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Wouldn’t this itself be a statement of knowledge? By anything, I don’t mean to include experience or having a sense of consciousness, which we all likely atleast feel certain about or in agreement about.

The question then is: why can’t we be certain, for example, in the fact that unicorns do not exist. The counter to this usually is: well, we cannot disprove all kinds of unicorns, such as invisible or undetectable ones, therefore we can’t know for sure.

However, doesn’t this assume that undetectable unicorns are possible in the first place? Assigning a very minimal probability to it doesn’t seem to work either: there is nothing stochastic about unicorns existing. They either exist or they don’t. Using a subjective interpretation of probability would bring its own problems, namely that it would beg the question of how to map our credences into probabilities, and how those credences would map to the real world.

As such, why is it wrong to then say “I am certain that unicorns don’t exist.” You may ask for proof of this and my proof would simply be “because we have not detected them.” If the counter is “how do you know that undetectable unicorns do not exist?”. I can simply state that those are not possible. This last step is an axiom, sure, but the notion of even considering undetectable unicorns as a possibility is also an axiom.

In other words, saying that we can’t know for sure that unicorns don’t exist relies upon axioms just as much as saying that unicorns certainly do not exist. And yet, the former is seen as rational and the latter not. Why?

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    Every "absolute" statement that applies to all statements without restriction can be subjects to "Liar-like" issues. Commented May 5, 2023 at 10:07
  • Yes, unicorns may exist: according to their "definition" nothing in it violates a natural law. Commented May 5, 2023 at 10:27
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    You hit a nerve in someone... Proof that nerves exist, I guess.
    – Scott Rowe
    Commented May 5, 2023 at 10:37
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    For a generalized discussion of this topic, see this PhilosophySE question. Commented May 5, 2023 at 11:09
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    Do we know for sure that "we can't know anything for sure"? If yes, then we know that for sure, if not, then there are (other) things we know for sure. (don't ask me how we know them :))
    – Nikos M.
    Commented May 5, 2023 at 13:20

5 Answers 5

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Questions of the form 'how do you know that x does not exist' are troublesome because they imply an unwarranted binary status, that one either knows or doesn't know. Moreover, 'know' is often taken to mean 'know with absolute certainty', which is an impossible and irrelevant threshold in most cases. If instead you consider questions of the form 'on what basis do you suppose that x does not exist?' you will find most of the conceptual difficulties fall away. I suppose that unicorns do not exist because: there is no evidence for them; it is highly improbable that they could exist in the wild without somebody noticing them; there is no evidence of 'missing links' which are somewhere in between horses and unicorns; etc etc.

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  • This seems like it should be obvious and unproblematic.
    – Scott Rowe
    Commented May 6, 2023 at 0:00
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As Kristian Berry has apparently pointed out in another question, the answer kinda depends on what you consider the initial statement to be. Like if it's a general expression of uncertainty, then the application to itself just affirms itself rather than contradicting itself. So if you can't know that this heuristic is true, then not being able to know that is yet another example on the long list where it holds AND confirmation of the conjecture that you can't know that the list is conclusive no matter how long it is.

However if you see it not as a heuristic but as a certainty, then it likely is a contradiction, because now you at least have 1 fix point in your entire logical universe, you'd KNOW FOR SURE for example that the search for absolute truth is futile, because you KNOW that it doesn't exist, except for that one case. Except it would likely still be iffy. Because of "HOW?". "How do you know that you know that you can't know anything else?". Like that proof of the fact would be somewhat necessary to know (for sure) and it would be another thing that you know. But if you can't know that (the proof), then this again affirms the statement, but also emphasizes that it's not a certainty, that it's not something that you can know for sure.

So given that assuming it's a certainty leads to a contradiction, the more likely interpretation is an expression of an overwhelming uncertainty that is not claiming to be a universal truth, in which case it would be self-affirming.

The general "problem" with certainty is that you can often deduce other certain statements from them so it's somewhat dangerous to claim with universal certainty, because that has consequences. Like the fantasy world of mathematics can span up entire universes as complex or more than our own reality (exemplified by the fact that they are quite useful to describe ours), based just on a small set of axioms and interactions. So be careful with axioms, they're the big bang of an entire alternate reality and you might not be fully aware of the consequences of them.

In other words, saying that we can’t know for sure that unicorns don’t exist relies upon axioms just as much as saying that unicorns certainly do not exist

The important parts of the first sentence is: "WE can’t know for sure that unicorns don’t exist"

With the implied part being ... "(as of right now) WE can’t know for sure that unicorns don’t exist

So this statement is already not "for sure" and of "universal certainty", but it's truth value is already limited in audience, time and space. So for "us", "here", "now" it is not possible. But for someone else, somewhere else and at a different time it could be possible. Now it's still a fairly strong statement of certainty, but there's probably still more wiggle room than for the second statement.

