Lukas Nabergall 1 001065-044 That which can be asserted without evidence can be dismissed without evidence. (Christopher Hitchens).

Do you agree? Consider the type of assertions an average person might make. The earth rotates around the sun. Water is composed of two parts hydrogen and one part oxygen. Maybe even that there exists a supreme being which created the universe. Why would a person assert that these propositions are true? It is reasonable to conjecture that the majority of those who list such assertions would typically respond by saying that they have seen photographs detailing the property of the objects, or they read the information in a textbook, or they were simply told that these assertions are valid from someone whom they trust implicitly. These explanations can, when considered independent of validity, be viewed as justifications for their assertions. But when does a justification become valid evidence? Furthermore, is evidence even necessary to assert the truth of a proposition? The first problem which must be addressed when determining the validity of Hitchens statement is the defining of evidence, in order to eventually deduce what may be considered a lack of evidence. Let us examine a typical definitionevidence is that which determines the validity of a proposition. From this reasonable demarcation, several deductions are apparent; for one, the evidence itself must be valid, otherwise it cannot be used to make inferences about any hypotheses. More broadly, the definition is nonconstructive as it defines evidence via its functionto determine the validity of propositions. For additional deductions about the nature of evidence, let us suppose we have a proposition shall call and we locate some evidence for , which we

. It is certainly reasonable to presume that this evidence may only lend credence for

and not fully determine the propositions validity. Thus we can conclude that evidence is probabilistic; it is something which increases the probability of a proposition Utilizing some basic mathematical notation, we could consequently call a set being true. * +

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Lukas Nabergall 2 001065-044 of pieces of evidence the body of evidence for if ( ) and ( ) ( ), meaning

that the probability of the proposition given the body of evidence must be , or guaranteed true, and the probability of of given any single piece of evidence must be greater than the probability to and to ).

alone (for a body of evidence against a proposition simply change

So what can affect the probability of a propositions validity? As a student heavily interested in mathematics, the first general form that comes to my mind is that of another proposition. In my mathematics research, I utilize theorems in order to prove theorems; equivalently, propositions can evidence the validity or invalidity of other propositions. Take, for instance, the hypothesis that I must be living to type this paper of my own volition. As evidence for that proposition, I apply the proposition that Homo sapiens must be alive in order to be conscious. This certainly increases the probability of the hypothesis validity, and hence is evidence for the hypothesis. Yet we come upon a dilemma if we consider a propositional foundation for evidence. Earlier we noted that the evidence for a proposition must be valid in order for the proposition validity to be logically derived from the evidence. What then causes us to consider a piece of propositional evidence valid? Because we have temporarily assumed a propositional basis for evidence, it must be another proposition which by inference implies the validity of the propositional evidence. This logical chain of evidence from proposition to proposition has no clear termination point, and therefore we have what can be referred to as an epistemic regress problem. There are two possible repairs to this propositional model of evidence and the resolution of the epistemic regress problem. Either there exist a series of axiomatic propositions from which all other propositions must be derived, or we must consider another foundational model for evidence. The idea of a set of axiomatic propositions, or propositions which are so fundamental

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Lukas Nabergall 3 001065-044 as to be reasonably assumed true in order to derive other propositions, certainly has potential. Axioms play a necessary role in virtually every branch of knowledge; specifically in mathematics and philosophy is it a longstanding problem to develop an axiomatic formulation from which all valid statements can be derived by logical inference. Thus it is logical for axiomatic propositions to form the foundation for evidence. For example, a possible axiom for evidence could be the assumption that our perceptions reflect the nature of existence in some way. Logically, this proposition cannot be deduced from other propositions and it is absolutely necessary to assume this in order to produce any of the theorems of the natural and human sciences. Yet this example also reveals another aspect to the foundation of evidencewhere do sensory perceptions fit into the evidential hierarchy? They are obviously independent of any propositional definition for evidence; in fact, it seems that sensory perceptions, or simply perceptions, form another basis of evidence, one concentrated specifically on deductions about the universe. While axiomatic propositions are necessary for purely logical areas of knowledge, like mathematics and philosophy, as well as to make inferences about the natural world, perceptions are necessary to experience the natural world. For example, we can apply pure mathematical theories in order to infer the properties of a black hole, but we require observations in order to conjecture about the universe, and the black hole, in the first place. This necessary and fundamental divide in the foundation of evidence, between axiomatic propositions and sensory perceptions, is akin to the divide between axioms and definitions in mathematics. The Zermelo-Fraenkel axiomatic system of set theory is the current best foundation for all of mathematics; yet we still require definitions in order to discover and prove new theorems. This is apparent in the ZF system itself, which specifies certain fundamental properties of sets but

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Lukas Nabergall 4 001065-044 never actually defines the notion of a set. Hence definitions are analogous to sensory perceptions and mathematical axioms are analogous to axiomatic propositions. It should be noted though that a definition is actually a form of an axiomatic proposition, assuming it satisfies the properties of an axiom. Now that we have a logical basis for evidence, we can turn to more specific issues about what may be considered a complete lack of evidence for a particular proposition. Let us consider the subject of the proposition being asserted; for instance, there is a clear and logical difference in how one analyzes an assertion stating the existence of an infinitely strong ant versus the assertion that there exists a dark colored rabbit. Even without any sensory perceptions, or objects reflecting sensory perceptions (like a photograph), any reasonable person would conclude that the second statement is probably true while the first is almost definitely false. The mass and chemical composition of an ant limits it to being able to handle a relatively small maximum load, and numerous evolutionary and statistical propositions suggest there being a rabbit with dark fur. Evidence for an assertion can also come from the application of proven propositions to the probability of this assertion being valid. Another specific issue regarding what may be considered valid evidence arises when we consider the uncertain basis and consequent questionable reliability of foreign evidence, or evidence presented by someone not oneself. Suppose that another person and I make equally reasonable propositions based on our claimed sensory perceptions, and we temporarily ignore whether or not these perceptions or this proposition conflict with known truths. It is clear that from a knowers perspective there is a fundamental difference between an assertion evidenced by perceptions which I claim and which another person claims; I know that my perceptions are legitimate (barring any hallucinogenic or staged cases), but I can never be entirely certain

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Lukas Nabergall 5 001065-044 whether the other persons perceptions are legitimate. Perhaps they are lying or they simply misconstrued something for something else; either way it is clear that claimed sensory perceptions cannot be considered valid evidence when presented by a foreign source. Logically this extends to hypotheses presented by oneself to some other person(s). Now that we have fully defined what can be considered evidence, and a lack of evidence, we have one remaining questionwhose responsibility is it to provide the evidence for an assertion? This burden of proof problem is heavily emphasized in the debate between religion and atheism; many examples have been proposed by atheists or agnostics to counter the claim by religion that it falls on the atheist to provide proof for the nonexistence of a deity. The Invisible Pink Unicorn is one of these examples; replace the typical deity with a unicorn which is invisible and pink, a paradox akin to contradictions in the natures of most deities, and the claim seems plainly absurd, even though almost nothing but the form taken by the deity has been altered. It is nonsensical to assert that the opposing party must prove that there does not exist such an Invisible Pink Unicorn. The realms of mathematics and science also emphasize that the burden of proof lies on the party that asserted the claim in the first place. Unless one has some form of evidence, no physicist would be required to reasonably consider the assertion that there are twenty planets in our solar system. This can be generalized to hold true for any asserted propositionthe burden of proof logically lies on the party who made the assertion.

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