QuickPoint 5: Any Claim to a Probability is Also a Claim to a Certainty

Are you saying you're certain that that's the probability distribution?

Are you saying you’re certain that that’s the probability distribution?

Whenever anyone says that some statement’s truth is probable, whether they give a numerical percentage or not, they are making a definite knowledge claim: that the statement’s truth is probable. Whether the probability is measured by a percentage, or relative to some other statement(s), the person is claiming that that is the probability’s measure.

In other words, the person claiming a probability is claiming a certainty about the probability, itself.

If such a person claims that his estimate of the probability is based on another probability, then the question becomes, “What is the prior probability based on?” The failure to provide at least one certainty at the foundation of one’s estimate of such probabilities leads to an infinite regress, or to a baseless circle–neither of which is rationally tenable.

Thus, for any claim of probability to be based in reason, it must be founded on at least one absolute certainty. And so a claim about the probability of any statement’s truth implies at least one claim to certain knowledge.


Related Posts:

Taking Philosophy Seriously…

Objectivism vs. Intrinsicism vs. Subjectivism: A Short Summary

The Arbitrary (from The Objectivism Seminar)

The Bible (New Testament) as Evidence

Proceeding from Axioms in Objectivism – YouTube Edition

Taking Philosophy Seriously…

…Means Not Committing The Fallacy of Self-Exclusion.

If philosophy is to be more than a useless mental exercise, or a “bauble of the intellect” as Leonard Peikoff puts it in OPAR, (1) any statement claimed as knowledge must be consistent with the very fact that the philosopher is claiming the truth of the proposition. If the truth of the proposition would invalidate the statement being made by its application to the speaker, then this is an example of the Fallacy of Self-Exclusion. The speaker must arbitrarily exclude himself from the statement in order to “validly” make it.

The most obvious example is the claim that knowledge is impossible to human beings. This statement is itself a claim to knowledge by a human being; so in stating it, the speaker is contradicting himself. (2)

But this fallacy occurs in many more subtle forms:

“There are no absolutes.” That is an absolute statement asserting a negative.

“We can never be 100% certain. All we can know are probabilities.” Well what’s the probability that that statement is true? It should have been put in the form of “There is X% probability that all we can know are probabilities.” Then, what is the value of X based on? More probabilistic premises? How does one avoid an infinite regress and establish a basis for the numbers if nothing is absolutely certain? You will have to come up with a theory that allows for certainty somewhere.

“Human beings are irrational creatures driven by their emotional impulses.” So you got into philosophy on a whim, and that statement is an expression of your emotional impulses? How could any of the irrational, emotionalist creatures around you possibly consider your personal emotional expression as some kind of “universal truth” about human nature?

So, the take-home point here is: whenever considering a proposition or theory in philosophy, especially something regarding epistemology or human nature, apply it to yourself first, to see if the statement is self-refuting. If it is, then the view is untenable as it stands. (3)

The following is an abridgment of a real conversation that I had in a public, online forum. It shows a real case of the Fallacy of Self-Exclusion in action (key parts are highlighted in red):

Him: […M]any people seem to embrace science and the natural world when they’ve left god and church. I seem to be going a step farther: I am coming to the conclusion that all our perceived realities are man-made – not just the religious and the spiritual, but our science as well. Nothing appears to be absolute. I have not settled on this view at all but I am seriously considering it.

All facts are contained within a reference frame or point of view in our heads, that we can’t escape from. We cannot even talk about a fact, an object, an event – out there external to us – w/o injecting our perspective.

It was Immanual Kant that said that when we look at what we consider the real world, we are still looking at it through our internal lens. There is no way to get outside ourselves to look at it objectively. This seems to be true b/c look at all the various opinions on any topic from religion, to spirituality, to economics, to politics, to morality, and even to science. We humans cannot appear to agree on anything.

We coalesse [sic] into groups that have similar perspectives and perceived realities to us individually. Others outside the group have a multitude of different realities when it comes to the topic being discussed. And there is no objective standards that can be used as an arbiter to decide between the differing views.

So this is postmodernism looking glass I guess: relative, subjective, individual, and socially developed.

I am reading a lot about it for and against, so the jury is still out for me.

Me: […] It does not follow that just because you are aware by means of your senses, that your awareness is distorted or subjective. Nor does it follow that just because you think by a means (namely, concepts) that your thinking is biased. Consider an analogy for Kant’s position: A friend calls at noon, and asks you to meet him at a restaurant at 6:30. You agree, and starting at 6:00, you drive there and meet him at 6:30. When you meet him, he says, “Wait, you drove here?”

You say, “Yes.”

“But you can’t really be here.”

“Excuse me?”

“You drove here.”

“Yes, I’m here, am I not?”

“No, it’s not the same. You drove here, and that means you’re not really here. To really be here, you had to just appear.”

“You mean, teleport?”

“Yes. If you had just teleported, you would really be here. But since you drove, you’re not really here.”

Your friend’s name happens to be Immanuel Kant, and you go on to discuss his theory about how the senses are invalid as a means of objective awareness of the “thing-in-itself”, just as driving is an invalid means of “objective travel to the destination-in-itself.”

