What is a "reasonable assumption", and what are the limitations of the concept?

In his earlier defense of his speculations, @Andrew_Loke made frequent use of the phrase “reasonable assumption”, and I think it is worth further inquiry as to what this phrase might mean, and what it’s conceptual and practical limitations might be.

(My background is in statistics, so I will couch my discussion in terms of statistical probability.)

A reasonable assumption, at first consideration, might be considered to be either (i) the assumption, out of a set of alternatives, that has the highest probability of being true, or (ii) an assumption that is more likely to be true than not.

The first definition runs into the issue that, if all the assumptions have a low probability, the “reasonable assumption” may be more likely to be false than to be true.

The second definition has the problem that, in many cases, a “reasonable assumption” may not exist.

Going beyond this, there is the question of how we assign probabilities. I would assert that this requires some knowledge of the factual context surrounding the assumption. I cannot know that the assumption that a given runner will win a race is “reasonable”, without some knowledge of the running abilities of that runner and their competitors.

Further, assumptions cannot be stacked without cost. If the probability of a single assumption is 95% (very “reasonable” by any reasonable definition), then the probability of ten such assumptions all being correct is only 36% (assuming, for simplicity, that the probabilities are independent). It is therefore very easy when stacking even reasonable assumptions to quickly get unreasonable speculation.

How does this relate to the “Five Hundred”?

The only substantive information we have on Paul’s ministry and the churches it founded is that which we can glean from Paul’s own Epistles, which contains only very sparse and fragmentary information on these churches’ dynamics. Acts, as well as being written decades later, tends to concentrate on uplifting heroics to the exclusion of sociologically useful information.

This is not, I would assert, sufficient factual context to confidently assign a probability to any given assumption about actions within the First Century church. I would therefore question whether any assumptions about this matter can meaningfully be described as “reasonable”.

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That is a good question. Isn’t reasonableness in the eye of the beholder?

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It seems to me this can be framed with prior probabilities, and then we can if new evidence moves the posterior probability. In the case of the Resurrection I don’t think there is any new evidence to be had (but I won’t argue the point). I suppose we could start with people unaware of the evidence and present it to them in a randomized trial?

I view “reasonable assumptions” as a literary device that takes the place of the conversational “don’t you agree with me?”. What the writer wants to do is start from premises that we all agree with, and then build from there. When used correctly, the reasonable assumptions should be something even critics of the author’s conclusions would agree to. In this case, the eye should belong to the skeptic.

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Nope. Not when the beholder is trying to convince someone else of the truth (or reasonableness) of a claim that everyone knows is disputable. IMO, if only to be generously respectful of the other person, the speaker (“the beholder”) is obligated to invite that other person to follow their reasoning, e.g. “would you agree with me that it is reasonable to assume X?”

In contexts such as the one @Tim seems to cite, “reasonable assumption” is misleading; this is at best an “assume for the sake of argument” situation, which is to me fundamentally different.

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I suppose I was not thinking a polemic context. Though this clearly is, so fair enough.

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I agree that ‘reasonable’ in casual human interaction is a judgment in “the eye of the beholder” but I don’t think the context here is polemics. Loke is trying to make a case, and that is apologetics, or just persuasion, not IMO polemics. My apologies if that is just a semantic quibble.

Consider how the scientists in our PS community would go about making an argument in favor of some particular evolutionary trajectory, speaking with laypeople or even with skeptics. We would be very careful with our assumptions, pointing them out as clearly as possible and attempting to convince the audience of the reasonableness of those assumptions. We would not, I hope, simply label something a “reasonable assumption” without doing the work to convince our audience of that judgment. We would never say “ah, well, reasonable is in the eye of the beholder.”

Just my opinion, now I’ll butt out and let others go deep on @Tim’s questions.

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How well does that work, when the data available to estimate prior probabilities (in this case on the social dynamics of the First Century church) is sparse almost to the point of non-existence? That’s something that always made me uncomfortable with a Bayesian framework – there is no differentiation or weighting based on how solid the prior probability is.

