Defining a hypothesis

R. C. Moore has an interesting comment that is at risk of being lost in the flood of recent comments, and I don’t want to let it just slip by, so I’m promoting it up here where I can answer it more easily.

RC is making the claim that my Gospel Hypothesis is not valid because it cannot be constructed via propositional logic.

DD said:


There’s no requirement that hypotheses must be formed by propositional logic. We just need to be able to predict what consequences would result from the situation described.

Sorry, I disagree, A testable hypothesis (which is the hypothesis at hand) must be valid in terms of propositional logic. You stated it yourself,

Not all statements make valid hypotheses, however. “Loki works in mysterious ways” is a statement that really covers just about any possible outcome. We can’t really look at, say, today’s weather report and tell whether it supports or refutes the statement that Loki works in mysterious ways. Likewise, inherently self-contradictory statements are untestable. If we say “Childless unmarried spouses have healthier children,” we’re not going to be able to describe an observable set of consequences against which we could compare the evidence.

The reason these hypotheses are invalid is because they cannot be correctly described using propositional logic.

You gave good examples, you just forgot some other failures, such as tautology and non sequeter.

Tautology and non-sequitur, however, are fallacies that describe incorrect conclusions, not incorrect premises. I think what’s happening here is that RC is getting a little ahead of the game and is trying to draw conclusions before we’re done defining the premises.


Reality itself is not formed by propositional logic, so it makes no sense to insist that we can only make hypotheses that are restricted to propositional logic alone.

I agree absolutely that reality is not governed by propositional logic, or any logic at all for that matter.

But hypotheses are not reality, they are a tool used by humans to reach truths about reality. Reality is not governed by the set of natural numbers either, but I cannot throw out their definition when using them as a tool.

Well, I phrased that badly. What I meant was that there is no sense in requiring the latter portions of a hypothesis to be logically derived from earlier portions. Or to put it a different way, it makes no sense to take the rules that apply to the complete process of drawing conclusions based on premises, and try to inject them into the preliminary process of defining what your premises are so that you can draw conclusions from them. That’s like insisting that all new aircraft have to pass a test flight before you’re allowed to attach the wings. If you haven’t added the wings yet, it’s not time for the test flight.

I think the reason you are missing my point is that in the rush to reach your conclusion, you are combining several hypothesis that are not independent, and thereby leaping over intrinsic problems. You did it again with your example in your last comment:

For example, if I propose a hypothesis that President Obama is a hologram and not a real person, on the basis of a weird dream and a strong subjective feeling, my basis for proposing the hypothesis is purely bogus. Yet the hypothesis is testable nonetheless: if he’s a mere hologram, you can walk through him and even see through him. It has testable consequences, despite its spurious origin, and therefore can still be a valid hypothesis.

Is the hypothesis that Obama is a hologram, or Obama not a real person? If I prove he is not a hologram, have a said anything about whether he is a real person?

Here I think is the point at which RC and I part ways in our thinking. To my way of looking at it, I am combining qualifiers in order to construct a more-specified hypothesis, i.e. one that is distinguishable from a broader group of similar hypotheses. I’m not just testing whether Obama is a hologram, and I’m not just testing whether he’s a real person, I’m investigating a more specific condition: whether some unknown agency is using holograms to simulate a non-existent president. By combining qualifiers, I can create a hypothesis that resembles one or more broader categories of hypotheses, while being distinguishable, in each case, from the broader category.

RC seems to be saying that there is some rule against using compound qualifiers to define a more-specific hypothesis, and/or some rule that says a hypothesis can only contain a single specifier and that additional specifiers are required to be derived from the first via valid propositional logic.

I don’t think there is any such restriction on how we define our hypotheses. I believe that it is perfectly legitimate to declare complex, testable hypotheses like, for example the hypothesis that Newtonian physics correctly describes phenomena above the atomic level and at speeds substantially less than the speed of light, while Einsteinian physics correctly describes phenomena below the subatomic level and at speeds approaching the speed of light, with more complex interactions of both physics near the boundaries between the two pairs of domains.

