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What exactly does objectivism say about certainty?

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I've recent been trying to understand what Ayn Rand's stance was on certainty and what most objectivists would have to say on the topic. I've searched through this forum and others and have found some information on the subject but I still find myself confused. I understand that Ayn Rand firmly believed in certainty and as I understand it, that is one of the fundamental statements of objectivism. However, what exactly does certainty mean? Here's an example I'm sure many people here have come across: Newtonian Physics. When Newton devised his understanding of physics, there was plenty of evidence to justify his assertions and nothing available to us that contradicted it. As everyone now knows, while his equations and predictions are useful, they are fundamentally wrong and have been shown to be by relativity. Before any evidence of relativity was uncovered, am I wrong in saying that an objectivist would have claimed we knew that Newtonian physics were correct with absolute certainty?

If the answer to the above question is "yes" then what exactly is the definition of absolute certainty or certainty in the context of objectivism? I've come across the term "contextual knowledge" several times. I'm not sure I fully grasp what this is, would that be relevant here?

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If you are building a tennis ball launcher that uses an actual tennis racket to launch the ball, you would be able, using only Newtonian physics, to state with absolute certainty how long to make the delay between dropping the ball and swinging the racket. If you were trying to determine the position of a satellite by triangulation with its radio frequency signal, you might need to make an adjustment in your calculations to account for relativity, depending on the purpose for which you are locating the satellite. No action is taken, or measurement is made, without a purpose, and that purpose is what determines the context. In the first example, your calculations are off by so slight a margin as to be irrelevant, since variations in the operation of the mechanism itself would obviate the need to correct them. In this context, Newtonian physics gives exactly the precision you need, and your certainty is absolute, contextually.

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The topic is covered in Peikoff's book Objectivism: The Philosophy of Ayn Rand in ch. 5. We can have it (certainty). A relevant quote is this:

Like possibilities, probabilities are asserted within a context and may be weakened or strengthened as it changes. If favorable evidence continues to be discovered, at some point the cognitive climax will be reached. The conclusion ceases to be a hypothesis and becomes knowledge. Such a conclusion is certain.

The concept of "certainty" designates knowledge from a particular perspective: it designates some complex items of knowledge considered in contrast to the transitional evidential states that precede them. (By extension, the term may be applied to all knowledge, perceptual and conceptual, to indicate that it is free of doubt.) A conclusion is "certain" when the evidence in its favor is conclusive; i.e., when it has been logically validated. At this stage, one has gone beyond "substantial" evidence. Rather, the total of the available evidence points in a single direction, and this evidence fulfills the standard of proof. In such a context, there is nothing to suggest even the possibility of another interpretation. There are, therefore, no longer any grounds for doubt.

The Newton question is difficult to answer because it is essentially impossible for us (ordinary people) to reproduce his knowledge. Let us recall that his laws were universal, not stated as "true in this range"; and there was no evidence to support (or disprove) the laws in very many contexts (the "mountain-to-molecule" range of sizes). Furthermore, there were observations of planetary motion that were known to be inconsistent with these laws, though I don't know what observations were known to Newton. I know that often Newton's laws are held up as an example of "contextual certainty", but I think that is a misapplication of the concept of certainty.

An example of contextual certainty would be the conclusion that all crows are black, a belief that many people have. It is true in a species-specific way, that the species of crow found in the US is black. However, "crow" is a broader concept, the full extent of which is usually unknown to us, and looking at species that exist elsewhere you can see that not all crow species are black. The "contextual" of contextual certainty amounts to identifying the context within which the conclusion has been validated.

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Thank you for the helpful responses, what you both said makes sense to me. So to summarize, would it be proper to say that when we make claims of certainty, it is assumed that we are specifically speaking within the range of observation that is currently available to us. For example, there are massive areas of the universe we are yet to observe. One of these areas we are yet to make any sort of contact with may contain a planet on which intelligent life resides. However, with the knowledge currently available to us, I would not be wrong in stating that "earth is the only planet which contains intelligent life" because it is assumed that I am speaking within the context of everything we have observed thus far. Would this be accurate?

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So to summarize, would it be proper to say that when we make claims of certainty, it is assumed that we are specifically speaking within the range of observation that is currently available to us.
Yes, although I hold that scientists (by the nature of their profession) have an obligation to be more explicit and always-aware of that context. Thus you should not say that you are certain of claim that has only been tested against a small sample of the relevant types. Thus a scientist should not make claims as to crow blackness based on their observations of just c. caurinus.
However, with the knowledge currently available to us, I would not be wrong in stating that "earth is the only planet which contains intelligent life" because it is assumed that I am speaking within the context of everything we have observed thus far.
That would be misleading. You did not explicitly say "in our solar system", and in discussions of life on other planets, "in our solar system" is not the assumed context -- the assumed context is "in the entire universe". You cannot assert with certainty that intelligent life does not exist on any other planet anywhere (nor can you assert with certainty that intelligent life does exist on another planet). You have no grounds for making an assertion one way or the other. What you actually have (some) evidence for is the conclusion that intelligent life does not exist elsewhere in our solar system.

Let me give you an analog. The proposition is "intelligent life does not exist at 69.690072, 18.981038 on Earth". You (presumably) cannot say "I am certain that that is so" based on the fact that you don't know of any intelligent life existing there. However, you could inspect that spot and become certain that there is no intelligent life there.

