# Is it possible to infer the non-existence of a thing?

Is it possible to rationally infer the non-existence of a phenomenon or a thing, because of a lack of evidence?

I've heard of the Null Hypothesis - I heard it says that you can infer that something does not exist due to a lack of evidence, until some sort of evidence is presented for the case.

• "the non existace of a thing"... How you define thing ? Something existent ? Mar 29, 2019 at 8:15
• Define a contradictory concept, like e.g three-sided square. Then, we have that the said concept must be empty i.e. there is no object that satisfirs the def of three-sided square. Mar 29, 2019 at 8:17
• Yes. Einstein inferred the non-existence of ether from our inability, in principle, to detect it under the final version of the classical ether theory (Lorentz's). Most physicists concur. It was a classical application of Occam's razor: "entities are not to be multiplied beyond necessity", see SEP on parsimony. Such arguments are open to defeasal by future evidence arising, if it supports the necessity. Another popular example is ruling out the Russell's teapot orbiting the Sun. Mar 29, 2019 at 9:34
• If it were possible in general. The world might be a much better place. The White Swan argument, often used badly to assail scientific empiricism states roughly that to be certain about the existance of a thing, one would have to check.every posdible location. That isn't possible. In part because parts of the.universe are inaccessible. Mar 29, 2019 at 12:45
• proofs lie in the assertion, not the negation. Mar 30, 2019 at 8:40

First concerning lack of evidence:

Lack of evidence is not evidence of lack.

From time immemorial there was no evidence for gravitational waves. Since 2016 we know: Gravitational waves exist.

Secondly, if a concept is contradictory - like a squared circle - then it does not reference an existing object; see Mauro's comment.

Aside: The null hypothesis from statistics does not deal with the non-existence or existence of objects. Instead, it deals with the probability of hypotheses.

As a point of clarification, in standard logic, existence is not treated as a property of things, but a property of concepts. One only references a 'thing' if that thing exists. Hence, one does not say of a thing that it does not exist, but instead one says of a concept that it is uninstantiated. For example, "the king of France does not exist" would be understood to mean the concept 'king of France' has no instances, or at least no unique instances.

One might object that this is too restrictive, and indeed there are other logics, called free logics, in which the rules governing existence are more liberal. We sometimes give names to things whose existence is conjectured. In the 19th century, some astronomers conjectured the existence of a small planet inside the orbit of Mercury, and it was given the name 'Vulcan'. It was intended to explain anomalies in the orbit of Mercury. Subsequently, in the light of relativity theory, it was shown that no such conjecture was needed, so we may reasonably infer "Vulcan does not exist". This would be an example of a non-existence claim being a plausible inference on the basis that a conjectured thing has no explanatory or predictive value. It is an application of the principle of parsimony, or Ockham's Razor.

Another type of example might be where extensive searching or testing has been conducted for the existence of a thing, but it has not been found. In the 1990s some astronomers conjectured the existence of a second star in our solar system, co-orbiting with the sun. It was proposed to be a small star, perhaps a red dwarf, about one light year distant, and with an eccentric orbit that periodically carried it through the Oort cloud. It was tentatively named 'Nemesis' and its existence was intended to explain various phenomena. Astronomers have searched for this star now for many years and have not detected it. Given that we should be able to detect the existence of a red dwarf at that range, it seems reasonable to conclude that it does not exist.

Another type of example might involve the existence of things whose description is vague or highly uncertain. We might plausibly infer that 'El Dorado' does not exist, since it has never been found, but the concept is so vague, it is just unclear. Is El Dorado a man, a city, or a kingdom? How much gold would be there if we did find it? Likewise for the legendary King Arthur of the Britons. There might have been some historical leader on whom the legend is based, but I would be inclined to say that the stories about Arthur are too fantastical to be true, so it would be reasonable to infer that Arthur did not exist.

The examples given above are abductive inferences. We conclude that there is no good reason to suppose the existence of something, but we cannot prove it. There are examples of deductive inferences of non-existence, which take the form of showing that if a thing exists then a contradiction would follow, hence by reductio no such thing exists. Mathematics contains proofs of this kind, e.g. there is no such thing as the largest prime number.

As to your comment about the null hypothesis, I would recommend not putting much weight on the concept. The idea that we should accept some position by default in the absence of evidence is at the least controversial, and at worse downright foolish. Null Hypothesis Signficance Testing, although common, is hugely overrated and overused. You might care to consult the book: The Cult of Statistical Significance by Ziliak and McCloskey. You should definitely read a recent article by Amrhein, Greenland and McShane, published in Nature, in which the authors, together with more than 800 other signatories, call for a restriction on the use of significance testing and confidence intervals.

If one assumes something does not exist then one can conclude, based on that assumption, that that something does not exist. The inference rule is called reiteration. As Magnus, et al, describe it in forall x (section 16.1), "This just allows us to repeat ourselves".

However, that something might still exist if the assumption of its nonexistence is false.

The assumptions leading to the nonexistence conclusion might be more complicated than outright assuming that something does not exist. Regardless, the inference still rests on those assumptions being true with the risk that they might not be true.

Regarding the null hypothesis, Wikipedia describes it as follows:

In inferential statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.

The null hypothesis claims that there is no relationship between measured phenomena. The existence of the phenomena are not in doubt. The only thing in doubt is whether there is a relationship between the phenomena. That relationship might be considered a "thing". One assumes the relationship does not exist, model what the data should look like if that were the case and then see how far the observed data deviate from that model. Even if available data does not show that a relationship exists, other data, that we currently lack, might.

Wikipedia notes:

This is analogous to the legal principle of presumption of innocence, in which a suspect or defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).

This leads to arguments from ignorance and when such arguments are fallacious. If the data does not allow us to reject the null hypothesis, does that mean there is no relationship or just that we weren't able to find the relationship with the evidence we have? See Douglas Walton's Arguments from Ignorance for a longer discussion of this.

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic. http://forallx.openlogicproject.org/

Walton, D. (2010). Arguments from ignorance. Penn State Press.

Wikipedia contributors. "Null hypothesis." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 22 Mar. 2019. Web. 29 Mar. 2019.