That’s a pretty complicated hypothesis, combining a number of compound specifiers that cannot be obtained by applying propositional logic to the other specifiers within the hypothesis. I believe it would be an even better example than the Gospel Hypothesis of something that ought to fail RC’s standards for a valid hypothesis. Yet if it cannot be a valid hypothesis, then it can never be tested, and thus can never describe a valid scientific conclusion. This would be rather a shock to a large number of physicists.

Here is your Gospel Hypothesis, broken down:

1. There exists an all-wise, all-knowing, all-powerful and all-loving Creator.

This is not a hypothesis, this is a definition: There can be only one Creator meeting these criteria, no lesser being qualifies.

A hypothesis is a definition. It defines the condition(s) that we’re going to compare against the real-world evidence in order to draw conclusions about whether the hypothetical description of the condition(s) is true. And notice, this is a compound definition: you cannot use propositional logic to derive the part that says “He is all-wise” from the part that says “He is all-knowing”, or “He is a Creator” from “He is all-loving”. Why am I allowed to combine these specifiers, which are not derived from one another, but not allowed to combine other specifiers on the grounds that they’re not mutually logically derived?

2. [He] wants a genuine, personal, eternal relationship with each of us.

This is a hypothesis, not derived form the basis (1). Since it is a non sequeter, it is one of an almost infinite number of hypotheses one could make not pertaining to the attributes of all-powerful, etc.

This looks to me like sequential processing. The Gospel Hypothesis is 1 (one) hypothesis, not a series of hypotheses derived from one another. In fact, you don’t derive hypotheses from hypotheses, you derive conclusions from hypotheses. Those conclusions may suggest further hypotheses, but each new hypothesis is independent from any hypotheses which may have preceded it. This is necessarily the case, because we need to be unbiased when considering whether or not the new hypothesis is true. Otherwise we run the risk of attaching the success of the earlier conclusion to the new, untested hypothesis, and thus reaching an unjustified conclusion in favor of the new hypothesis.

Your criteria for the choice of this hypothesis, is your next hypothesis:
3. He is willing and able to become one of us, dwell among us for a time, and then die for us so that we can be together forever

You see the problem already. You have biased the hypothetical structure towards the outcome you want.

No, what I’ve done is to specify the precise condition I wish to test. This is a perfectly valid approach, because the more specific our hypothesis, the more precisely we can measure how consistent the real-world facts are with that specific hypothesis. What’s more, this is a highly commendable approach, because it allows us to test multiple similar hypotheses that differ only in certain specific details, giving us the ability to extract much more detailed and fine-grained information from the available evidence.

The key point here is that specifying the hypothesis in no way constrains the evidence itself. It’s futile to try and bias a hypothesis, because when you get to the part where you compare the hypothesis to the evidence, the evidence is either going to be consistent with the consequences of the hypothesis (in which case we’re justified in concluding that the hypothesis is true) or it’s going to be inconsistent with the hypothesis (in which case we’re justified in rejecting it). That’s why the scientific method has been so successful in allowing biased and imperfect humans to discover genuine real-world truth.

Let’s suppose, for example, that we get all racist and say, “All members of <insert ethnic group here> have smaller brains than members of <insert our own ethnic group here>.” If you wanted a biased hypothesis, it would have to look something like that. But what happens when you take that hypothesis and test it by measuring the brain size of both ethnic groups? The expected consequence that follows from the biased hypothesis is that there will be a significant correlation between ethnicity and measured brain size. If the measurements are consistent with this hypothesis, then it’s true, and if not, then it’s false. The bias of the hypothesis itself is irrelevant.

If you think about it, every hypothesis is “biased,” since it asserts the truth of a proposition that might be either true or false. The point is that we don’t just accept that bias. We test it, and decide its truth or falsehood based on whether or not the condition described is consistent with what we find in the real world.

The basis for hypothesis (3) is unproven hypothesis (2), not the basis (1). Convenient, but as someone who has spent quite a few hours trying for program computers in ML (a propositional logic programming language), you can expect only halts.

