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Two Different Types of Certainty?

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This is nitpicking. The problem is that you think that C1 rather C2 is the proper definition of certainty.

No I don't and, I know what I believe better than anyone else.

"Certainty" doesn't have an intrinsic meaning. It is a word that stands for one, and in this case, more than one, concept. A "proper" definition is one that identifies, by means of an essential genus and differentia, the referents of the concepts in reality. What I identified as C1 and C2 are not definitions, proper or otherwise. They are two concepts that are both denoted by the word "certainty."

It is vitally important that concepts be properly defined, and also that we not multiply our concepts beyond necessity. As I've argued, we need the concept "certainty" to contrast conclusions from those which are merely possible or probable.

What then do you make of Ayn Rand's statements when she speaks of "degrees of certainty" for things which are possible or probable? Is she using the word "certainty" improperly?

We already have a concept to cover the senses and the axioms ("self-evident"), so we don't need another concept (your C1 "certainty") to do the work twice over, particularly when "certainty" treated as C2 is already at work picking out a different distinction.

It is perfectly legitimate to have more than one concept with the same referents. Would you argue that "We already have a concept to cover rational animals ("man") so we don't need another concept ("human being") to do the work twice over?"

All referents of the concept I call C1 are also referents of the concept C2, but not the other way around in the same way that all referents of the concept "man" are also referents of the concept "animal." C1 is a narrower concept and there is a good reason to distinguish C1s from other C2s just as there is a good reason to distinguish man from other animals.

Added: There is also no justification for forming a concept that groups together the sensory given, the axioms, and causal explanations, but not conclusions that are fully supported by the evidence. There is no fundamental difference there.

I think we both agree that a "certain" conclusion is one for which there is conclusive evidence. But, often depending on the context, there may be different entity-appropriate standards of proof used to determine when a conclusion is conclusive. There is nothing wrong, and it is often useful, to make a distinction between conclusive arguments on the basis of the nature of the evidence and the standards of proof used to establish that the conclusion is true.

There is also no fundamental similarity between the sensory given, the axioms, and causal explanation that is not already covered by the concept "knowledge."

The most important fundamental similarity is that a C1 -- an axiom, sense perception, or a valid, proper causal explanation -- can never be overturned by later evidence, while other conclusive arguments might be.

I know we agree that this is true of axioms and the validity of the senses, but it is true of complex causal identifications as well. What kind of evidence would it take to overturn Ayn Rand's conclusion that "It is only the concept of life that makes the concept of value possible?" It is based on the causal relationship between the essential nature of living things and the essential nature of "value" as such.

But there is a fundamental difference between the given and axioms on one hand, and causal explanations and other inferences on the other. It is precisely the difference between the self-evident and the inferred.

That is true as well, but all it means is that we can subdivide C1 further into C1a and C1b.

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Actually, I was comparing "100% certainty" (C1) to "certainty beyond a reasonable doubt" (C2). (C2 is "as good as it gets" when judging people. C1 is possible with other entities.) Sometime

Poisoning the well is the fallacy of saying that a person is a bad or unreliable source, therefore her arguments shouldn't be paid attention to.

No, that would be an ad hominem. Poisoning the Well is a sub-class of ad hominem.

Poisoning the well is a logical fallacy where adverse information about someone is pre-emptively presented to an audience, with the intention of discrediting or ridiculing everything that person is about to say. [Emphasis added.]

The paragraph in question was your very first paragraph (here) and you presented it "pre-emptively" -- i.e., before presenting my arguments and your counter arguments.

It certainly contained "adverse information" ("Betsy's view [...] is completely wrong [...] philosophically dangerous [...] almost indistinguishable from mainstream philosophical ideas [...] inconsistent with the Objectivist view [...] refuted countless times in the Objectivist literature ..."), before any justification for those negative assessments was presented. Why?

I have, however, attached a value judgment to my assessment of your position.

What made it Poisoning the Well was that you attached it before you ever even presented my position.

What made it worse was that you never really justified some of your charges and others were based on a strawman and not on my actual position at all, but I will deal with that in my next post.

