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Nate T.

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Posts posted by Nate T.

  1. There is another aspect of your post I'd like to comment about:

    The latter prescribes the use of force should initiatory force be used, and is therefore retributive force and just. The former threatens physical force if a certain action is not taken. It is a threat, therefore coercion, which is used to elicit action, and is therefore an initiation of force and unjust.

    It seems that you are drawing a distinction between just and unjust law based upon whether obedience of the law requires an action. If I follow you correctly, a law based on murder would be proper in your view because it requires you to perform a certain action in order to warrant legal action (here, murdering someone); you are compelled not to take an action under threat of penalty, and if you do nothing, no harm will come to you. Similarly, the mugger example is an instance of force initiation because you are compelled to take some action under threat of penalty.

    At the primary level of physical force this may be a plausible enough distinction to make; if you hit me, I'll hit you back, otherwise I won't. However, when you start getting into types of force being used further from the perceptual level, this criterion for determining proper and improper force is incorrect. The example I'll give is the example you originally gave me: fraud. You can agree to deliver goods and then "do nothing" by collecting money and not delivering goods. This is an instance of "not doing anything" that is nonetheless a rights violation by virtue of the voluntary agreement you've entered into (as in my original reply to this example). Another example would be for a company to knowingly withhold knowledge of a products' possibly fatal side effect.

    Edit: A third example ties in to this thread: if there is only one job immediately available for a person in a small town to take, and it pays very little, is the employer "forcing" the person to take the job or starve to death? If so, is the employer no better than the mugger?

    Because of this, I submit that the "forces you to act"/"forces you not to act" distinction is at best non-essential for deciding propriety of laws. A more fundamental criterion is the one that David, I, and others on this thread have given, which is that protection of individual rights and only protection of individual rights merits the use of force.

  2. Some laws are the codification of consequences should certain actions be taken, and are therefore prescriptions of retributive force and just. Some laws are threats of force to be used if certain actions are not taken, and are therefore not retributive but initiatory and unjust.

    The "consequences" in the case of either a just or an unjust law is the threat of force (being arrested and thrown into jail for murder is force, just as much as being mugged)-- that what makes it a law as opposed to something with no legal consequences, like a resolution. The only issue in deciding propriety is whether that use of force is retributive (hence proper) or an initiation of force itself (hence improper). You decide based on whether the law in question prohibits violations of individual rights.

    Identifying certain actions as "threats" or "coercion" as a means of delegitimizing them is confusing the issue. Put differently, being a "threat" or "coercive" on its own is not sufficient to make an action or law improper.

  3. I second Jake's suggestion that there may be a libertarian/anarchist "Force = Bad" premise operating here. It's not true that the use of force is unequivocably bad in all circumstances; it depends upon the purposes of its use. Here, the threat of the government to use force in response to a murder is more akin to self-defense against the mugger: both are in service of protecting individual rights. It is this, and not semantic issues about what constitutes "initiating" force, that is important in deciding when the use of force is justified.

  4. Why does the government not have a choice in making law? There's nothing naturally mandatory in the existence of laws; individuals choose to create laws.

    I wasn't sufficiently clear. The government does have choice in what laws it enacts, since these decisions are made by individual people. I did not mean to claim that laws are determined as a matter of physical law or fate; governments (by which I mean their members) choose to enact both good laws and bad laws all the time.

    However, the laws they pass have consequences. If the goal of the government in question is to protect individual rights (which is a purpose set down by ethics), then only laws of a certain nature will act to support that end, such as laws prohibiting murder, rape, theft, etc. The fact that a law does not protect individual rights has consequences for those living under the government which passes these laws-- and it is these consequences, measured against the standard of protecting the ability of free, rational individuals to pursue their own happiness (and trade with other such individuals), that determine the propriety of the law in question.

    Your mugger's ultimatum fails this test for "good law" because one cannot live and prosper in an environment where one's life and property is in jeopardy; "force and mind are opposites." Governments can pass any laws they want-- but they cannot escape the consequences of these laws on the members of the society they govern. This is parallel to the situation of individuals in ethics, since man is free to act in many different ways, but only certain ways based upon his nature will lead to his flourishing.

    Edit: Spelling; Rewording.

