount of anything to the universe as a whole.
A question that occurred to me based upon this thought process is whether or not "universe" is a proper term at all (note that even if "universe" is proper, it is not a concept but rather an instance of the concept "collection"). The issue I'm having is that, since so many properties like "time", "space", "number of entities" do not apply to the universe, which properties do (i.e. what is its identity)? You could say "the universe is that collection which contains everything that exists", but attributes must be finite (the omitted measurements may be any quantity, but they must be some quantity). So, what exactly is the universe? I don't have an answer, and comments are greatly appreciated.
I should note here that I have been approaching this issue metaphysically. The essence of my argument is that nothing in metaphysics necessitates the existence of an edge of the universe (and therefore nothing necessitates space being limited). At the same time, however, I'm not sure that anything in metaphysics necessitates the absence of such an edge (though I would be open to such an argument). Therefore, as of now the question remains in my mind one for the physical sciences (though I do not count the current discussions of the size of the universe within the scientific community as at all valid).
That was a hefty post, so to sum up: Dr. B claims that infinity is invalid on metaphysical and psycho-epistemological grounds because the number of entities is limited, and then goes on to claim that time is finite but unlimited. I claim that Dr. B's claim of the finite-but-unlimited nature of time applies equally well to space, and therefore to the number of entities, and therefore the metaphysical and psycho-epistemological arguments are invalidated, and infinity is restored as a proper term. I end with some speculation on the propriety of the term "universe", and specify that my argument is purely metaphysical, and that the issue might have to be settled by the physical sciences.
Part I Part II Part III
P.S. Even if you don't accept the finite-but-unlimited nature of space, the finite-but-unlimited nature of time invalidates at least the metaphysical argument against infinity. We can talk about what happened n seconds ago, and we can also talk about what happened n+1 seconds ago, no matter what the value of n is, by Dr. Binswanger's own admission. Therefore, every number we could come up with has something to refer to.
P.S. Even if you don't accept the finite-but-unlimited nature of space, the finite-but-unlimited nature of time invalidates at least the metaphysical argument against infinity. We can talk about what happened n seconds ago, and we can also talk about what happened n+1 seconds ago, no matter what the value of n is, by Dr. Binswanger's own admission. Therefore, every number we could come up with has something to refer to.
Thursday, May 15, 2008
Selected Topics in the Philosophy of Science, Part I: Gödel's Theorem
A few weeks ago I listened to Dr. Binswanger's lecture "Selected Topics in the Philosophy of Science", and I noted three topics that seemed wrong to me in some way. I've been listening to it again, and will share my thoughts as the issues come up.
The first topic I want to cover is Gödel's Theorem. Dr. Binswanger doesn't talk about it in this lecture, but he does say that he had talked about it in a previous lecture. Since I don't know the content of the previous lecture, I'm not going to criticize Dr. Binswanger's discussion of the issue, but rather the common view I've seen amongst Objectivists who know anything about the theorem.
Many Objectivists say that since the theorem says that there is knowledge that cannot be gained through reason and yet can be known to be true, it must be wrong. But what does the theorem actually say? Like many issues in math and science (see, for example, the second half of this comic), there are two interpretations: the interpretation that actually reflects the math or science involved, and the interpretation that takes the wording of the first interpretation and proceeds to apply it in completely inappropriate contexts. The popular expression of the theorem, that there are statements we can know to be true but can never verify by logic, is not supported by the math and was in fact vehemently fought by Gödel himself. In essence, what the theorem actually says is this (it's slightly more nuanced, but that's not relevant to my point): If you have a finite set of propositions taken as given and are only allowed to use deductive reasoning from those propositions, there exist certain statements which you cannot prove. So, rather than proving that reason is not our only means of knowledge, the theorem proves that deduction is not our only means of knowledge.
Now I should point out that the theorem technically only applies to formal mathematical systems complex enough to express algebra, and not to knowledge in general, but the points I want to make remain true: first, that the theorem is correct (and as ironcladly proven as the Pythagorean theorem), and, more importantly, that the popular formulation of science is almost always different from the actual meaning. Before you jump to criticize something from math or science as philosophically invalid, you have to make sure you know what the actual science says, instead of what the popular interpretation of that science is.
The first topic I want to cover is Gödel's Theorem. Dr. Binswanger doesn't talk about it in this lecture, but he does say that he had talked about it in a previous lecture. Since I don't know the content of the previous lecture, I'm not going to criticize Dr. Binswanger's discussion of the issue, but rather the common view I've seen amongst Objectivists who know anything about the theorem.
