lemas = lemmas or lemmata [http://dictionary.reference.com/search?q=lemma]

A couple of the two most relevant definitions given at that link:

1. a subsidiary proposition introduced in proving some other proposition; a helping theorem. [Dictionary.com Unabridged]

1. A subsidiary proposition assumed to be valid and used to demonstrate a principal proposition. [The American Heritage® Dictionary of the English Language, Fourth Edition]

So, you see, assumptions can form lemmata.

“I have no idea why criticisms of torture are so poor. “

With regard to torture: I believe you will find that every argument possible for or anti torture will have as its basis or bases unprovable lemmata, or biases. Whether utilitarian, moralistic, etc., the argument will come from a prevailing world view formed in the miasma of other assumptions about reality.

One might as easily say that the Universe itself has reached its life-sustaining state through a series of extremely destructive occurrences; why then must humans turn from destruction, torture, and so many other Universal properties?

Given the many assumption-based lemmata, there is really no wonder that we are in a constant state of di-lemma.

—A comment I left recently at tdaxp.


In truth, most lemmas acceptable by scientists and philosophers are assumed to be true by all parties in any debate:  This means, contrary to the comment I left at tdaxp, those lemmas are used within an argument which will be agreeable to the persons involved in the debate or proof-seeking, simply because the use of any other lemmas — that is, controversial lemmas — defeats the point of “winning” the proof or showing the proof to your interlocutor.

However, from a skeptical p.o.v., one might say that such agreement over bases of proofs is merely that:  agreement.  The agreement is not proof itself, but merely the utilization of facts which all may agree are facts; which is to say, it is the use of common assumptions.

We can show this to be true of any argument in which undisputed lemmas are used by following a skeptical inquiry — the most common skeptical inquiry.  We can use infinite regress, or ask Why? or Is that so? of any lemma offered.

Infinite regress has some utility for breaking up ossified belief systems, mostly for showing any dogmatist that he has not fully contemplated his own beliefs.  But infinite regress cannot show us the answer to any given question; e.g., whether torture can be justified or delegitimized.  What it may show us is this:  Where does an individual dogmatist draw the line on reason?  How does he stand, what are his fundamental biases, his superstitions?  Etc.  Infinite regress is fundamentally (it would seem) a method for defining humans; once defined, we know better how to negotiate with them or influence them.  This utility has the advantage of directing us in our effort to argue a case contra another’s arguments; that is, the general assumptive aspect of lemmas can be used in any proof-making, tailored to convince our opponent in a debate, since, as implied above, many other arguments would be blasted as “bromides” or worse by our interlocutor if our chosen lemmas just happen to have an assumptive base our interlocutor does not share.

As for myself, I would not use torture for any of a thousand offered reasons justifying its utility in a thousand different circumstances; however, I can imagine situations in which I would.  Having imagined those, I have a better tool for avoiding those eventualities. Some others in the world might work opposite, or would seek to create those eventualities. For whatever reasons.