What is the definition of validity under possible world semantics?

Why does inconsistency entail validity?

We use logic to structure the system of mathematics. Lord Russell was described as bewildered upon learning that original premises must be accepted on some human's "say so". Since human knowledge is so fragile (it cannot have all conclusions backed up by premises), is the final justification "It works, based on axioms accepted on faith"? In short, where do you recommend that "evidence for evidence" might be found, if such exists in the anterior phases of syllogistic construction. Somewhere I have read (if I can rely upon what little recall I still have) Lord Russell, even to the end, did not desire to rely on inductive reasoning to advance knowledge, preferring to rely on deductive reasoning. Thanks. Your individual and panel contributions make our world better.

It seems that certain ethical theories are often criticized for contradiction ordinary ethical thinking, or common moral intuitions. Why should this matter, though? Is there a good reason to believe that ordinary common moral intuitions are infallible, and that more refined ethical systems ought not contradict such intuitions?

What is the name of the logical fallacy that describes an argument in which facts are selectively chosen to support a predetermined conclusion? Is it "begging the question"? If not, what is it? (And, no, this isn't an exam question or paper topic; I'm a professional writer trying to remember something he was taught 30 years ago in a writing class.)

Why is C.I. Lewis' strict implication not taken seriously in this day and age? Clarence Irving Lewis was known for criticizing material implication and for instead proposing strict implication. Why is he, his criticisms, and his proposed strict implication not taken seriously today? Many contemporary logic, philosophy, and mathematical texts refer to material implication rather than strict implication.

Can tautology be defined as "unnecessary repetition of information"? In other words, does tautology have the same sense as repetition? Thanks.

Do we have a duty to strive towards a life without contradiction? Can a person, for example, both eat meat and hold the belief that animals should not be willfully killed for private gain?

When someone says "That seems(or does not seem) logical" it is not always easy to know how they define "logical". Is it meaningful at all? I guess the question relates to the use of something that seems to be a looser term than e.g. "deductively valid" or the like, which refers to a particular system of inference and specific rules for determining truth or falsehood of propositions. Do you have any idea as to what the term commonly refers to?

It has long seemed to me that philosophers do not seem concerned with illusion, i.e., the appearance of reasoning that SEEMS valid but is at least questionable if not illusory. The Greek philosophers that I read in school seemed particularly questionable. My impression was that much of their argumentation was illusory, i.e., based on claims that are unidentified assumptions. An example of illusion is the argument that since everything has a cause, there must be a FIRST cause. This SOUNDS sound but of course is not. Causality is not simple and is not a matter of logic. Causality has to do with nature and we know very little about nature. For all we know the universe has been going on forever, i.e., had no beginning. Moreover, if EVERYTHING has a cause, then there cannot be a FIRST cause which is exempt from having a cause. Are there philosophers who are concerned with this problem of illusory or unfounded philosophical reasoning? I would love to read their ideas. Please note that I'm not calling...