Judge and prepare to be judged.

Sounds good to me.

Edited by Betsy
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The most important fundamental similarity is that a C1 -- an axiom, sense perception, or a valid, proper causal explanation -- can never be overturned by later evidence, while other conclusive arguments might be.

What conclusion that doesn't rely upon axiom, sense perception, or a valid, proper causal explanation has a valid role in man's cognition? So far you have cited conclusions involving mens rea, but isn't it true that there are inductive principles by which to validly and with causal explanations, infer such conclusions? Again I think this all comes down to some unspecified, unwarranted doubt you have that is (for you) precluding certainty by a rational standard, hence we are told that we must make do with certainty by an irrational standard.

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When judging people, the principle is "innocent until proven guilty." The person who makes negative assertions about another person bears the burden of proof. If he does not present the evidence necessary to prove his assertion, his assertion is properly dismissed as arbitrary.

Your view is dangerous because, as I suggested, it seriously resembles the analytic-synthetic dichotomy.

"Suggesting" a "resemblance" to something dangerous does not prove that it is dangerous.

But to add more: It is also dangerous because it severely delimits the realm of what we can be certain about.

That needs to be proved and not just asserted.

As you know, Dr. Peikoff's C2 definition of certainty is essential to refuting skepticism. Skepticism is pretty dangerous, wouldn't you agree?

Yes, but since I agree that Dr. Peikoff's C2 definition of certainty is valid, why is my view "dangerous?"

Your view is also dangerous because it suggests that there is a difference between certainty in theory an certainty in practice. C1, theoretical certainty, is all we can really have, but you allow that for practical purposes we can say that things are C2 certain. The theory-practice dichotomy is dangerous.

I agree that the theory-practice dichotomy is dangerous, but since I do not believe that "theoretical certainty is all we can really have" and do hold that inductively derived causal inferences can fall under the C1 category, what does the theory-practice dichotomy have to do with my views?

Well, if you think the analytic-synthetic dichotomy is false, and if the theory-practice dichotomy is false, and skepticism is false, then a view that is hard to distinguish from them is going to be false and therefore dangerous.

I can distinguish my views from the analytic-synthetic dichotomy, the theory-practice dichotomy, and skepticism. You are asserting they are the same, but you have the burden of proof here, so please prove it.

This is more nitpicking. I also mentioned the Objectivist literature, which has also been discussed numerous times in this thread, specifically Dr. Peikoff's section on certainty in OPAR. That is the most relevant source, since it is the best evidence we have about Ayn Rand's view of certainty. I would also think that citing the title of lecture courses is not "uncited." But, incidentally, I believe the material from "The Art of Thinking" is lecture 6. Let's focus on OPAR, though, because that's what most people have access to. And it's all I need to make my point.

I'm afraid not. It may be "nitpicking" but you have the burden of proof and you have to be much more specific than that.

How would you like to be up on murder charges with a District Attorney who argues, "You'll find all the evidence you need to convict Noumenalself at the scene of the crime. The prosecution rests."

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How do you use the term?

Word usage has a certain degree of optionality and this is not a problem as long as a person defines his terms, particularly when he can be misunderstood, and uses his terms consistently without equivocation.

For instance, Ayn Rand used the term "certainty" in both the C1 and C2 senses. She also used the word "value" to stand for anything a person seeks to gain and/or keep (whether it was good or bad) in some contexts, and used the same word to mean only rational, proper values in other contexts. Since she always made clear what she meant, I don't have a problem with that.

Edited by Betsy
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When judging people, the principle is "innocent until proven guilty." The person who makes negative assertions about another person bears the burden of proof. If he does not present the evidence necessary to prove his assertion, his assertion is properly dismissed as arbitrary.

