Why do people deny evolution?

you should spend time with the various words like "axiom" nd "theory". They have precise meanings different than yours.

Youre dancing very close to "its only a theory"

There is a fundamental difference between fact and theory

You use them interchangeably

Natural selection is one of the basic axioms of Neo-darwinistic theory. In science (or any other area of theorizing) you can never use deductions drawn from your axioms to prove the axioms themselves. That would merely be "circular" reasoning. An axiom is, and must remain, an unquestioned (and unproven) "starting point" in any theory.

Then you should spend time with the various words like "axiom" nd "theory". They have precise meanings different than yours.

An axiom or postulate is a premise or starting point of reasoning.... The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'[2][3] As used in modern logic, an axiom is simply a premise or starting point for reasoning.[4] Axioms define and delimit the realm of analysis; the truth of an axiom is taken for granted within the particular domain of analysis, and serves as a starting point for deducing and inferring other truths.

A lesson learned by mathematics in the last 150 years is that it is useful to strip the meaning away from the mathematical assertions (axioms, postulates, propositions, theorems) and definitions. One must concede the need for primitive notions, or undefined terms or concepts, in any study. Such abstraction or formalization makes mathematical knowledge more general, capable of multiple different meanings, and therefore useful in multiple contexts. Alessandro Padoa, Mario Pieri, and Giuseppe Peano were pioneers in this movement.

Axioms play a key role not only in mathematics, but also in other sciences, notably in theoretical physics. In particular, the monumental work of Isaac Newton is essentially based on Euclid's axioms, augmented by a postulate on the non-relation of spacetime and the physics taking place in it at any moment.

In 1905, Newton's axioms were replaced by those of Albert Einstein's special relativity, and later on by those of general relativity.

"As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy....Among the ancient Greek philosophers an axiom was a claim which could be seen to be true without any need for proof....The root meaning of the word 'postulate' is to 'demand'; for instance, Euclid demands of us that we agree that some things can be done, e.g. any two points can be joined by a straight line, etc

your definition of axiom leaves out the most salient thing, AXIOMS are UNIVESRAL TRUTHS THAT ARE SELF_EVIDENT

Axioms define and delimit the realm of analysis; the truth of an axiom is taken for granted within the particular domain of analysis, and serves as a starting point for deducing and inferring other truths.

I'm going to assume that you composed this response before reading the excerpt I cited in the post immediately preceding yours.

What difference does it make anyway, as far as what we're talking about?

aying that any art of a thory is "axiomatic" is kind of back handed. ANY part of a thory needs to be evidenced or it gets discarded

If everyone decides to discard segments of Darwinism or neo Darwinism, just let em gather the evidence, post it to something like Nature or Science and let everyone have at it.

There are still hangers-on who attempt to somehow cram every new discovery into some form of random mutation and natural selection, but it's not convincing.

no, the article was a "point counterpoint" discussion (ll journl hve thee". NO real evidence was presented, evaluated , or lab data produced.

That's exactly what has been done, according the acknowledgment of all 15

One of a bunch of points is that, should a specific genomic transition occur and it occurs many times with (as plasticity defines) several different phenotypes erupt, and an environmental change ccyrs so that only on of the "hopeful monsters" survives, IS THAT NOT NATURAL SELECTION IN ACTION??

No genes to play with, just plenty of environmental evidence in which the phenotyic morphing appears to be "th result of a selection event".

All these means of gene transfer fail to explain how many thousands of endemicspecies morph without any genetic changes.

the team's findings suggest that hybridisation is very important to these birds' evolution. In particular, they saw that the rise and fall of pointed beaks in one species - once again, the medium ground finch - was driven by hybridisation with a different, pointed-beak species...."When you look at their results, you can see the trees are quite messy, in terms of the traditional species groupings."

This study provides one of the first genome-wide comparisons of genetic and epigenetic mutations among related species of organisms. There were relatively more epimutations than genetic CNV mutations among the five species of Darwin’s finches, which suggests that epimutations are a major component of genome variation during evolutionary change. There was also a statistically significant correlation between the number of epigenetic differences and phylogenetic distance between finches (figs. 1 and 3), indicating that the number of epigenetic changes continues to accumulate over long periods of evolutionary time (2–3 Myr). In contrast, there was no significant relationship between the number of genetic CNV changes and phylogenetic distance.

Epigenetic changes are broadly defined as “molecular processes around DNA that regulate genome activity independent of DNA sequence and are mitotically stable"...Environmental factors have been shown to promote the epigenetic transgenerational inheritance of phenotypic variants (Skinner et al. 2010). In recent years, the importance of environmental cues in the induction of such variation has been widely acknowledged (Bonduriansky 2012).

Natural selection is a process in which environmental factors influence the survival and reproductive success of individuals bearing different phenotypes. Only selection on phenotypic traits with a heritable basis can lead to evolutionary change (Endler 1986). Observations indicate that epigenetic mechanisms have a role in influencing genomic variability (Huttley 2004; Ying and Huttley 2011). As epigenetic changes are also influenced by environmental factors, and can be heritable across generations (Skinner et al. 2010), they provide another molecular mechanism that can influence evolutionary change. Although Lamarck (1802) proposed that environmental factors can influence inheritance directly, his mechanism has not been widely recognized as a component of modern evolutionary theory (Day and Bonduriansky 2011). Recent work in epigenetics shows that epigenetic changes can, in fact, increase the heritable phenotypic variation available to natural selection