You guys seem to be talking about "logical proof",

Right, and mathematical proof, which is essentially the same thing.

and I understand where you are coming from; but this is by definition a science forum,

It's the 'General Philosophy' forum in the 'philosophy' hierarchy on Sciforums. This thread is making a critical point concerning imprecise, poorly-defined but nevertheless rhetorically aggressive usage of the word 'proof' in a number of threads in this and the neighboring 'religion' forum.

I mean be careful when to say “logical proof” (philosophical argument) or “scientific proof” (something that can be interpreted as a fact from a scientific standpoint). ‘Cause if the regular frequenters of SF see that you are stating arguments based on “logical proof” as scientific facts, it is going to rain on you, and I don't mean get-an-umbrella kind of rain, I mean start-building-an-ark-and-get-ready-for-the-action kind of rain...

I don't know what you meant to communicate there.

You do seem to be suggesting that there's something called "scientific proof" which is entirely different than "logical proof". Presumably this 'scientific proof' is both more convincing and more appropriate here on Sciforums, even when people are discussing religion in the philosophy fora.

Unfortunately, I don't know what this "scientific proof" actually is. And I'm pretty certain that nobody else around here does either, including you.

My experience as a university science major was that the ideal in science is that it conform to something reasonably close to the second definition in the first post:

More formally, a deductively valid argument starting from true premises, that yields the conclusion.

In physics, that deductive validity is often pretty obvious, since it ideally takes the form of logical derivation of mathematical formulae. That's what all that mathematics is doing on the pages of advanced physics testbooks, it's deriving results that might be useful in revealing relationships between variables or in calculating something.

In sciences like biology, it's usually more informal. But even if arguments are stated in ordinary language instead of formal mathematical symbolism, there's always an assumption that conclusions do logically flow from the evidence and possess some logical connection to observations.

Probably the most obvious way that 'proof' in science differs from the definition of 'proof' that I just quoted is that the premises in scientific arguments are rarely if ever known to be true with 100% certainty. Instead, scientific propositions typically have informal weights, ranging from highly corroborated and almost certainly true all the way down to speculative hypothetical guesses. But while the weights assigned to conclusions are going to vary depending on the weights assigned to premises, it's always expected that deductive connections will exist between premises and conclusion.

(This btw, is the kind of problem that's motivated the creation of fuzzy logic. This is logic that replaces two-valued (T or F) truth assignments with a continuous range of truth values from 0 to 1.)

In other words, what I'm arguing here is that "scientific proof" isn't something that's separate and disjoint from "logical proof". Instead, scientific proof is an ilustration of logical proof in action, when it's applied to discovering new and hitherto unknown things about the physical universe.

Perhaps part of the confusion about this subject is due to the fact that scientists, mathematicians and logicians typically use the word 'proof' to refer to the chain of deductive reasoning that ties premises together with the conclusions that are drawn from them. While out on the street among laymen, the word 'proof' is often used to refer to a single slam-dunk observation that somehow makes a particular conclusion inescapable.

'The new information was proof that George committed the crime.' Of course technically speaking, the new information isn't 'proof' at all, it's 'evidence'. Proof, the chain of deductive implications in other words, is what ties the new evidence together with the conclusion that George is probably guilty.