Many Objectivists say that since the theorem says that there is knowledge that cannot be gained through reason and yet can be known to be true, it must be wrong. But what does the theorem actually say? Like many issues in math and science (see, for example, the second half of this comic), there are two interpretations: the interpretation that actually reflects the math or science involved, and the interpretation that takes the wording of the first interpretation and proceeds to apply it in completely inappropriate contexts. The popular expression of the theorem, that there are statements we can know to be true but can never verify by logic, is not supported by the math and was in fact vehemently fought by Gödel himself. In essence, what the theorem actually says is this (it's slightly more nuanced, but that's not relevant to my point): If you have a finite set of propositions taken as given and are only allowed to use deductive reasoning from those propositions, there exist certain statements which you cannot prove. So, rather than proving that reason is not our only means of knowledge, the theorem proves that deduction is not our only means of knowledge.
Now I should point out that the theorem technically only applies to formal mathematical systems complex enough to express algebra, and not to knowledge in general, but the points I want to make remain true: first, that the theorem is correct (and as ironcladly proven as the Pythagorean theorem), and, more importantly, that the popular formulation of science is almost always different from the actual meaning. Before you jump to criticize something from math or science as philosophically invalid, you have to make sure you know what the actual science says, instead of what the popular interpretation of that science is.
Which "mark used to clarify meaning by indicating separation of words into sentences and clauses and phrases" am I?
Via Gus:
You Are a Colon |
 You are very orderly and fact driven. You aren't concerned much with theories or dreams... only what's true or untrue. You are brilliant and incredibly learned. Anything you know is well researched. You like to make lists and sort through things step by step. You aren't subject to whim or emotions. Your friends see you as a constant source of knowledge and advice. (But they are a little sick of you being right all of the time!) You excel in: Leadership positions You get along best with: The Semi-Colon |
Fall Semester Scheduling
Course Descriptions:
BME 101 Introduction to Biomedical Engineering:
"An introductory overview of the multidisciplinary field of biomedical engineering. Application of elementary engineering principles to the analysis of physiological systems. Includes basic introduction to the use of computers as tools for solving engineering problems. Course topics include biomechanics, cell and tissue engineering, biosignals and bio-instrumentation, medical imaging, medical optics, and bioethics[sic!]. Includes some guest lectures by biomedical engineering faculty"ECE 111 Introduction to Signals and Circuits:
"Analysis techniques for DC and AC circuits"MTH 235 Linear Algebra:
"Finite-dimensional vector spaces over R and C axiomatically and with coordinate calculations. Forms, linear transformations, matrices, eigenspaces"BIO 112 Biology Perspectives I:
"The first semester of a two-course introductory sequence for students with a strong background in science. Topics include biochemistry, molecular and cellular evolution, cell reproduction, fundamentals of genetics, and molecular biology. This course differs from BIO 110 in that there is greater emphasis on experimental approaches, data analysis, and quantitative methods, and may include reading original papers. A significant writing component includes preparation of a book review (from selected titles, such as The Selfish Gene). Note, both BIO 110 and BIO 112 are designed to prepare students who intend to major in biology."CHM 203 Organic Chemistry I:
"An introduction to organic chemistry that focuses on chemical bonding, structure and stereochemistry, reactions and reaction mechanisms of organic compounds."CHM 207 Organic Chemistry I Laboratory:
"One lab lecture and lab session per week provide an introduction to the characterization and reactivity of organic molecules. The course provides an introduction to modern laboratory techniques used in organic chemistry."BCS 110 Neural Foundations of Behavio(u)r:
"Introduces the structure and organization of the brain, and its role in perception, movement, thinking, and other behavio[u]r. Topics include the brain as a special kind of computer [ed: That could end badly], localization of function, effects of brain damage and disorders, differences between human and animal brains, sex differences, perception and control of movement, sleep, regulation of body stages and emotions, and development and aging."BCS 111 Foundations of Cognitive Science:
"Introduces the organization of mental processes underlying cognition and behavio[u]r. Topics include perception, language processing, learning, and memory. Integrates knowledge of cognition generated from the fields of cognitive psychology, artificial intelligence, neuroscience, linguistics, and philosophy [ed: that probably will end badly]."If I get this schedule, I'll be in science-nerd Valhalla. Keep your fingers crossed!
Wednesday, May 14, 2008
An Excellent Answer to a Common Emotional Argument
When discussing ending government entitlements, one of the most common responses is something along the lines of "but what if a member of disadvantaged group, through no fault of his own, needs currently entitled good/service and can't afford it? Would you really let said member suffer?" Intellectually, the answer to this question is the same as the reasons behind your general argument to end the entitlement: One person's need does not entail a claim on another's life. Why, then, is this question so often presented and why does it seem difficult to answer satisfactorily?