As I’ve pointed out before, though, I don’t have 3 separate hypotheses derived from one another. I have one hypothesis that is highly specified, through the application of compound qualifiers. The rules RC says I’m breaking are rules that apply to the process of drawing conclusions based on the premises, but you can’t start that process until your premises have been defined, and all I’m doing in stating the Gospel Hypothesis is defining what the premise (singular) is. I want to test for a highly specific condition, and therefore my hypothesis requires a corresponding specificity.

So bad logic, and yet I agree you have reached the correct conclusion. This is I think, because we have lots of empirical data that support your description of the Christian dilemma, and a real dilemma it is. The entire field of apologetics exists not because of some philosophical argument, but because the data shows a real problem for the Christian philosophy.

At least we both agree on the main thing. :) My apologies to RC for picking apart his comment, but I felt like I needed to the reasons for my technique.

 
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Posted in Comment Rescue. 17 Comments »

17 Responses to “Defining a hypothesis”

  1. R. C. Moore Says:

    DD–

    **I often get ahead of myself, but ironically, I that is my objection to your discussion**

    This is a very verbose rebuttal, too verbose for a reply. Arguments must be built from the ground up, but you are attacking from so many problematic angles, a cogent reply is impossible. So let me try to find the first premise in your argument, and go against that.

    You said:


    A hypothesis is a definition. It defines the condition(s) that we’re going to compare against the real-world evidence in order to draw conclusions about whether the hypothetical description of the condition(s) is true. And notice, this is a compound definition: you cannot use propositional logic to derive the part that says “He is all-wise” from the part that says “He is all-knowing”, or “He is a Creator” from “He is all-loving”. Why am I allowed to combine these specifiers, which are not derived from one another, but not allowed to combine other specifiers on the grounds that they’re not mutually logically derived?

    First off, read what you wrote. You reject my position that a definitions and hypotheses are not the same, insisting they are, and then proceed to complain about the combining of specifiers as not being allowed in an hypothesis. This is a bait and switch argument, and you should know better.

    Definitions (which are really axioms) provide the basis for a logical argument. These definitions can be very formally derived, or they can be definitions accepted for the moment in order to proceed with an argument, as we are doing here.

    Definitions can be meta-defined from other definitions. We have no requirement that they be true in reality (because we are engaging in philosophy here, not science), only that they not be contradictory, and there is no requirement that they be complete.

    Because this is a game we are playing. No objective truth is about to be revealed. We are just hoping for a self-consistent “proof”.

    Once the definitions are in place, we can make a “query” using the “facts” we have defined. This is the hypothesis. We process the facts to see if it violates any of the propositions of the hypothesis. We are now dealing with variables.

    A question is not a definition (if you object we are “defining” the hypothesis, you are really just objecting to the problems we run into using language, where words shift meaning mid-stride).

    Formal prepositional logic would show the problem immediately, but I do not know how to demonstrate that here (bad argument I know), maybe others can give it shot to show whether I am right or wrong.

    The next level of where your argument fails is when one tries to use Bayesian inference to begin testing your hypothesis, but before I go there, I think it is important to understand the difference between facts and queries.

    The reason I think this is important, and not just a argument over style, is that by ignoring the distinction between facts and queries, you are ignoring conflicting facts, which defeat (or at a minimum require a re-evaluation of) your Myth Hypothesis.

  2. R. C. Moore Says:

    Looking back, one more thing I did not stress:


    And notice, this is a compound definition: you cannot use propositional logic to derive the part that says “He is all-wise” from the part that says “He is all-knowing”, or “He is a Creator” from “He is all-loving”. Why am I allowed to combine these specifiers, which are not derived from one another, but not allowed to combine other specifiers on the grounds that they’re not mutually logically derived?

    There can logically be only one entity with the “all” specifiers, we call this entity Creator. It is a label substitution. If is a compound definition, as you call it, because we are trying to meet a condition of minimum completeness to justify the label substitution.