  5. I'm obviously not being very clear. Please, allow me to try again.

    My argument is that, in order to safeguard a laissez-faire capitalist market and economy, laws against the initiation of force must exist. But laws are an initiation of force. If you started with a blank slate, and wanted to create a society with laissez-fair capitalism, you would first have to create laws which protect that capitalism. The individuals in the society would not have initiated force in any way, yet the government's first action would be to say, in effect, "Follow the rules, or something bad will happen to you." Which is coercion.

    Yes, if someone breaks a law and the government uses force against them in retaliation, that is not an initiation of force. But that's not when the force began. The force began, was initiated, when the government threatened the citizens with force if they failed to comply with the laws.

    At first, I considered this to simply be an issue of consequences. You are free to break the law, but you are not free to escape the consequences of going to jail, or paying a fine. Therefore, a law is not force - it merely tells what the consequences are if action is taken; like when the doctor tells you, "Continue to smoke and you'll die in a year." This is not a threat, simply a statement of fact - cause and effect. But that argument falls apart when used in the case of a mugger and his victim. Is the mugger's demand of, "Give me your money or die" simply a statement of fact - cause and effect? Or is it force?

    Well, if all of the laws on the books do nothing but forbid various kinds of force initiation, then there would be no reason to object to them, by the first sentence in your second paragraph. Any other laws shouldn't be there in the first place. Are you asking how to distinguish good law from bad law? Or how to tell when the use of force is justified in the first place?

    In a sense, law is an expression of causality every bit as much as gravity-- which is the recognition that in a social setting men need to live without the threat of initiation of force by others in order to pursue their own ends with their rational faculty and trade peaceably. To meet this need, the initiation of of force ought to be barred in its various guises, but in a predictable, objective way so that everyone involved can plan their lives accordingly: i.e., proper laws. This is why (among other reasons) a mugger's ultimatum of "your money or your life" is not a law, but a government prohibition against murder is: they serve very different ends.

    I should mention that improper laws, laws that confiscate property from people to redistribute from others, say, are an initiation of force. This is true because, even though these bad laws may be enacted by the same formal process as good laws, they serve the wrong purpose-- the purpose that laws were meant to stop. So good laws are those that prevent the initiation of force, bad laws are an initiation of force.

    One last thing-- the example of the mugger. In this case, the mugger would be using force. To say that the dilemma the mugger puts people in is just a matter of cause and effect ignores the fact that the mugger has a choice in the matter: he has chosen to violate the rights of others. That's what makes him morally (and legally) culpable.

  6. Nate T. - How would the existence of laws not be an initiation of force? Suppose a man approaches you on the street and says, "Hand over your money or I'll kill you." This is clearly an initiation of force. He's giving you a false choice. Sure, you could choose to let him kill you, but you'd rather not. Your hand is forced. Now, suppose there's a law which says, "If you sell a product that doesn't do what you claim it does, the government will take your money." This would be protection against fraud (which isn't allowed in laissez-faire capitalism). Undoubtably, there are people out there who would like to sell products that don't do what they claim they do. In such cases, the government is initiating force in much the same way the mugger is: the government is providing a false choice. People would rather sell products which don't do what they claim to do, but because of the law they do not.

    First, I'm confused by your usage of the phrase "false choice." You've given two examples of this type of choice, a mugger asking you to choose between your life and your cash, and the government "forcing" a company to choose between truthfully advertising what it is selling and some kind of legal consequence. How are these two choices "false" as against other kinds of choices? I ask because you seem to be determining when force is initiated based upon these kinds of choices. For example, does a law against murder induce a similar choice: either do not murder anyone or face severe criminal penalties? If not, how is this different from the above examples? If so, does this mean the prohibition of murder is an initiation of force?

    In any case, the example you give is that of fraud, which is a species of initiating force-- I'm not sure why you think fraud would not be illegal under a laissez-faire system. If you agree to certain conditions in a contract and fail to deliver, you have by virtue of your possession effectively stolen that which you promised to deliver; that which you have illicitly kept is not yours by right. To see how this justifies retaliatory force on the part of the government using your example: if a company sells a product and fraudulently claims it has certain properties* it does not, the company has stolen your money by violating the agreement it made with you to deliver goods of a certain nature. The government is then justified in using retaliatory force on your behalf to correct the situation.

    *You'll have to find a lawyer, judge, or other person knowledgeable about the workings of the law to determine how much information or omission thereof is necessary to constitute fraud.

