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Hypotheses are either true or not. Justin is either a murderer or not. There is either a God or not.

If statements are either true or false, how can it be the case that certain forms of evidence weakly support a hypothesis and others strongly support a hypothesis? Shouldn’t it be the case that you either have evidence to believe in a hypothesis or you don’t, in a binary sense?

Even in the case of evidence A and B where A includes B, this seems to make no sense. For example, let’s assume that we are trying to figure out if John is a murderer.

A = We found John’s DNA on the body B = We found John’s DNA on the body and we saw a text conversation about how he wants to kill the victim

On the face of it, B seems to be better evidence than A. But before analyzing whether a statement is true, it must first be meaningful. In what sense is B better evidence than A? Sure B may include more items that would be characteristic of John being a murderer, but it would only make a difference if the additional reasons warrant a belief that John is the murderer.

But as mentioned before, you either have enough evidence to warrant a belief or you don’t. If you don’t, how can it make sense to even call the evidence you have weak? If it wasn’t enough for you to believe it, then isn’t it the equivalent as there being no evidence?

20 people saying that a person revived from the dead is no better than 1 person saying that a person revived since neither warrant a belief that he revived due to the exceptional nature of the claim.

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  • How can there be any doubt that some evidence is stronger than others? Is this really a philosophy question?
    – D. Halsey
    Commented Apr 30, 2023 at 0:50
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    @D.Halsey Questioning the obvious is a hallmark of philosophy.
    – J D
    Commented Apr 30, 2023 at 0:50
  • "Hypotheses are either true or not" is false, or, more generously, overly simplistic. Hypotheses are not formal sentences, they are typically somewhat vague and surrounded by auxiliary assumptions that can be dropped or replaced without change to their substance. In the presence of vagueness and ambiguity of context binary logic does not apply and one uses fuzzy and/or probabilistic measures that explicitly quantify "truth". "Weak" and "strong" are loose qualitative expressions of such quantification. A is "stronger" than B when, say, the probability conditioned on A is higher than on B.
    – Conifold
    Commented Apr 30, 2023 at 0:52
  • @Conifold If a statement is vague, then it is neither true, false, probable, or improbable. Since it is now meaningless unless context is given. A statement that is clearly understood to mean the same to atleast two people such as “God exists” would imply that it is either true or false to atleast those people. Any in between is impossible
    – user62907
    Commented Apr 30, 2023 at 2:02
  • Anything is meaningless unless context is given, vague or otherwise. "Clearly understood to mean the same to at least two people" can very well be clearly understood as vague by all those people. Even if “God exists” were not vague (which it very much is considering the range of interpretations of God and existence), that would not entail anything about other hypotheses. And asserting that something is impossible does not make it so, especially when it is obviously the case.
    – Conifold
    Commented Apr 30, 2023 at 2:58

4 Answers 4

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Is the idea of weak and strong evidence incoherent?

No. Different types of evidence have different strengths in relation to each other to the extent that they can exclude alternative explanations for what has occurred.

In criminal trials, for example, strong evidence can point to the defendant, but might still allow the defense to argue that the evidence can be interpreted to include a second person as the perpetrator. Stronger evidence would exclude even the possibility that an alternative reading is credible.

As suggested by your post, such exclusion is the signature value of DNA evidence.

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  • If an alternative reading is credible, then that implies you don’t have enough evidence to believe in the original reading. In other words, you don’t have evidence or reason to believe it. If “stronger” evidence now results in the alternative reading being excluded, you now have evidence. This seems to be just going from no evidence to evidence which doesn’t contradict my post.
    – user62907
    Commented Apr 30, 2023 at 1:59
  • I was about to write a detailed and thoroughly erudite response, when Stevan V. Saban replied adequately in one sentence: "If you believe each piece of evidence reduces the uncertainty in the choice, then every piece of evidence has value and is not equivalent to no evidence." Commented Apr 30, 2023 at 19:01
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You are painting yourself into a corner by starting with the position that statements are either true or false. Many statements are matters of opinion and many are uncertain for want of the ability to confirm whether they are right or wrong. We are confronted by such statements daily, and making sensible judgements about them can be hugely important. Consider statements such as: the best way to lower inflation is x; the right treatment for your brain cancer is y; x murdered z; Marco Ocram would make a better president than Donald Trump; Conifold knows more about philosophy than I do. Ok, forget that last statement, which is clearly true, but the others are all statements of the sort that might be true or false and we have to make practical judgements about them if we are to decide what to do for the best.

Suppose you have brain cancer, and you go to your quack who says there are two optional treatments that might work- treatment A has cured 999 out of the 1000 patients who tried it, while treatment B has cured 1 out of the 1000 patients who have tried it. Your quack goes on to toss a coin, asks you to call it, hears you call 'heads', then announces that he'll give you treatment B. I assume that you will happily accept that, since you believe that there is no way of knowing whether either treatment will cure you, so you might as well just accept either of them at random.

If you disagree with my last sentence, consider other versions of the scenario, with different values in place of the 999 and the 1.