If he provides no relevant evidence then his assertion is properly dismissed as arbitrary, as with any unsupported assertion - when judging people or with anything else. However, "innocent until proven guilty", as effective as it may be in its insistence upon non-arbitrary assertions and meeting a burden of proof, is not evidence warranting doubts about guilt in a particular framework of evidence. Thus your reply does not answer my point that there are inductive principles by which to validly and with causal explanations, validly infer a conclusion of guilt such that no doubts remain, and does nothing to explain the basis of your insurmountable doubts - you know, the ones that force you to adopt an irrational standard of proof when judging others.

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Peikoff is using scare quotes!!!

Is he, or is he using quote quotes?

Observe that in every instance where he puts the word "tautology" in quotes, you can replace that quoted word with the phrase "what they call a tautology" without losing any meaning whatsoever.

It follows that there are no grounds on which to distinguish "analytic" from "synthetic" propositions. Whether one states that "A man is a rational animal," or that "A man has only two eyes"—in both cases, the predicated characteristics are true of man and are, therefore, included in the concept "man." The meaning of the first statement is: "A certain type of entity, including all its characteristics (among which are rationality and animality) is: a rational animal." The meaning of the second is: "A certain type of entity, including all its characteristics (among which is the possession of only two eyes) has: only two eyes." Each of these statements is an instance of the Law of Identity; each is a "tautology"; to deny either is to contradict the meaning of the concept "man," and thus to endorse a self-contradiction.

A similar type of analysis is applicable to every true statement. Every truth about a given existent(s) reduces, in basic pattern, to: "X is: one or more of the things which it is." The predicate in such a case states some characteristic(s) of the subject; but since it is a characteristic of the subject, the concept(s) designating the subject in fact includes the predicate from the outset. If one wishes to use the term "tautology" in this context, then all truths are "tautological." (And, by the same reasoning, all falsehoods are self-contradictions.)

When making a statement about an existent, one has, ultimately, only two alternatives: "X (which means X, the existent, including all its characteristics) is what it is"—or: "X is not what it is." The choice between truth and falsehood is the choice between "tautology" (in the sense explained) and self-contradiction. [Emphasis added]

The meaning of the above paragraph is that what modern philosophers call a "tautology" is what we consider to be an instance of the Law of Identity -- and it applies to all truths.

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You cannot have your doubt and certainty too. It simply makes no sense to say that our conclusions about others can be certain because they can be highly probable but not certain.

This is an example of the confusion caused by equivocating between two concepts denoted by the same word. Our conclusions about others can be certain (C2) because they can be highly probable but not certain (C1).

Why not just say what you mean: that such conclusions can be highly probable but not certain?

Using "highly probable" for conclusive conclusions (C2) and "certain" for conclusive conclusions that cannot be doubted (C1) is one way around the ambiguity and one I prefer myself. Nonetheless, I recognize that others are using the word "certain" for both C1 and C2. For instance, Ayn Rand herself used the phrase "degrees of certainty" which makes no sense if you hold that something is either certain or it is not.

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Using "highly probable" for conclusive conclusions (C2) and "certain" for conclusive conclusions that cannot be doubted (C1) is one way around the ambiguity and one I prefer myself.

But a conclusion is not conclusive if it is merely probable (in the framework of OPAR ch. 5). At that stage, there are still objective grounds to remain in doubt. To make it conclusive it must be certain (again, in the framework of OPAR ch. 5). Your solution was to vary the standard of proof so that the conclusion does not rely upon axiom, sense perception, or a valid, proper causal explanation. How such a conclusion can have a valid role in man's cognition remains an unanswered question.

Edited by Seeker
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There is only one way out that I can see and that is to:

1. Acknowledge that the conclusion is certain within the meaning of OPAR ch. 5

2. Confirm that the conclusion is based upon axiom, sense perception, or a valid, proper causal explanation.

3. Set a standard of proof of that admits of reasonable doubt, e.g. "very highly probable".

So what this would say, in effect, is: "The conclusion that Mr. X is guilty conclusively and certainly meets the standard of being very highly probable, though doubts remain."

Notwithstanding that rather bizarre construction, and setting aside that "very highly probable" is not what the criminal law actually provides, this still fails to explain what objective doubts exist (to Betsy). Hence my remarks about unspecified, unwarranted doubt. I am truly at a loss to explain that.