  7. But look at this conversation as it has evolved in this short amount of time. The two negatives that were in the OP has been the focus. Am I optimistic that we can understand this side of us, and choose not to follow that path. Yes, I am. As I said, just as we are capable of self-destruction, we too are capable of wondrous things. Optimistic and pessimistic are all in the way you perceive the message at hand. There was only a minute part of that OP that pointed to a negative. What do you really think the intended focus was? Do unto others as you would have them do unto you.

    I'm puzzled by this response. Intended focus notwithstanding, it seems to me you're the pessimist here, given the views of human nature you've set forth in the OP, in particular that everyone is capable of murder irrespective of their character.

  8. OP,

    There are certain inherent characteristics that make up each one of us.

    Do you mean to say here that the essence of who we are (what we are "made up of" as it were) is inherently given, that is, is determined? If not, what do you mean? If so, then that might explain why you say the following:

    I know that I am capable of anything any of you are. ... I know that under the right circumstances I am capable of committing murder, and so are you. I know under the right circumstances I am capable of following whatever my hearts desire is. And so are you, even if that included having an affair with your wife or girlfriend, after all, I’d be following one of the core principles of Objectivism. I am, in essence no different from anyone on this board because this is human nature.

    Even at the level of inherent characteristics, people are not all interchangeable-- some have more aptitude for certain tasks and skills than others.

    More to the point, people make themselves into who they are, by the choices they make as they live their lives. This is the meaning of Rand's saying that man is a being of self-made soul. Moreover, it is this chosen component of your personality that defines your essence. So you see what kind of a claim it is when you accuse an Objectivist of when you assert that he is capable of murder. If you think that I can commit murder because you think you can, then all I can say is: speak for yourself.

    I'll also mention that "following your heart's desire" is certainly not Objectivism.

  9. I'm having a problem reconciling laissez-faire capitalism with the existence of any government at all. If laissez-faire capitalism means no government interference, then the only way laissez-faire capitalism could exist is in an anarchy. Laws are a form of coercion, coercion is a form of force, therefore government laws interfere in the market - they coerce people to act a certain way, therefore laissez-faire capitalism could only exist in a society with no laws - i.e. anarchy.

    Has anyone reasoned a way out of this problem?

    Objectivism makes a distinction between the initiation of force, retaliatory force, and defensive force. The initiation of force is what criminals, invading foreign powers, or improperly acting governments do-- deprive you of your life, liberty or property without your consent, broadly speaking. To combat criminals and invaders who attempt to initiate force, the government is vested with a monopoly on retaliatory force to stop and punish those criminals (as well as foreign invaders). When government help is temporarily out of reach, an individual that finds his rights threatened in an emergency situation may use defensive force in self-defense.

    So to specifically answer your post, some (if not most) of what the government does nowadays is an improper use of force. This does not change the fact that the existence of some kind of government to keep peace, enforce property rights and settle legal disputes is necessary in a civilized society. The government ought only use its monopoly on force to protect individual rights, and nothing else.

    This is the broad outline-- actually filling in the details of what constitutes force being initiated, retaliatory or defensive is a task left for law.

  10. trivias7,

    There's a difference between Rands' dramatizing events in a novel to make a literary point (such as the example you gave, as well as the "rape scene" in the Fountainhead which is the other example typically given) and her actual ethical philosophy, about which she (and others) have written quite a lot.

    Also, I do not think that because some people misconstrue the philosophy of Objectivism (by demonizing emotions, for instance, or adopting Rand's personal preferences like smoking, orange hair, etc., as some kind of moral mandate) that the philosophy itself is "idealistic" in the sense of its practice being unattainable. It simply means that some people misunderstand or misapply the philosophy for whatever reason.

  11. I disagree. It is true that you often see behavior of the type you list above. People are not always rational, and are unaccustomed to thinking carefully about certain issues-- this is a consequence of accepting the ideas of pragmatism and (sometimes) outright irrationality in our culture today. It is also true that some people expect to be helped for no reason than the fact that they need it-- this is a consequence of the idea of altruism in today's society.

    However, just because these ideas are commonly held and accepted does not make it part of man's nature, just as the prevalence of slavery in the U.S. up to 150 years ago proves that enslaving others is part of man's nature. One cannot accept the ideas in one's culture as a given-- one must check them against an objective measure of ethics, which is man's life as a rational being. It is, on the other hand, man's nature that he must be rational and make use of his mind to survive. Hence, Objectivism is distinguished from the other systems you mention in that the moral is that which yields the good for man's life (his long term flourishing, that is) in practice, instead of pain and death.