Also whether there are unicorns depends on your definition of a unicorn. For examples: Rhinos are 1 horned, narwhals even have the spiral and these goats are 4 legged land animals with a spiraled horn, so given that unicorn sightings precede the development of modern biological taxonomies, it's entirely possible to confuse a goat with a horse from afar. So what even is it that you assert can't exist? Like even if it currently doesn't exist, is it impossible for such a thing to develop over time (under any and all conditions)? Because to claim with certainty that it doesn't exist would be strong enough to mandate that.

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Not substantively. The common language idea is an imprecise restatement of the mathematical fact that p-value doesn't go to zero for any finite set of measurements. This fact is implicit in the definition of the p-value and not itself a measurement, so there is no recursion or contradiction.

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  • The p-value doesn’t exist in the real world
    – user62907
    Commented May 5, 2023 at 18:36
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Descartes' Epistemology - SEP

https://plato.stanford.edu/entries/descartes-epistemology/

I distinguish the two as follows: there is conviction [persuasio] when there remains some reason which might lead us to doubt, but knowledge [scientia] is conviction based on a reason so strong that it can never be shaken by any stronger reason. (24 May 1640 letter to Regius, AT 3:65, CSMK 147)

I shall now expound for a second time the basis on which it seems to me that all human certainty can be founded. First of all, as soon as we think that we correctly perceive something, we are spontaneously convinced that it is true. Now if this conviction is so firm that it is impossible for us ever to have any reason for doubting what we are convinced of, then there are no further questions for us to ask: we have everything that we could reasonably want. … For the supposition which we are making here is of a conviction so firm that it is quite incapable of being destroyed; and such a conviction is clearly the same as the most perfect certainty. (AT 7:144f, CSM 2:103)

SEP - "These passages (and others) suggest an account wherein doubt is the contrast of certainty. As my certainty increases, my doubt decreases; conversely, as my doubt increases, my certainty decreases."

George Box

All models are wrong, but some are useful.

In a bivalent logic model, certainty and doubt are mutually exclusive. There is either certainty or there is doubt. But they do not co-exist or overlap in the model. This is called the excluded middle.

In a fuzzy logic model, certainty and doubt overlap. There are degrees of certainty and doubt where increasing certainty diminishes doubt and increasing doubt diminishes certainty.

Baruch Spinoza describes the relationship between pleasure and pain using the fuzzy logic model. He says intense pleasure drives out pain and intense pain drives out pleasure.

Recognizing and Quantifying Uncertainty

https://psycnet.apa.org/record/2017-09556-007

People view uncertain events as knowable in principle (epistemic uncertainty), as fundamentally random (aleatory uncertainty), or as some mixture of the two.

To quantify aleatory uncertainty mathematicians, scientists, and other experts apply the conventional methods of probability and statistics. To quantify epistemic uncertainty experts use more recently developed methods associated with the fields of data science, machine learning, and artificial intelligence.

Bayes' Theorem - SEP

https://plato.stanford.edu/entries/bayes-theorem/

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology.

Ramana Maharshi

Nobody doubts that he exists, though he may doubt the existence of God. If he finds out the truth about himself and discovers his own source, this is all that is required.

Book of Job

"When the sons of God gathered before the Lord, Satan also came among them! God said, "From whence do you come?" Satan replied, "From roaming the earth and patrolling it!"

Answer

The question then is: why can’t we be certain, for example, in the fact that unicorns do not exist.

Because it is reasonable to doubt the assertion that unicorns do not exist. This doubt can be based on the vague human perceptions of what is or is not a unicorn (goat, rhino, horse); or on the fact that many creatures in the past and present roam and patrol the earth undetected by humans when we roam the earth and patrol it.

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  • There can be a comfortable gap between doubt and certainty, where it isn't urgent which way something goes. This is a lot better than getting wrapped up in everything that comes along.
    – Scott Rowe
    Commented May 5, 2023 at 23:58
  • "Using a subjective interpretation of probability would bring its own problems, namely that it would beg the question of how to map our credences into probabilities, and how those credences would map to the real world." Applied philosophers in fact use arbitrary and subjective math models to Quantify Uncertainty. In some domains the math appears objective. Economists claim to measure "utility" using arbitrary and subjective math models that have certain objective attributes that map preferences to behavior, etc. My answer relates to quantifying uncertainy based on different ways of reasoning. Commented May 6, 2023 at 0:25
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"Unicorns are not detected yet." ----- X

"Unicorns are undetectable." ----- A

"Unicorns does not exist." ---------- B

For, X to be true A or B is true.

X = A||B.

X = TRUE.

A|| B = TRUE.

A is true OR B is true.

Now, if you are able to prove that A is FALSE; then B must be TRUE.

This is a case of DISJUNCTIVE SYLLOGISM.

The above argument is a valid one. However, it is not sound as there is no way to prove that A is FALSE.

So, using pen-paper, we can prove that unicorns do not exist by assuming that they are not undetectable. However, to make this valid argument a sound one; A must be proved to be FALSE. If you consider A must be false just because of your ignorance, then B is TRUE only because of your ignorance.

PS:- The symbols I used in this answer is most commonly used in boolean algebra as I don't have the access to use symbols taken as convention in propositional logic.

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