    Now, try to apply this label to the further definitions given the GH. These further definitions are not necessary for the original label. They are definitions of convenience, made in order to advance the argument. This is allowed by logic, but we must be very,very clear — we have created a new label. The two labels cannot be substituted freely, (in formal terms, the we have “bound” the labels to variables, and substitutions (meaning how we now use them in the argument, and what is implied are now subject to restrictions).

    I think what is implied is that you have taken the label “Creator” and created the label “Christian God” with the GH. This creates problems in taking the logic forward, because the GH is inductive.

    Interestingly, it does not create problems for the Myth Hypothesis, correctly stated, as far as I can see, because it is deductive.

    Hm.

  3. cl Says:

    DD,

    I’m investigating a more specific condition: whether some unknown agency is using holograms to simulate a non-existent president.

    Yet in our discussion on miracles, you vehemently denied that causal connections could be verified sans post hoc reasoning. So what’s the use of investigating “whether some unknown agency is using holograms to simulate a non-existent president?”

    I believe that it is perfectly legitimate to declare complex, testable hypotheses like, for example the hypothesis that Newtonian physics correctly describes phenomena above the atomic level and at speeds substantially less than the speed of light, while Einsteinian physics correctly describes phenomena below the subatomic level and at speeds approaching the speed of light, with more complex interactions of both physics near the boundaries between the two pairs of domains.

    I agree, and that’s why I dispute your GH. To make an analogy, Newtonian physics doesn’t describe phenomena above the atomic level and at speeds approaching the speed of light, does it?

    ..the more specific our hypothesis, the more precisely we can measure how consistent the real-world facts are with that specific hypothesis.

    I agree, and since your so-called Gospel Hypothesis is pathetically unspecific as you’ve already conceded, were Jayman, Facilis and myself really that out-of-line for demanding that your predictions accurately represent what the Gospel specifically states?

    R.C.,

    I think what is implied is that [DD has] taken the label “Creator” and created the label “Christian God” with the GH.

    ..all while denying that the GH is Christianity!

  4. Hunt Says:

    My pedestrian analysis is this: The controversy involved with the hypothesis-inductive process of a scientific investigation arises because hypotheses must necessarily be formulated from existing knowledge. You can simply grab a hypothesis out of the air, and many have done it. They’re usually called geniuses when they get it right, but further thought on the matter brings the supposition that blind luck was actually a subconsciously ingrained knowledge-base and that the hypothesis was not premonition, but based as are others: on existing knowledge. For people who oppose your conclusion, this brings the natural objection: You formulated your hypothesis to fit the observed data. Well, yes, of course we did! This seems obvious, but it forms the entire basis of the whole “just-so stories” objection to evolutionary theory, to name just one. The true utility of a hypothesis is whether it can predict new, as yet unknown, knowledge, which can be confirmed. If, in formulating your hypothesis, you use all available data and then derive something that simple reconfirms the data you used to form your hypothesis, you have not created a useful hypothesis.

  5. Hunt Says:

    And I didn’t mean that as a detraction to the GH, which I think is pretty well-formed. The foundational data to base it on is the “Gospel” in question. Setting aside our reservations about forming a hypothesis based on a revealed religious text (this would not, then, be a scientific hypothesis) cl’s objection is no doubt related to the correct use of fitting the foundational data. The huge problem here, and the thing that probably renders the whole enterprise moot, is that cl is currently engaged in constructing exactly the kind of “just-so” hypothesis to fit the data that creationists always jeer evolutionists about. Unless the new hypothesis can render some kind of new information about our world or God, it’s useless.

  6. cl Says:

    Hunt,

    This is tangential, but your following paragraph explains some of Derren Brown’s techniques perfectly:

    My pedestrian analysis is this: The controversy involved with the hypothesis-inductive process of a scientific investigation arises because hypotheses must necessarily be formulated from existing knowledge. You can simply grab a hypothesis out of the air, and many have done it. They’re usually called geniuses when they get it right, but further thought on the matter brings the supposition that blind luck was actually a subconsciously ingrained knowledge-base and that the hypothesis was not premonition, but based as are others: on existing knowledge.