    There are some factual implications that aren't right in your post too, such as the notion that Objectivism requires people to be "isolated", and the role of charity, but I'll leave that for others.

  12. Can someone give me the Objectivist position on these questions?

    1. What is it about the nature of the universe that says that the universe must exist.

    2. What do you think of the Kallam argument posed by William Lane Craig?

    A good lead to the first question is a nice essay that Peikoff wrote about the analytic/synthetic dichotomy, which is what you seem to be bringing up here. Objectivism does not accept the analytic/synthetic dichotomy as valid, and instead upholds the distinction of metaphysical vs. man made, elaborated upon in the essay of the same name by Ayn Rand (in "Philosophy : Who Needs It?", I believe).

    The idea here is to be is to be necessary; a fact which is true is true unconditionally, and there is no way it can be otherwise. To your example about being born: while at one time it was possible for your parents not to have conceived you (this being a man-made choice) now that you exist, you exist necessarily, and there is nothing contingent about your existence now. Also, even though its possible to imagine the facts as other than they are (Peikoff gives the example of imagining ice sinking in water) the fact that one can imagine the facts as otherwise does not change that they are facts.

    Philosophers that try to talk about "contingent truths" are speaking implicitly from the standpoint of someone who thinks they can make reality other than what it is by wishing it so (apart from volitional action)-- they feel free to dream up "possible worlds" and thereby argue that ours wasn't necessary since they can imagine the facts to be otherwise. But A is A, of course. A special case of this is the religious frame, that regards facts as contingent on God's will-- things are contingent in that God could have willed them to be otherwise.

    As for the second argument about the universe having a cause, the minor premise is faulty. The universe is all that exists-- time is defined in terms of change among things that exist, i.e., in the universe. So speaking of beginnings and endings outside of all that exist is nonsensical.

  13. THAT'S the big question. WHAT have you got to lose? I think specifics here are important. The usual argument for the wager is that "I'm happy being this way" so what could you show to convince them otherwise? What specifically would they be gaining that they could view as being HAPPIER than their fantasy?

    Well, the whole "it makes me feel good, so I do it" argument is distinct from Pascal's Wager on the surface: the former being an explicit argument from emotionalism and the latter being a rather rationalistic justification of same. But in any case, being religious is harmful because as the rational animal one uses reason to survive-- and so you surrender your means of survival when you in turn surrender the principle of living by reason. It's pretty much what Richard Parker was saying above.

  14. How can I argue against Pascal's Wager? For those who don't know, it basically means "I may as well believe in God, because 'what do I have to lose?' If I die and believe and it's true, I go to heaven. If I don't, I go to hell. If it's not real, I don't lose anything. Why not believe?"

    A couple points for arguing against Pascal's Wager:

    First: epistemologically. Obviously, the idea of God is arbitrary (in the sense of Peikoff), and so any calculation of probability expectations is impossible since you don't know the sample space (and in fact the entire "expectation" calculation is occurring outside of reality). Meaning (flippantly assuming the premises for the moment) either you "might" really piss off Satan, Allah, the FSM or any other arbitrary entities by deciding to be Christian, or (more literally) there's only one "possibility" open to you, which is to accept reality and all of the facts therein at face value and not dream up alternatives.

    Next: a false assumption. You've got a hell of a lot (so to speak) to lose choosing to be religious rather than reality-oriented in this life, and this doesn't appear in the expectation.

    Finally: even assuming you accept Pascal's Wager, it doesn't really say anything about whether you actually accept the existence of God, just that you should go through life pretending that there is one "just in case." So it's not really an argument for the existence of God at all.

    As an aside, it's very interesting to note the parallel between the Christian argument of Pascal's Wager and the "Precautionary Principle" of the environmentalists-- both are similar fallacies.

  15. ... but they would respond that you can't prove that man has consciousness.

    First, Rand regards free will as directly observable through introspection, in that we can observe ourselves choosing to do things all the time-- the fact that Skinner regards this as unreliable or unacceptable is a consequence of his desire to use exclusively the methods of physics in psychology ("It cannot be recorded, or measured by any known scientific measure." in your quotation). However, in any given field, one must use the standards of measurement and proof appropriate to the subject. As a side note, Peikoff has a nice discussion of this in Objectivism: The Philosophy of Ayn Rand.