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Yes, although I hold that scientists (by the nature of their profession) have an obligation to be more explicit and always-aware of that context. Thus you should not say that you are certain of claim that has only been tested against a small sample of the relevant types. Thus a scientist should not make claims as to crow blackness based on their observations of just c. caurinus.That would be misleading. You did not explicitly say "in our solar system", and in discussions of life on other planets, "in our solar system" is not the assumed context -- the assumed context is "in the entire universe". You cannot assert with certainty that intelligent life does not exist on any other planet anywhere (nor can you assert with certainty that intelligent life does exist on another planet). You have no grounds for making an assertion one way or the other. What you actually have (some) evidence for is the conclusion that intelligent life does not exist elsewhere in our solar system.

Let me give you an analog. The proposition is "intelligent life does not exist at 69.690072, 18.981038 on Earth". You (presumably) cannot say "I am certain that that is so" based on the fact that you don't know of any intelligent life existing there. However, you could inspect that spot and become certain that there is no intelligent life there.

That makes a lot of sense, I totally agree. Normally, when I have questions about Objectivism they are due to a person struggle I am having, trying to figure out what I believe or what is true. However, in this case, my confusion stemmed more from what I'd been hearing from other Objectivists. Maybe where I'd come into conflict with some people here is with examples that are presumably less likely. For example, if you've ever witnessed or taken part in a theist v.s. atheist debate, something that's often brought up is Russell's teapot; Russell wrote:

If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes.

He basically goes on to compare the teapot to god in that a god could be defined in such away to be impossible to disprove. However, just because the existence of the teapot cannot be disproven, that does not mean the teapot exists (and the same would be said of a god). In the case of the teapot, we could safely say that we have no evidence of its existence. With this example, what I would say is, "There is no reason to believe such a teapot exists, however, I cannot say with absolutely certainty that one does not."

What would Objectivism or what would people here say in response to this? I imagine that one would point out that to posit the existence of Russell's teapot is arbitrary and therefore belief in it irrational. However, I would still hold to my above statement. What do you think?

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This is what I would say in response to the teapot person:

"I know for certain you are making the teapot up, because if it cannot be seen it with current technology, you had no means to acknowledge its existence."

That's a logical response, but would you say it is incompatible with my own? ("There is no reason to believe such a teapot exists, however, I cannot say with absolutely certainty that one does not.") We know that this person made up the teapot but we still cannot be certain that the teapot does not exist. The same logic can be used on my previous example of intelligent life on a planet besides earth. Someone can make the claim that intelligent life exists on a planet in one of the areas of the universe we have not yet observed. The fact that no one on earth has observed the planet the man is speaking of means we can say to him "We know for certain you are making the intelligent life up." However, we would not know for certain that intelligent life does not exist on a planet besides earth.

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He basically goes on to compare the teapot to god in that a god could be defined in such away to be impossible to disprove.
I/we reject that approach because it inverts the logical ordering of thing and name. If you have reason to believe that a thing exists, it is valid to assign a name to it. It is not valid to assign a name when there is no evidence for the thing that the thing is supposed to be a name of. "Teapot" is a valid kind, so Russel's claim that "nobody would be able to disprove my assertion" is actually false, given our new telescopes and spaceships. OTOH, "invisible, undetectable teapot" is not a valid kind. Teapots exist, invisible, undetectable teapots do not.

The claim "there exist a 1 cubic inch teapot orbiting at location X" is an arbitrary claim, as is the claim "there exist an invisible, undetectable teapot of no particular size orbiting in no particular location". The latter claim is worse than the former claim, because in principle no evidence for the latter arbitrary claim can ever be presented; whereas you could present evidence for that actual small orbiting teapot, just as evidence was finally presented to prove that Neptune existed and that the Giant Muntjac exists.

what I would say is, "There is no reason to believe such a teapot exists, however, I cannot say with absolutely certainty that one does not."
On principled grounds, we refuse to accept any unproven assertion, and granting legitimacy to an unproven assertion by accepting its claim to being truth enough to talk about it is fundamentally irrational. Alternatively, we might sarcastically reply "You are mistaken: there is a miniature screwdriver orbiting the Sun. No wait, it is a transparent cosmic jellyfish. Oops, I meant a convention of miniature angels dancing on the head of a microscopic pin". Arbitrary claims should not be taken at all seriously. Rather than saying "I cannot say it is not", you should refuse to entertain the question, since it is entirely outside the domain of cognition.
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Arbitrary claims should not be taken at all seriously. Rather than saying "I cannot say it is not", you should refuse to entertain the question, since it is entirely outside the domain of cognition.

That makes sense to me. There is no sense in taking an arbitrary claim seriously because it would be pointless to do so. I have had conversations however where a person will respond to an arbitrary claim with "I know for certain your claim is false". For example: "I know for certain that the transparent cosmic jellyfish does not exist." I believe that in principle it is wrong to say we know for certain these claims are false. That would mean it is impossible for an arbitrary claim to "accidentally" be correct and would, I believe, be a misuse of the word certain. However, I do agree that the correct response to such claims is to simply not acknowledge them unless some kind of evidence is presented in which case they would cease to be arbitrary.

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