    Back to the discussion, you said,

    The true utility of a hypothesis is whether it can predict new, as yet unknown, knowledge, which can be confirmed. If, in formulating your hypothesis, you use all available data and then derive something that simple reconfirms the data you used to form your hypothesis, you have not created a useful hypothesis.

    I appreciate that concern, and I’ll certainly factor this into my alternative hypothesis.

    The huge problem here, and the thing that probably renders the whole enterprise moot, is that cl is currently engaged in constructing exactly the kind of “just-so” hypothesis to fit the data that creationists always jeer evolutionists about.

    Can you elaborate on what you mean here? Do you say this because I purport to offer an hypothesis that accurately represents what the Bible claims? Do you suppose, then, that because the alternative hypothesis I offer is based off the Bible that such somehow renders it invalid? If so, why? Because the way I see it – as we must take paleontological evidence at face value – we must take the Bible at face value. It’s claims are either true or false. Once we’ve reached a position where we can agree that we’ve summarized the Bible’s positions at least fairly accurately – and admittedly such might be a difficult task – then we can certainly postulate the real-world evidence one might expect to see were the Bible in fact correct.

    Unless the new hypothesis can render some kind of new information about our world or God, it’s useless.

    So on what grounds, then, do you suppose DD’s GH is well-formed? It offers us zero new information about our world or God, and all the information it does offer us about God is lifted from the Bible – so mustn’t your concern that my alternative hypothesis is tainted because it’s taken from the Bible also apply to DD’s GH? The only difference is that DD flatly denies his GH is Christianity, whereas I’m attempting to offer an accurate summation of Christianity we can use in this discussion.

    Lastly, DD still has not explained how his GH is not Christianity, yet it consists of entirely Christian pre-conceptions about God. I’ll be patient.

  7. Arthur Says:

    RC,

    I’m still laboring—under the limitations Alethea has seen fit to place on my brain—to understand what the problem is.

    Deacon posits a simplified Christianesque God, saying (I think):

    1) He exists;

    2) He wants to be with us; and

    3) He’s all-wise, all-knowing, all-loving and all-powerful.

    He calls this, for better or for worse, the Gospel Hypothesis (I recognize that there are issues with the use of Christian vocabulary).

    For the Myth Hypothesis, he says:

    1) people made God up.

    As far as I can tell, this all basically boils down to the GH defining God as being here, since He is the primary source of information about Himself (the notorious #2). Otherwise, other people are people’s primary source of information about Him—the defining attribute of the MH.

    I apologize in advance for just plain not getting it, but what grievous error in reasoning has been committed in this formulation? It’s a false dichotomy? It’s “knowledge without work”? Or is it that the whole project just isn’t useful? Or is there some other category of shortcoming that I’m missing?

    The formulation itself seems pretty straightforward (or did I commit a breach of reasoning or usefulness of my own in the paraphrase?); Deacon’s provided examples of predictions one might reasonably make for either case; and there’s plenty of room for refinement, or expansion, or the addition of new or improved hypotheses, as future discussion might require.

    And—complaints about imperfect consonance with the New Testament aside—the GH seems to me to sum up a perhaps rudimentary, perhaps ignorant and childish, but certainly familiar, conception of God. With such an abstruse and emotionally fraught subject, doesn’t it make some sort of sense to start with broad strokes and bright colors?

    Are your objections of a type that could be dumbed-down? For a hypothetical audience of untutored laypeople?

  8. John Morales Says:

    Arthur, cf. http://www.edge.org/3rd_culture/dawkins06/dawkins06_index.html – “A universe with a God would look quite different from a universe without one.”

  9. John Morales Says:

    My error – malformed link. Should be Richard Dawkins.

  10. John Morales Says:

    Also a quick note on terminology; as I see it, both the MH and the GH are propositions, and the hypothesis, such as it is, is that the former matches our intersubjective reality (R) better than the latter.

    More visually, the hypothesis is: |MH-R| < |GH-R|

  11. Hunt Says:

    cl,

    Once we’ve reached a position where we can agree that we’ve summarized the Bible’s positions at least fairly accurately – and admittedly such might be a difficult task – then we can certainly postulate the real-world evidence one might expect to see were the Bible in fact correct.