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Peikoff is using scare quotes!!!

Is he, or is he using quote quotes?

Observe that in every instance where he puts the word "tautology" in quotes, you can replace that quoted word with the phrase "what they call a tautology" without losing any meaning whatsoever.

The meaning of the above paragraph is that what modern philosophers call a "tautology" is what we consider to be an instance of the Law of Identity -- and it applies to all truths.

Were you invoking Peikoff's authority on me, or using Peikoff to prove my argument wrong?

If the latter, observe that modern philosophy always dismisses the tautology as inconsequential, uninteresting, and utterly devoid of intellectual and conceptual content, whereas Ayn Rand always upheld identity as one of the most important facts there are, the most fundamental, the most full of intellectual and conceptual content.

I agree that Peikoff was using scare quotes. Tautology is an anti-concept. It is the attempt to destroy the concept identity.

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What then do you make of Ayn Rand's statements when she speaks of "degrees of certainty" for things which are possible or probable? Is she using the word "certainty" improperly?

While acknowledging that there can be degrees of certainty, I don't think this has anything to do with two (or more) concepts of certainty; but rather it has to do with the amount of information one has on the subject (not the nature of the subject, as in volitional or non-volitional).

For any given subject, one can have information that logically requires one to come to a conclusion regarding that subject, if one is upholding reason and reality as the standard. The conclusion can be either possible, probable or certain. Certainty means that all of the information one has on the subject points to one and only one logical (non-contradictory) conclusion. However, it is possible to get even more information regarding the subject that still does not invalidate the previous conclusion, and thus increases one's certainty of one's conclusion. This is what degrees of certainty means. It does not mean that one had some doubt that later information renders void; it only means that any new information strengthens one's case that one is certain about the conclusion. This can happen with either volitional or non-volitional subjects of study.

For example, one can be certain that one is in love with someone after a date or two. After many new dates one becomes even more certain that one is in love with this person. It's the same conclusion but based on even more facts about the person. There was no doubt after the first couple of dates, and as one continues to go out with this person one becomes even more convinced that one is in love. So, it is not as if one was using one concept of certainty after the first few dates, and then switches to another concept of certainty after going out with the person for many, many times. It's the same concept, but has becomes strengthened by getting even more information.

In this way, it is possible to become certain of one's lover's character, and even more certain after many dates. The certainty grows with each moment one spends with one's lover.

So, yes, there can be degrees of certainty; but one had to be certain regarding the information one did have, and then become even more certain as more information is discovered.

And as I mentioned, this doesn't have anything to do with the nature of the subject, but rather on the amount of information available regarding the subject. With more information one's certainty can grow, but that can only happen if one was certain past a certain point. If one was not certain, then becoming certain based on the information does not go from certain to certain, but rather from possible to probable to certain -- and then even more certain.

I think one also has to be careful in reading things from either Miss Rand's personal journals or her extemporaneous answers to questions. These were not necessarily her final answer to an issue. To get her final answer one has to look at her published works where she had ample time to edit and to clarify.

In that regard, there is also a difference between what someone might say on a message board in a quick reply to someone that may not have been scrupulously edited in the heat of a discussion (even though, in a sense, it is published -- i.e. made available to the public) versus a longer essay that one had time to edit before sending out (and maybe pre-reviewed by an editor for at least clarity). I find myself saying things at times on these message boards that makes perfect sense to me, but then I realize that I took some context for granted and that the reader may not understand what I'm saying with the clarity that I have on the topic after a more careful review. But, I think that is understood on these discussion boards.

It should also be understood for things a person may write in private that was not meant for anyone else to view, such as personal journals. And even though Miss Rand was a genius and often stated what she meant even in extemporaneous answers to questions, I don't think it is proper to hold her to the same exacting standards for these types of entries.

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So, yes, there can be degrees of certainty; but one had to be certain regarding the information one did have, and then become even more certain as more information is discovered.