The answer is that this is primarily an emotional argument: the question is set up in such a way that leaving the person without his good or service causes an extremely negative emotional response. Who wants to leave grandma without her pills? One way to answer this argument is to point out, correctly, that emotions are not methods of cognition. But, as Dr. Hsieh points out in a post on the We Stand FIRM blog, the emotional nature of the argument suggests a perfect answer:
The answer is that this is primarily an emotional argument: the question is set up in such a way that leaving the person without his good or service causes an extremely negative emotional response. Who wants to leave grandma without her pills? One way to answer this argument is to point out, correctly, that emotions are not methods of cognition. But, as Dr. Hsieh points out in a post on the We Stand FIRM blog, the emotional nature of the argument suggests a perfect answer:
"[T]he very fact that such examples tug at the sympathies of normal decent Americans also means that those Americans will be forthcoming with voluntary charity. And I fully support giving to charities that are consistent with my values and priorities."The flaw, then, in this typical counter-argument is that the questioner is assuming a false dichotomy between forced "charity" and complete self-reliance. In fact, as Dr. Hsieh so eloquently demonstrates, there is a third, appropriate alternative: voluntary charity.
Tuesday, May 13, 2008
Superhero Engineering
When people ask me what I want to do, I often have trouble. I feel uncomfortable simply saying biomedical and/or neural engineering, first because most people don't know what that is, but more importantly because that doesn't quite cover what I want to do. Today's biomedical engineering is almost exclusively focused on improving the lives of sick/disabled people to the standard of a healthy life, which, while being an extremely worthy endeavor, does not particularly interest me. Much more interesting to me is a field largely untouched: improving healthy human beings.
The best way I've thought of to describe this to people who aren't me is to think of Batman, without the annoying emotional issues. He wasn't born with super powers, but using technology and ingenuity he elevated himself to the level of superhero. The differences between me and Batman include the fact that I will not limit my improvements to myself (if others are willing to pay), I don't intend to become a vigilante, I won't limit my improvements to super strength and abilities that can only be used in odd circumstances, and, most importantly, I will mainly focus on improving people from the inside using biomedical technology, rather than making really cool suits and devices.
At some point in the future I hope to post a few of my ideas about what I want to do (which will also explain why I'm studying what I'm studying), but for now I'll be content with describing myself with the new term I just came up with: Superhero Engineering.
P.S. I don't expect to be able to make my services available to the public (or myself, for that matter) for at least six years, sorry ^_^
The best way I've thought of to describe this to people who aren't me is to think of Batman, without the annoying emotional issues. He wasn't born with super powers, but using technology and ingenuity he elevated himself to the level of superhero. The differences between me and Batman include the fact that I will not limit my improvements to myself (if others are willing to pay), I don't intend to become a vigilante, I won't limit my improvements to super strength and abilities that can only be used in odd circumstances, and, most importantly, I will mainly focus on improving people from the inside using biomedical technology, rather than making really cool suits and devices.
At some point in the future I hope to post a few of my ideas about what I want to do (which will also explain why I'm studying what I'm studying), but for now I'll be content with describing myself with the new term I just came up with: Superhero Engineering.
P.S. I don't expect to be able to make my services available to the public (or myself, for that matter) for at least six years, sorry ^_^
Writing to Your Audience in Academia
One of the most important principles in communicating ideas, especially formal writing (which this blog is not), is that you must decide to what kind of audience you intend to write (so that you know what level of knowledge to assume and what level of knowledge you must establish). The alternatives to deciding on an audience are to either implicitly assume your audience knows nothing beyond basic English, requiring you to reduce all of your ideas to sense-perception and integrate your entire hierarchy explicitly (a near-impossible task that would fill a library if completed) or implicitly assume your audience knows everything you know, meaning you don't have to communicate anything at all. I don't tend to have trouble with this principle in most cases, but there is one context in which I, and many others that I know of, have trouble defining the audience: academic work.
Whether writing an essay for class or answering problems on an exam, at least part of the purpose is to communicate to the professor that you understand the material. The problem is, you aren't doing this directly (you don't write an essay to your math teacher saying "I understand partial differentiation, and here's proof), you do it indirectly by proving that understanding by applying it. This is where defining the audience becomes a problem: What can you assume about your audience's knowledge?