    I agree completely, but I still don’t see the utility of trying to construct a hypothesis that simply fits all data points and can do no better. For instance, if yours is a God who listens to all pray, but coyly decides to opt out of every conceivable prayer study, or will disappear from view upon any close scrutiny, you’re not asserting a hypothesis, you’re telling a story. On the other hand, if you can come up with something that predicts future discovered facts, then I’m all ears.

    So on what grounds, then, do you suppose DD’s GH is well-formed? It offers us zero new information about our world or God, and all the information it does offer us about God is lifted from the Bible – so mustn’t your concern that my alternative hypothesis is tainted because it’s taken from the Bible also apply to DD’s GH? The only difference is that DD flatly denies his GH is Christianity, whereas I’m attempting to offer an accurate summation of Christianity we can use in this discussion.

    I can’t, of course, put words in anyone’s mouth, so all misinterpretation is my fault, but IMO the GH is an attempt to abstract the gist of Christianity without actually positing Christianity. Abstractions of entities are not the entities themselves, just as abstract classes, like “mammals,” can’t be equated with more specific subclasses, like “cats.” All cats are mammals, however, not all mammals are cats. Thus, oddly enough, Christianity can fit the GH, the generalized abstraction, without the GH fitting Christianity. And if you think that’s a clever dodge, you would be right. J

    But my real point is that useful hypotheses don’t simply fit data, if they do then they really are no more than description. Let’s take the MH. Whatever you think of it, this is a great hypothesis, since it predicts loads of future experimental results — no prayer study will ever be statistically significant, miracles will not happen, God will not intercede in human affairs, and so on. Its predictive potential is limitless. And it can easily be falsified. By now atheists have come to consider the MH as confirmed theory if not law. Myth Theory states that the world will appear as if there is no God, therefore there is every reason to believe there is no God. Even so, it can be refuted, of course. If Intelligent Design came up with some extraordinary results, or someone presented an irrefutable Anthropic Principle argument, then MT might be overthrown.

  12. Arthur Says:

    cl,

    …we must take the Bible at face value. It’s claims are either true or false.

    Does this obligation exist for other books which make extra-naturalistic claims?

  13. Arthur Says:

    John Morales,

    As it happens, I’m working my way through The Ancestor’s Tale as we speak:

    There is still room for human judgement, but it is judgement about what will eventually turn out to be the undisputable truth.

    He’s talking about the tree of life, but I like it for all sorts of stuff.

  14. R. C. Moore Says:

    cl said —

    …we must take the Bible at face value. It’s claims are either true or false.

    Taking something at face value usually means that no investigation is possible.

    That definitely does not apply to the Bible. As and example, many of the claims of Exodus have been thoroughly investigated and found to be false.

  15. John Morales Says:

    Hm, I wonder whether history better matches the MH or the GH? :)

  16. Deacon Duncan Says:

    RC —

    I’m sorry, but I just can’t make out what rules you are using to decide when my hypothesis is philosophy, when it is an exercise in propositional logic, and when it is what I think it is: a hypothesis. I did try to give it my best shot, and I thought I was understanding you somewhat, but apparently that’s not so. Maybe you could explain to me what the general rules are first, as you understand them, and then we can talk about how to apply those rules to construct a hypothesis as specific as the one I wish to consider?

  17. R.C Moore Says:


    Maybe you could explain to me what the general rules are first, as you understand them, and then we can talk about how to apply those rules to construct a hypothesis as specific as the one I wish to consider?

    The primary rule is that an hypothesis must be a question. Can you rephrase the GH as a question?

    For instance the MH:

    Can myth explain the supernatural narrative of the Gospels? (I assume we have little interest here in challenging the historical narrative, other than its application in supporting the supernatural narrative)

    Or perhaps: Can the Gospels be distinguished from other narratives that are taken to by myths?

    I will give the GH a shot:
    ….

    Sorry, for the life of me, I can’t. It is a description of a belief system, arbitrary in it’s construction.