The fact that you are aware by some means, does not indicate that you are not really aware.

In order to make a claim of knowledge about anything, including the knowledge of the “invalidity” of the senses, you must assume that your senses give you a basis for actual knowledge. So a claim that the senses are invalid is self-contradicting.

It is true that, ultimately, you can only ever see through your own eyes, and hear through your own ears, but this is still seeing and hearing.

Him: […] I am not making a claim about the invalidity of the senses. I am suggesting that the sensory stimulus is not interpreted the same for everyone but is interpreted based on their prior experience and cultural upbringing.

Something that is interesting – people that have experienced severe epileptic seizures and have had the hemispheres of their brains separated to reduce them, where each hemisphere can’t communicate with the other, suggests our brains make things up. In one case, a researcher used an optical device to flash visual messages to a patient who had had this procedure, in such a way that the message reaches only one hemisphere of the brain. So keep in mind that the right hemisphere is not verbally dominant but it can receive and act on a verbal message. So he flashes a command to the patient that says, “smile.” The patient smiles. He flashes “tap,” and the patient taps. The left brain doesn’t know what is going on at this point b/c it never received that message. Even when given those commands the patient says he didn’t see anything. Now the researcher flashes a command to the right hemisphere, “walk.” The patient gets up and starts to walk. When the researcher asks why he is doing this – a verbal inquiry handled by the left hemisphere and the one that didn’t get the command – the patient answers, “I’m going to the fridge to get a Coke.” The left hemisphere made up a perfectly good reason, and also probably based on past experience, but unrelated to what prompted the action. What are we to make of such things?

Me: I think it would be helpful here to define what I mean when I say “reality.” I think that your use of the term “reality” agrees with many modern philosophers, but that this use is improper because it confuses an important distinction. We should be careful to distinguish the difference between reality and beliefs. That is, (roughly speaking) between the physical world as it exists, “out there” and the content of one’s consciousness that is supposed to refer to that world. I like [moderator]’s definition in his signature: “Reality is that which, when you stop believing in it, doesn’t go away.”

If we take a simple example: You are standing at the side of a busy street. You see a car coming at 40 mph, but you decide that that car is “not a part of your reality,” you close your eyes, believe with all your will that that car is unreal, and you step out in front of it. Does that car disappear and allow you to cross safely? No, because that car is real. It’s reality will still confront you, even if you manage to convince yourself that it is just an appearance in your head.

Or another example: You convince yourself that you don’t need food to live, but only prayer. You fast continuously, but pray a lot. Will this stop you from getting hungry, losing weight, and eventually dying? Try it. Will this work for someone else who is a true believer? Ask them to try it, and see what they say 5 weeks later.

Your belief in something does not make it “true for you.” There is not “my reality” and “your reality,” but only reality, which is the world that each of us perceives, and my belief and your belief. If my belief corresponds to this one reality, I am right; if it does not, I am wrong. If I have a belief that a car speeding at me won’t hurt me, and I step in front of it based on that belief, I won’t get the result that I expect, because I am wrong.
It is the conceptual interpretation of what your senses give you that is subject to past experiences and cultural ideas. You and a Hindu will both see an object shaped like a book on a table. It is real to both of you. But conceptually, he may recognize it as the Sama Veda, whereas you might not, for any number of reasons (too far away, can’t read the language on the cover, etc.) But you both see the same object, and that object is real.

In the case of the epileptic surgery patient, I see someone who has a specific disability in dealing with reality due to the physical manipulation of his brain. Brain injuries and schizophrenia can also cause problems in perceiving reality and reasoning about it. What does this prove? That reality is subjective? It only proves that some people can be incapable of dealing with reality in various ways. If the researcher had done that experiment with your average man on the street, who had not had his brain operated on, would he have gotten the same result? Almost certainly not.

But do you see the irony of what you’re asking here? You are basically saying, “Look, here is a real, objective fact you should take into consideration. Doesn’t this objective fact show that reality is subjective, and that a fact for one person is not a fact for another?” How can it? How can any fact show that there really are no facts? If reality is subjective, then it is not real in any way that matters, or that distinguishes it from fantasy. If this is the case, I could just as easily concoct my own fantasy and use it to “prove” anything. I could just flatly contradict your example, and say, “No, in my reality, he was able to tell the researcher that he walked because he was told to,” and I would be just as “right” as you are.

At root, you either have to accept the axiom that “existence exists,” (i.e. reality is real) or you have no basis for any conclusion whatsoever. This is why it’s an axiom. Without it, you can’t think any thought or make any statement without falling into self-contradiction.


(1) Objectivism: The Philosophy of Ayn Rand

(2) This is a self-contradiction so long as the proposition, “I am a human being,” is held to be true. Thus, the only way out of self-contradiction is to assert the absurd position, “I am not a human being.” Regardless, if one states, “Knowledge is impossible to [me, or a class to which I belong,]” then it is a self-contradiction.

This fallacy is also sometimes called a “performative contradiction” or a “self-refuting idea.”

(3) Instances of the Fallacy of Self-Exclusion generally employ “stolen concepts.” See Ayn Rand Lexicon: http://aynrandlexicon.com/lexicon/stolen_concept,_fallacy_of.html