Would you please cite the page in OPAR (or anywhere in Objectivist literature) where it says that (a conclusion)* can go from possible to probable to certain to even more certain? Somehow I must have overlooked it.

How can you go from having zero doubt to having less than zero doubt?

*Edit - we are here referring to conclusions, I think, not emotional states

Edited by Seeker
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One thing I wish to add about Thomas' remarks is that his explanation of "more certain" constitutes a kind of intellectual fudging. He says that there isn't any doubt about the conclusion, but introduces a new concept: strength of one's case. But all that does conceptually is undermine certainty once again by introducing a new kind of inequality which is PRECISELY what certainty is NOT all about. What does it mean to have a weaker case in the context of certainty? If it does not mean having doubts then it means nothing at all.

Certainty is a precious intellectual concept. We must not destroy it through usages that undermine it.

Edited by Seeker
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Certainty means that all of the information one has on the subject points to one and only one logical (non-contradictory) conclusion. However, it is possible to get even more information regarding the subject that still does not invalidate the previous conclusion, and thus increases one's certainty of one's conclusion.
Given the first sentence, I don't see how the second could be true. If you have N units of information and they all show X, then adding an observation still means that all N+1 pieces of information show X, and you are just as certain as you were before. The concept of "degree" applied to "all" makes no sense.
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"Strength of case" and "degree of certainty" make sense relative to the evidentiary continuum - possible, probable, and certain. But Betsy has sought to justify her use of "certain" on that evidentiary scale, by varying the standard of proof either to go beyond axiom, sense perception, or a valid, proper causal explanation, or permitting unspecified, unwarranted doubt. I can accept Rand's label for the evidentiary continuum - it's not a problem provided that everyone understands that "degrees of certainty" is an indivisible expression naming that continuum, because it doesn't affect what certainty is: the terminus wherein no doubt remains. I can also accept certainty as a feeling that, like any feeling, can be stronger or weaker depending on the circumstances.

But those expressions are not relevant here. What ARE relevant are the mistaken ideas that there is a valid role in human cognition for conclusions that are not based upon axiom, sense perception, or a valid, proper causal explanation; that we ought to have unspecified, insurmountable doubts when making inferences about other's motives; and that certainty, once achieved, can be made more certain still. None of those ideas are valid; none correspond to reality; all must be rejected.

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I think some of the responders to my recent post are squabbling over what I meant by the term "all" when it comes to certainty. Man is not omniscient -- he is not aware of every single fact in the universe regarding a particular subject. However, this does not lead to any undermining of what is meant by the term "certain," and it doesn't leave room for doubt once one has enough information to come to a conclusion with contextually absolute certainty. I would say what I am getting at is more like the idea of the spiral theory of knowledge.

In the spiral theory of knowledge, one comes to understand something based on one's context of knowledge (the facts one has that are integrated), and then continues to integrate up and down the hierarchy of knowledge as more information becomes available. For an active consciousness, one doesn't reach a conclusion that is certain, and then not take into account any more (new and relevant) information one has on the subject. One is continuously integrating.

For example, let's say one has enough information to conclude that a meteor hit the earth 65 million years ago because one has the evidence, say, in the layers of earth that are spread out over a wide area that could only have come from a meteor (isotopes of a type of mineral). At this point, one is certain that a meteor has hit the earth 65 million years ago.

Later, one gets even more information, but of a different nature that doesn't have anything directly to do with isotopes discovered over a wide area of the earth. Say, something along the lines of evidence for giant floods along coastlines that can't be explained in any other way. At this point, one is even more certain that it must have been a meteor, because one has integrated the new information and can't come to any other conclusion.

Still later, a giant crater is discovered that wasn't known about before because it is beneath the ocean and wasn't detectable on the surface of the ocean. This new information is integrated and leads to one and only one conclusion, that a meteor struck the earth 65 million years ago, and one is even more certain of it due to the new information that one has integrated.