Sometimes the assignment is such that you can assume the professor's full knowledge (such as an essay about a topic that the professor didn't teach to you himself), or sometimes you can assume that your audience is your classmates at their best, but in most cases you are in the middle. For example, if your assignment is to write an essay applying Maslow's motivational theory to an article in the newspaper, you can't necessarily assume your professor's full knowledge because that could lead to an essay which any psychologist would understand but wouldn't prove that you have a full grasp of the theory. Similarly, you can't assume your classmates' knowledge, because you don't need to reteach the theory in the essay. You must choose a middle ground audience, one that doesn't exist, that, in this example, has a basic grasp of Maslow's theory but may need a bit of explanation whenever you apply one of the points of the theory.
That this is a problem is expressed in the classroom in two ways which distort the issue. The first is when an assignment is announced and a student asks "how much detail will we need to put?" or some similar question. This is not exactly the right question, because the same audience may need very little detail on some points and explicit, in-depth detail on others, and the same applies to your assignment. A similar way the problem presents itself is when a professor (particularly in math and science courses) instructs the student to "show their work". While this is a valid instruction in that it tells students not to assume that the audience will know everything they, or the professor, knows, it is invalid in that it leaves no guidance beyond excluding that one extreme; if taken literally, the student showing his work on a calculus exam will have to trace his process of inducing the concept of "number", among many other things. The proper issue at hand in both of these cases is: Write to the correct audience.
But how is that audience properly determined? I don't have a complete answer, and I certainly welcome comments. I do think a good lead to the question is suggested above: The purpose of the assignment is to communicate indirectly to your professor what you know, so you must choose your audience in order to achieve that purpose.
P.S. Just before publishing this I realized another example of where this was an issue for me: The The Fountainhead essay contest. I knew I could assume my audience had read the book, but did I have to assume they only had a basic, shallow understanding? Could I assume that my audience was the actual judges, who have extensive knowledge and years of study of Objectivism? This was a significant issue, and I intend to contact ARI with a similar question for the Atlas Shrugged essay contest this fall.
Whether writing an essay for class or answering problems on an exam, at least part of the purpose is to communicate to the professor that you understand the material. The problem is, you aren't doing this directly (you don't write an essay to your math teacher saying "I understand partial differentiation, and here's proof), you do it indirectly by proving that understanding by applying it. This is where defining the audience becomes a problem: What can you assume about your audience's knowledge?
Sometimes the assignment is such that you can assume the professor's full knowledge (such as an essay about a topic that the professor didn't teach to you himself), or sometimes you can assume that your audience is your classmates at their best, but in most cases you are in the middle. For example, if your assignment is to write an essay applying Maslow's motivational theory to an article in the newspaper, you can't necessarily assume your professor's full knowledge because that could lead to an essay which any psychologist would understand but wouldn't prove that you have a full grasp of the theory. Similarly, you can't assume your classmates' knowledge, because you don't need to reteach the theory in the essay. You must choose a middle ground audience, one that doesn't exist, that, in this example, has a basic grasp of Maslow's theory but may need a bit of explanation whenever you apply one of the points of the theory.
That this is a problem is expressed in the classroom in two ways which distort the issue. The first is when an assignment is announced and a student asks "how much detail will we need to put?" or some similar question. This is not exactly the right question, because the same audience may need very little detail on some points and explicit, in-depth detail on others, and the same applies to your assignment. A similar way the problem presents itself is when a professor (particularly in math and science courses) instructs the student to "show their work". While this is a valid instruction in that it tells students not to assume that the audience will know everything they, or the professor, knows, it is invalid in that it leaves no guidance beyond excluding that one extreme; if taken literally, the student showing his work on a calculus exam will have to trace his process of inducing the concept of "number", among many other things. The proper issue at hand in both of these cases is: Write to the correct audience.
But how is that audience properly determined? I don't have a complete answer, and I certainly welcome comments. I do think a good lead to the question is suggested above: The purpose of the assignment is to communicate indirectly to your professor what you know, so you must choose your audience in order to achieve that purpose.
P.S. Just before publishing this I realized another example of where this was an issue for me: The The Fountainhead essay contest. I knew I could assume my audience had read the book, but did I have to assume they only had a basic, shallow understanding? Could I assume that my audience was the actual judges, who have extensive knowledge and years of study of Objectivism? This was a significant issue, and I intend to contact ARI with a similar question for the Atlas Shrugged essay contest this fall.
I'm Back!
So this blog has been down for about five months, mainly because it wasn't going anywhere and I was busy with classes anyway. I'm going to try again, shooting for at least one post a week at first, increasing frequency as I get into the groove.
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