Does "most" include "all" ?

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Re: Does "most" include "all" ?

Postby michaelt » Sun Jan 19, 2014 7:25 pm

This question asks what can be inferred, not what is possible.
The question asks what can be inferred from what is possible and what isn't: for "all" artists to be not insightful.

You don't know that 100 is possible given most...
Why is that? Could you please elaborate why we do not know that 100 is a possibility when given just "most"?

Everything above 51 is contingent upon information you don't have with just most.
Everything, including 100. Yet after the additional information is given, 100 gets excluded.

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Re: Does "most" include "all" ?

Postby Jeffort » Mon Jan 20, 2014 12:05 am

It sounds like you are now understanding it properly michealt. I think in the last few posts the two of you are pretty much saying the same things and just getting a little tripped up by the different ways each of you are describing the same concepts.

Your description of how you interpret consistent is correct. The word most only guarantees 51 and that's all you can treat as for sure 100% true when making inferences from application of the premise. Most being consistent with it actually being all/100% is just a hypothetical possibility a most premise by itself doesn't automatically exclude/prohibit from being possible, meaning you cannot infer that some are not from a most premise. That's really the entire purpose for understanding that most allows for all, so that you don't falsely conclude most also establishes that some are not, since by itself it doesn't. That's the main point of talking about consistent with vs what each quantifier guarantees is true, to avoid making false inferences from quantifiers.

You can only use the guaranteed minimums/maximums a quantifier establishes for making valid inferences from those premises and cannot validly assume any of the possibilities/things consistent with the premise but not guaranteed by it are for sure true and then use that as evidence to support an inference. I think you are seeing it that way and that in the question the additional *rarely* premise is what establishes not all being true in this situation, not the most premise. If you are seeing it this way you've got it right for the most part.

Simplified version: You can only base inferences off the bare minimum/maximum a quantifier explicitly guarantees, not off quantities that are consistent with the quantifier but not proven/guaranteed to be true from the premise by itself. Things consistent with/possible under a premise are just things it doesn't for sure prove are true or false, they are just things the premise doesn't establish/determine are one way or another, leaving them up in the air in the land of things we don't have enough evidence to nail down and say for sure either way, thus no inferences can be based on assumptions about what is actually true/false in this grey area of possibilities because they are left logically uncertain by the open ended aspect of the quantifier with what is possible beyond the bare minimum it guarantees.

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