Notice that for each step of integration, one has to conclusively arrive at one and only one conclusion with certainty, that a meteor struck the earth 65 million years ago. The discovery of the floods and the discovery of the crater do not bring one to question one's earlier certain conclusion, in fact they strengthen one's case. But for each step, all of the available information leads to one and only one conclusion. It's just that "all" has changed as one gets more and more information.

One had enough evidence (at least according to some scientists) that it had to be a meteor because only meteors contain that particular isotope, and one found it over a wide area at a level of 65 million years ago. So all of that evidence pointed to one and only one conclusion.

The evidence for the floods is a different type of evidence that has nothing whatsoever to do with isotopes, but rather a large disturbance of water near the coastline. And all of that evidence leads to one and only one conclusion.

Similarly, once one finds the crater, that could only have been caused by a meteor (rather than say a volcano), and all of that evidence leads to one and only one conclusion.

The point is that man's knowledge grows. It doesn't remain static. And as one's knowledge grows by integrating more and more information, one's certainty about a conclusion can also grow.

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Thomas, I must once again disagree. I understand what you are saying in regards to a growing context of knowledge. I agree that which each discovery there is more evidence in support of the conclusion. But more evidence does not mean more certainty, and this is not a trivial problem. To be more certain later implies being less certain earlier - and since certainty is freedom from doubt, being less certain earlier means being more doubtful earlier. There is no way out of that problem other than to abandon your inappropriate use of the word "certainty" in this context.

Edited by Seeker
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Thomas,

Would you agree with this picture of the continuum of evidence?

--- Some evidence (conclusion is possible)

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--- Much evidence (conclusion is probable)

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--- Conclusive evidence (conclusion is certain; the standard of proof has been reached)

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\ / Additional evidence (conclusion is certain; the standard of proof has been surpassed)

Once you reach the standard of proof, you are certain. But this does not mean that the continuum of evidence halts. As you gather more and more evidence, your end point of certainty expands beyond the point where you met the standard of proof. So, anything beyond the standard of proof is a higher degree of certainty. Do you think that makes sense?

Edited by MisterSwig
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It doesn't make sense, because the evidentiary continuum is fundamentally about resolving doubt. Once all doubt is resolved, you are at the end and can go no farther.
Perhaps the problem arises because of the two kinds of continua -- one that's open-ended on one end like the integers, and a continuously subdividable interval like that between 0% and 100%. The evidentiary continuum is the latter kind; but you can still continue to pile up evidence so you can have 100 pieces of evidence, a thousand, a million or more. Certainty is not about the total count of bits of evidence, it's about the proportion of evidence -- 100%.
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Once you reach the standard of proof, you are certain. But this does not mean that the continuum of evidence halts. As you gather more and more evidence, your end point of certainty expands beyond the point where you met the standard of proof. So, anything beyond the standard of proof is a higher degree of certainty. Do you think that makes sense?

Yes, I think that is a good summation that as one's knowledge grows, so does one's certainty about a given subject. It does not mean that one's certainty after reaching the standard of proof is less than full certainty -- one is fully certain of the conclusion. And any more information about that subject further confirms and re-instates that conclusion.

In the case of the meteor hitting the earth 65 million years ago, some scientists were absolutely convinced of that occurrence by analyzing the soil samples and finding that isotope that can only come from meteors. Once the other information was obtained, the floods and the crater, their position would have been: Well, of course, because a meteor hit the earth 65 million years ago. But they aren't going to disregard that further information just because they were already convinced that a meteor hit the earth 65 million years ago.

When it comes to judging someone's character, I do think innocent until proven guilty is a good guide, but it is insufficient in demonstrating that someone is, in fact, virtuous because one has to have the facts to back that up.

As someone walks into the store I operate, I don't think: "Aha! Here comes another swindler!" No, I give them the benefit of the doubt (since I don't know them), and consider them to be rational. As I gather more information about them during the process of helping them frame their picture, I gather more information, not only about their character, but also about what colors they like, what frames they like, and so on. At some point in time during this process, I am certain they like what I have shown them, and that a sales is being made. They pay me, I complete the job, and they come in to pick it up and they love the final product. Now I am absolutely certain that they like my style of framing.