I know this was meant in jest, but it raises some interesting issues in my mind. Wouldn’t the outcome be liable to depend more on the rhetorical skill and ‘personability’ (i.e. their ability to make people want to agree with them) of the presenter and tendency of people to agree or disagree with arguments they don’t understand (I seem to remember reports of talks that Dembski has given to religious audiences that have left the audience befuddled but approving), than on the strength of the underlying argument?

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Pondering @swamidass’ post leads me to the conclusion that there is a further limitation that I had not previously thought of. “Reasonable” may be sufficiently ambiguous as to preclude clarity of definition.

I would therefore like to propose ‘soft’ (i.e. unreliable) and ‘firm’ (i.e. reliable) assumptions as an alternative. It would of course be a spectrum, rather than a binary choice.

A soft assumption would be an assumption that either has low probability (e.g. if there are a large number of rival assumptions, none of which are much firmer than the others), or if we simply lack sufficient hard contextual evidence to assess its probability with any firmness.

A firm assumption would be one for which we can make a firm probability assessment, and that assessment yields a reasonably high probability.

Further to a comment I made in my OP, but perhaps failed to emphasise sufficiently, even if you start off with a reasonably firm assumption, each additional assumption you add to it in a line of reasoning will necessarily soften the conclusion.

This is a well known phenomenon in statistics, where each incremental assumption you make (even very firm ones like taking the sample mean or variance as proxies for the population values) softens the model and renders it more difficult to get a significant result.

I am suggesting that, given our lack of hard information about the social dynamics of the Early Church, any assumptions about their actions will be necessarily soft. This is particularly true given that it was a comparatively young institution which, as yet, had not had time to develop the formal structures, traditions and standard practices that would render its actions more predictable. Contrast with the Roman authorities at the time, or the Church a millennium hence.

I am also suggesting that, even if we grant, for the sake of argument, that the individual assumptions about the Early Church’s actions are firm, the question remains how many of these assumptions can be brought together in an argument before that argument inevitably softens significantly.

I am sure that there will still be a degree of divergence of opinion on this subject, but I hope that imposing some sort of structure on the issue will yield more common ground than viewing the assumptions in a vacuum.

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Isn’t that the same as saying that reasonableness is purely subjective?

Lacking any objective criteria, it would tend to attenuate the impact of such a “reasonable assumption” on reasoned discourse. It becomes merely ‘I believe’, rather than ‘any rational person would accept’.

It also becomes a tool more suited to gentle persuasion, rather than high-handed bludgeoning of a skeptical audience.

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Well, regardless, it shouldn’t be used for high handed bludgeoning…is that what this is about?

If by “this” you mean this thread, then no, only very peripherally. That comment was, as it was presented, my initial thoughts evoked by your post. It was actually posted two hours (and a long walk) before the other post. Moderation posted them out of order.

My OP was something I would’ve posted last year, but the thread was abruptly closed before I could do so. Then, as now, it was an attempt to take a step back from the argument over individual assumptions, and look at the robustness of the assumption-forming process.

Take it as you will.

Addendum: yours was another of those brief, cryptic posts that leave me wondering if I’ve discerned your meaning.

That being so, I’ll expand upon my point, in case it is relevant. My thinking is that if you have an objectively-valid assumption, you can, to some extent, get away with a more blunt presentation of it (not however claiming that this is an optimal strategy). If it is subjectively-valid assumption, there is a greater need to persuade your listener to see it through your eyes. Blunt presentation is more likely to elicit blunt refusal to see things from your viewpoint.

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I know you didn’t mean me. I’m just saying that even if “reasonable” is objective and empirically/logically determinable, it shouldn’t be deployed as a weapon. I’m sorry about the times that has been done to you, and appreciate you clarifying it wasn’t directed at me.

How does this discourse avoid devolution into that interminable debate about objective vs. subjective?

Voting with one’s feet is a good way. I don’t remember such debates being either particularly enlightening or particularly interesting – so will happily leave them to those with a more positive opinion of them.