    Besides this, there is another flaw at work behind the assumption that man's thoughts and actions are entirely determined by his environment, which is the Fallacy of the Stolen Concept. That is, by accepting the position that man has no control over his thoughts and actions, you accept that your claims of knowledge are merely imprinted on you by your environment, albeit in possibly very complicated ways. But if this is so, how can you know that your original conclusion of the truth of determinism is valid to begin with? After all, we know that men make mistakes; suppose your environment lead you to accept faulty ideas which influenced your acceptance of such deterministic theories-- how could you demonstrate otherwise?

    This argument is really getting at the Objectivist principle that reason entails free will (and the place to find this is OPAR, as I mentioned above).

  16. What is the Objectivist opinion of (and answers) to Behaviorology?

    As far as Behaviorism in psychology goes, Rand wrote an article called "The Stimulus and the Response" in her collection of essays "Philosophy: Who needs it." Some points from the essay: One of Skinner's flaws was the attempt to cast psychology as a "hard" science by denying the existence of man's consciousness. Another is the destruction of morality by reducing all of human behavior to environmental conditioning, with obvious implications in politics. She traces through the implications of these views via a critique of Skinner's "Beyond Freedom and Dignity."

    Edit: I should mention I don't really have time to formulate an answer, but I recommend the article I give in this post as a good response to behaviorism.

  17. Well, I suppose it's nice to see some positive regard in the media for the kind of entrepreneur shown in the video, especially a positive mention of Hayek. But other than that, I found (1) the priest's explicit equation of "value" with "human service" and (2) the priest's tactic of twisting the Christian bromide of "love the sinner, hate the sin" into "capitalism is evil, but capitalists aren't necessarily so, see?" to be a nice confirmation of what I would have expected. <_<

  18. Peikoff claims that it is common practice in Philosophy to use two concepts to explain the same existent, to provide for different angles. I can't find any examples of the use of this technique...

    I remembered an example of two concepts with the same referent which are distinct by the method of their formation: "chordate" and "renate", meaning organisms having spines and hearts, respectively. These concepts are justified by their importance in classification in biology. However, it happens that every chordate is a renate and every renate is a chordate. This doesn't mean that having a spine is the same thing as having a heart, though. B)

  19. Number of entities subsumed under the concept and distance from the perceptual level are not even close to being related. Distance from the perceptual level is how many levels of *abstraction* lie between the concept and being able to point at some object. There may be billions of insects and only a few thousand concretes subsumed under an abstraction like "system", but insect is smack on the perceptual level (you can point at a bug), whereas "system" is off there in the stratosphere somewhere.

    Now, regarding the abstract-ness of "existance":

    It's important in these types of discussions to remember that a word (especially in English, mother of all contextual languages) may denote more than one concept in different usages.

    If you are using the term "existance" in the same sense that you'd use the term "universe", it's not actually a concept, because a concept is an integration of two or more units. You can't integrate two or more everythings, hence the word has the same status as a proper noun in that there's only one "everything".

    Now, if you're using it as a quality of things that exist, I *think* you could rightfully call it a concept in the same way you would call any quality (like "red" or "volitional") a concept. In that case, it's a first-level abstraction because you can (sort of) point to it.

    JMeganSnow,

    Good point-- I shouldn't have phrased it using the term "subsumed." I was trying to get across the following idea: in order to create an abstract concept, you ultimately need to have seen a whole lot of concretes, namely all of the concretes needed to form all of the concepts below the abstract concept in question in the hierarchy. These concretes aren't subsumed under the concept, as you noted, but they do rest upon it in the sense that without those concretes, the abstract concept would not have been possible. The more abstract the concept, the more concretes it rests on in this sense. Is this an okay way to think about how abstract something is?

    Regarding "existence" though, it's been mentioned in the thread that existence is actually a fairly abstract concept, since you have to be reasoning way up at the level of philosophy to explicitly identify it, even though you've been implicitly recognizing it the whole time. So even though referents of "existence" are literally everywhere, you wouldn't regard them as such since you wouldn't have a reason to consider them in that light until you're already pretty advanced.

  20. Thanks for your responses, everyone.

    softwarenerd,

    When you use the terms "base" and "top" as two directions along some dimension, what dimension is that? For instance, if one were to take "vertebrate" and "poodle", which one is above and which one below, and in what sense?