Later, they come in with even more pictures to frame and I am even more certain that they will become good, long-term customers.

In this case, the standard of proof was that a sale was made and that the customer is satisfied with the final product. When they come in for more, our profits increase and continue to increase as the customer buys more and more framing from me. And I think the idea of being more certain is similar. The profit one gets from doing integrations is increased as one gets more and even more information.

Likewise for judging someone's character. They are innocent until proven guilty -- if they have been accused of doing some wrong. But if they have not been accused of anything that remotely points to them, then innocent until proven guilty doesn't really make sense. When a customer comes into my store I don't think, "Hey, that guy is innocent of the murder I just heard about until proven guilty!" Because there is no relationship in my mind between that guy, who I don't know, and the story I just heard about over the radio. Rather, I give him the benefit of the doubt that he is rational ( and therefore not out to do me any harm). So, I deal with him as a civilized human being.

As I gather more information, at some point I will be convinced that he is rational, and if no further information contradicts that assessment, then I become even more certain of his rationality (and therefore of his honesty and the other virtues, and therefore of his rational character).

However, if one tries to deal with a person on straight terms and only gets babble in return, then one can begin to assess his character as not being too sound. And the only way to correct this is to be open and honest about the situation. In other words, the level of directness regarding a situation is a good guide as to whether or not someone is being honest about his role in it.

But it is not two types of certainty: One applying to inanimate matter, and one applying to volitional beings.

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Betsy, please let me ask this. What, in your view, is the difference between the certainty you advocate and the certainty that Dr. Peikoff advocates in OPAR Ch. 5?

Sometimes I use "certainty" in the C2 sense to mean "conclusive" exactly as Dr. Peikoff does in Ch. 5. Sometimes I use "certainty" in the C1 sense to mean "beyond all doubt." I can also point to places in Ayn Rand's writings where she used the word "certainty" to mean C1 and other places where she used it to mean C2. Context is everything.

Because there is clearly a difference. I think that when Dr. Peikoff says certain, he doesn't mean "highly probable" - he means certain - and you do not agree with that.

Correct me if I am wrong, but you seem to be using the word "certain" as if it had only one, intrinsically correct, meaning. This is not the case. The same word can denote more than one concept which is why dictionaries have multiple definitions for the same word.

I am trying to get at the linchpin of the disagreement. It seems to boil down to the fact that we cannot read minds, so we cannot know men's motives (what causes people to do things) and that the lack of that causal connection is (for you) a barrier to (contextual) certainty about men's motives. Is that correct?

More precisely, the fact that we cannot read minds does not prevent us from having "conclusive" (C2) certainty, but it is a barrier to ever having absolute, 100% (C1) certainty.

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That is not what you said here. You said "You can't be 100% certain that someone else is moral in his past and present actions either, just certain beyond a reasonable doubt which is as good as it gets."

Overtly, you've made a distinction, you did not attribute one version of this belief to someone else, you made this statement yourself, and you refer to both as "certain".

Actually, I was comparing "100% certainty" (C1) to "certainty beyond a reasonable doubt" (C2). (C2 is "as good as it gets" when judging people. C1 is possible with other entities.)

The facts speak for themselves. The distinction between C1 and C2 as you defined these expressions here is nonexistent. The meaning of "conclusive evidence, logically validated, that fulfills a standard of proof" is "conclusions derived and inferred from sense perception using rules of logic to preserve identity".

Sometimes. All conclusions that are beyond all doubt (C1) are also conclusive (C2), but not the other way around. Some conclusive (C2) conclusions are based on a standard of proof such as "beyond a reasonable doubt," that does not exclude all doubt. In the chain of reasoning that leads up to a such conclusive conclusion there may be unknowns such that the causal chain between perception and conclusion has gaps in it.

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There are so many interesting posts here I would like to answer right away, but I have limited time to do so. As a result, I am answering them as time allows, rather slowly, in the order in which they were posted.

Noumenalself 's post #45 is next ... tomorrow.

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