Defining a hypothesisJune 1, 2009 — Deacon Duncan
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.
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.