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Galt's oath does cover acts risking death.
Ayn Rand did not use or misuse Occam's razor. It has no fundamental role in theory formation. Theories are cognitive explanations of reality, not floating abstractions manipulated to 'correspond' to facts, from which we arbitrarily choose the simplest. Two different theories that have predicted the same result are still contradictory. At least one of them is wrong, which does not depend on a preference for relative simplicity.
A form of "simplicity" that is required is what Ayn Rand called "Rand's razor", an epistemological principle for the proper formation of concepts in accordance with what she informally called the "crow epistemology", which is the fact that there is only so much that we can simultaneously retain in our mind at the same time.
Concepts are a system of cognitive classification. As Ayn Rand put it, a "crucial aspect of the cognitive role of concepts" is that "concepts represent condensations of knowledge, which make further study and the division of cognitive labor possible." That is done through a hierarchy of abstractions from abstractions.
"The range of what man can hold in the focus of his conscious awareness at any given moment, is limited. The essence, therefore, of man's incomparable cognitive power is the ability to reduce a vast amount of information to a minimal number of units—which is the task performed by his conceptual faculty. And the principle of unit-economy is one of that faculty's essential guiding principles."
The form of such "simplicity" required for cognition is that principle of cognitive "unit economy". Ayn Rand expressed it as what she called "Rand's razor": "Concepts are not to be multiplied beyond necessity—the corollary of which is: nor are they to be integrated in disregard of necessity". That is objective necessity, not preference, and is not Occam's razor, let alone based on Popper's negative notion of falsifiability.
For the full explanation see Ayn Rand's Introduction to Objectivist Epistemology.
On the topic of theism, it implies atheism (a-theism): not believing in the supernatural. It does not allow for agnosticism, a perpetual state of accepting not knowing what to think. It is not necessary or possible to disprove arbitrary assertions in order to not believe them or their possibility (assertion of possibility also requires proof that something is possible). And when the arbitrary assertions are self contradictory or contradict what we already know, as theism usually is, one can further deny their possibility, not just not believe it.
On a humorous note,
with regard to Schroedinger's cat, I found the cat frozen and dead in a refrigerator in a game called NetHack once. Once unthawed, my pet dog gained both an experience level and teleportitis upon consuming the cat. Fortunately I had a "magic" whistle that summoned the dog from anywhere on the dungeon level. ;)
For example we have the Halting Problem, Göedel's Incompleteness Theorum, and Tarski's Undefinability Theorum to go with it. These and more do demonstrate that certain things are, so far as we can reason, un-knowable. Of course, Schrödinger's feline companion may have something to say about it. Or not, we can't say.
Even if we were to reduce logic to numbers (Gödel numbering IIRC), Turing and Church showed that we still could not prove certain things as true or not. And this is in the realm of computers, math, and logic.
Perhaps the great irony for non-agnostics is that there is one and only one way to prove, or "know" there is a creator god. It must make itself present to you and provide you with the historical knowledge sufficient to be unequivocal proof. Conversely, there is no proving the negative.
At most, assume we are able to create the ability to see into the past - at any time on Earth in any location (great story for this: The Light of Other Days - Clarke and Baxter). Could we prove there is no god? No. All we could prove was whether events portrayed in religious texts actually happened.
I suspect, based on the context provided, that she was misusing Occam's Razor. The Razor is not a proof tool, it is a tool for extracting bits. Besides, assuming you have the god theorem and the "it just happened, m'kay" theorem and they predicted the same results, then Occam would say to select the God one because it has the fewest assumptions.
Naturally, I am not saying that is the correct answer, merely the simplest and thus the best match for Occam. Occam's Razor is not a top for logic. It is explicitly a tool for selecting between competing theories that predict the same outcomes - and not based on a provable logic just on a preference for simplicity.
Incidentally if she was misusing Occam's in the common guise of "the simplest answer is best", that would be incorrect as that comes from the law of parsimony.
Yet even that "law" is not a tool of logic, but one of convenience and the scientific method's preference for simplicity because we expect falsifiability. The more complex the explanation the more we have which needs to be falsifiable.
As others have questioned: Some implausible scenario from the movie Armageddon, would I do what Bruce Willis' character did? Almost certainly.
Lastly, I'd comment what a silly topic this is for a survey. But it was fun to play.
An objectivist could be agnostic, thus not necessarily atheist. You can call Buddhism an atheist religion as there are no personal gods in it. Indeed, if there is one tenet shared by all groups of Buddhists, it is that there is no creator god. I mention all of that because the Buddhists do believe in a post-death existence of sorts, though it is not surrounding a "soul", and not quite "reincarnation" as is commonly used.
There are enlightened/ascended beings but they are not what we'd call deities. Even then among the Buddhists system they are generally regarded as symbolic anyway. I mention this because
With atheism there are two poles if you will: "god does not exist" and "I have no proof or evidence god exists, so I do not have a belief in god existing" (yes, semantically belief means no proof but this is the way the phrasing is used).
So I'd say it may be likely that an Objectivist is atheistic, it would not be certain. Even among atheist Objectivists, I'd expect them to be more of the nontheist side. But maybe that's just me.
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