    Distance from the perceptual level. Since the concept in question is "existence", which isn't a subdivision of another concept, I measure distance from the perceptual level in this case by the number of entities subsumed under the concept. By this measure, I would consider "vertebrate" to be farther from the perceptual level than "poodle", since you can get "poodle" pretty directly by observing a number of different types of dogs, which are more or less perceptual entities, as opposed to understanding the concept "vertebrate" which requires having seen a very large number of species of animals that both do and do not have backbones and enough study of biology to recognize the distinction as important.

    intellectualammo,

    It's wide, but it is not a high-level concept ... In OPAR, Peikoff refers to "existence" as the "first concept at the base of knowledge."

    I agree that it's a wide concept, but it seems like the explicit grasp of "existence" requires a huge number of observations and a context in which you're thinking about philosophy, which already requires extensive knowledge. If I'm taking "base of knowledge" to mean the base of the hierarchy of knowledge, then it can't be true that you have to explicitly grasp the concept of "existence" before grasping anything else.

    RichardParker,

    But while the concept “existence” is *explicitly* grasped only after a long process of abstracting, differentiating and integrating many, many lower level concepts, it must be and is *implicitly* assumed during this entire process. The infant, when it first begins to form its earliest perceptions from sensory data grasps that *something* exists, but only much, much later does the same individual grasp the idea of being qua being, that the word “existence” has as its referent *everything* that exists. The implicit *foundation* for all knowledge is that something exists, in other words, that existence exists.

    So the sense in which "existence" as an axiomatic concept is the base of knowledge is not that it is a first-order concept (since it can't be if it requires so much knowledge to even justify forming), but that it is implicit in all other concepts and needs to be implicitly recognized for the advancement of knowledge to proceed? I do remember a passage in IOE in which Rand states that the importance of the axiomatic concepts are that they provide much-needed correction for a fallible volitional conceptual consciousness.

  21. "Existence" is an axiomatic concept that has as its referents everything that exists, right? So that includes all of the concepts you've made so far-- and as such, "existence" ought to be at the top, what with it subsuming everything else in your hierarchy of knowledge as its referents.

    On the other hand, Rand states repeatedly that these axiomatic concepts form the base of all knowledge-- and "existence" can only e defined ostensively. This suggests it's at the base of your hierarchy of knowledge, since you can't analyze it in terms of simpler concepts.

    Which is it? My head is hurting from thinking in circles about it. :dough:

  22. Yeah, that's another caveat he gave us. It has to be used under some fairly specific circumstances. I think it still has a pretty broad application, though.

    *Wonders if this is my teacher*

    All righty. I'll give you the example he gave us. It's tricky to explain things with fractions in this format, but I'll try....

    The work looks good-- and I don't think I'm your teacher, since i haven't covered any tricks for partial fractions decompositions yet, so no need to worry about any premature grading. :-P

    But I think the method you were given is true under these conditions. If you have distinct linear factors in the denominator like

    stuff(x)/((x - a)(x - b )...(x - n)) = A/(x - a) + B/(x - b ) + ... + N/(x - n)

    you can always separate as follows by multiplying by the denominator of the original fraction:

    stuff(x) = A(x - b ) ... (x - n) + B(x - a)(x - c) ... (x - n) + ...

    and so since this is true for arbitrary x you can get your hands on a simpler equation by a judicious choice of x. In this case, if you wanted A, you can get your hands on it by noting that for linear nonrepeating factors the factor (x - a) is in every term except the one involving A, so setting x = a just as in your method gives

    stuff(a) = A(a - b ) ... (a - n); i.e., A = stuff(a)/((a - b )...(a - n))

    This goes bad if you have quadratics and other nasty things, since you may have factors appearing in every term or factors missing from several terms-- you might be able to do something similar but I'd do it on a case-by-case basis just to be sure. So it seems under the conditions your instructor stipulated, this is valid.

    But as this is Objectivism Online and not Planet Math, I should try to answer your original question. It's obviously best to see why a trick works rather than just accept it on faith, certainly. Lacking a kind of proof like the one above, this goes into the general question of when to accept ideas/methods as valid by authorities, and that of course depends greatly on the context. In math, you can usually depend on the fact that these kinds of "folk" techniques like the above have a demonstration that the instructor either doesn't know or doesn't have time for.

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