And to address your point about theories- theories are descriptions of a sort. You should not expect them to be absolutely right or wrong. Let me illustrate the point in the following way. Suppose I present you with an image of a face which is utterly blurred and ask whether it is an image of your face. You would not be able to tell. Now, suppose I gradually sharpen the focus over a period of several hours. Over that time you will reach a point at which you will have a good idea whether or not the face is yours, before you reach a point at which you are certain of it. The gradual sharpening of focus is a practical example of increasing the strength of the evidence about whether the face is yours. There are countless other ways in which we sift and weight evidence.

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  • I like your face example, but I think I might get what TM is getting at. Let's say the blurred face is Eric's, but it shares traits (pixels) with John's. From one point of view it might be said that that those shared pixels are only actual evidence of Eric's face. They can't be evidence of John's face, because the face is not John's. (Sorry if I'm misrepresenting TM here). So is it true we often use 'evidence' in ways which actually only mean something like 'apparent evidence'? Commented Apr 30, 2023 at 11:19
  • +1 Face metaphor
    – J D
    Commented Apr 30, 2023 at 14:39
  • Wow. Amazing example. Your examples are always brilliant. Thinking about that example though, I would argue your certainty in it being your face isn’t actually increasing gradually. At the beginning, you have no idea it’s your face. But even when it reaches the point where you start to think it might be yours but also might be others. you are STILL not sure that it is yours. And to me, not knowing at all and not being sure are equivalent: you do not have evidence yet that it is your face. Once you are certain that no other face is possible except yours, only then do you have evidence.
    – user62907
    Commented Apr 30, 2023 at 19:27
  • @Futilitarian I don’t think you’re misinterpreting. I believe we’re getting to the same root of the concept. It is not the case that at the beginning, there is a 70% chance it is Eric’s face and there is a 30% chance it is not. Rather, you either have enough evidence to conclude it is Eric’s or you don’t. I think any “in between” state is functionally the same as not knowing something at all. Assigning a “probability” to things seems to give you an illusion of knowledge that isn’t there
    – user62907
    Commented Apr 30, 2023 at 19:31
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Your Question Shows Black and White Thinking

"Hypotheses are either true or not." (emphasis mine)

This is not true. Hypotheses can be very complicated, and therefore, they are often viewed probabilistically instead of using black-and-white truth. Propositions themselves, while they can be seen as either true or false or not both according to the principle of bivalence, are much more likely in practice to be seen in the light of a non-bivalent logic.

"If statements are either true or false" (emphasis mine)

Again, in formal systems, such as those of mathematics, this might be true, but generally in the real world, statements in natural language are a more complex affair and may not revolve around the oversimplified classical Laws of Thought that are a hallmark of particular academic disciplines like mathematical logic.

The Example of Legal Standards

"In what sense is B better evidence than A?"

The concept of evidence is domain-specific. The fields of mathematics and sciences have their methods and evidence. In law, one way of assessing the strength of evidence is classifying them by legal standards of burden of proof. In the US, there are categories:

  • Some evidence
  • Reasonable indications
  • Reasonable suspicion
  • Reasonable to believe
  • Probable cause
  • Some credible evidence
  • Preponderance of the evidence
  • Clear and convincing evidence
  • Beyond reasonable doubt

So, if a judge reads a report that a lab says "X may have been at the crime scene", then this is "some evidence". If a detective testifies "X is likely have to committed a crime", that might be "some credible evidence". If the witness confesses, and produces a recording to the commission of the crime, this evidence, corroborated by other evidence, might meet the standard of "beyond reasonable doubt".

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  • A single hypothesis being probabilistically true seems incoherent. What does it mean to say that God has a 20% chance of existing? It is not only incoherent but also unfalsifiable.
    – user62907
    Commented Apr 30, 2023 at 2:04
  • @thinkingman No one would put a percentage to a claim like that , but lots of people would say that the existence of God is either very likely or very unlikely. Inductive reasoning doesn't have to result in numerical percentages! Commented Apr 30, 2023 at 2:23
  • How do you prove a statement such as “X is very likely” or “X is very unlikely”. How do you prove a statement such as “A is more likely than B”? I fail to see how you can. Especially since the very term likely or unlikely is subject to many different interpretations
    – user62907
    Commented Apr 30, 2023 at 2:37
  • @thinkingman winning the lottery is very unlikely. Not winning is very likely. What's the problem there? Commented Apr 30, 2023 at 9:15
  • @MarcoOcram Winning or not winning the lottery isn't really a hypothesis. It's an event. A dice rolling on a 6 is an event. A hypothesis is a theory that explains an event. The "probability" of a dice rolling on a 6 DUE to chance as opposed to it being rigged is undefined. The probability of an event may be defined but the probability of a theory seems to make no sense.
    – user62907
    Commented Apr 30, 2023 at 9:30
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On the face of it, B seems to be better evidence than A.

B is better. B = A + text message

you either have enough evidence to warrant a belief or you don’t. If you don’t, how can it make sense to even call the evidence you have weak? If it wasn’t enough for you to believe it, then isn’t it the equivalent as there being no evidence?

Why use vague words like "weak"? There is simply not enough evidence a make true false choice other than an educated guess. Consider tri-state logic instead. True:False:Requires more info. What is lacking in True False scenarios is the level of certainty behind each choice. If you believe each piece of evidence reduces the uncertainty in the choice, then every piece of evidence has value and is not equivalent to no evidence.

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