Axioms are tautological assertions
Axioms are tautological assertions , logical validity's or mathematical redundancies(1=1). Many attempt to downplay a fallacious rhetorical tautology3 by equivocating between logical validity's and argumentation schemes which are non-sequiturs which might be called the fallacy of Innocence by association. "What happens , happens" also says the same thing twice but as part of an explanatory propositional schema is fallacious.
We need to differentiate between tautological propositions(fallacies), assertions(validity's) and expressions(colloquial way of speaking such as sporting event commentary or second guessing in an informal setting).
In Tautology Journals the authors equivocated between these three main tautological constructs in order to obfuscate that Aristotle, Lucretius, James Hutton, PattrickMatthew, Prof. Owen, Darwin and JohnWilkins constructed ...formal propositions which cannot be disputed .... All scientific theories such as Newton's inverse square law are formal propositions which can be disputed, tested or potentially Popper falsified.
Logically valid but unintended and thus a Logical Tautology(Tautology4) - http://en.wikipedia.org/wiki/Tautology_(logic). A tautology that arises as an unintended consequence of automated theorem verification. The intention wasn't to be poetic neither deceptive nor to affirm the logical validity or axiomatic, faith or hopeful basis for our existence that (A or not-A) or (1 = 1) implies. It has all to do with Pragmatics.
Repetition of the same idea in different words. (http://tautology.net/) such as Creationism isn't science, where a single word essentially says the same thing twice. The word Science in the context used, the intention was: Creationism isn't materialistic, where the Pragmatics with "science" was the materialist belief system. Creationism is defined as not being materialistic thus the sentence really reduces to: Something which is defined as not being materialistic, isn't materialistic and therefore materialism is the correct world view which says the same thing twice making the conclusion a non-sequitur. Perhaps materialism is the correct world view but not as a result of the argumentation scheme.
In logic, a tautology(Tautology1) is a proposition that is already true by definition, not because of any logical deduction. There isn't really a process of logical deduction than can be used to deduce that 1=1 - we simply believe it to hold in our domain.
It might not be true though in another domain, distant past or distant future as shown by Prof. Herrmann (http://www.serve.com/herrmann/main.html) from US naval academy. He referred to extrapolations of nuclear decay rates in our domain to infer that the earth is therefore 5bil years old as "set theoretic error of generalization" or something to that effect. Using the math of Ultra-Logics he proved that the present laws of physics can't be extrapolated to the distant past or future because back then there might have been different laws, which means that all photon impressions on photographic plates of "distant" galaxies are basically pretty pictures. They can't tell you how the universe was made. The public don't know about it because the science popularizers publishing on CNN don't inform them. There are about 300 mathematicians knowledgeable about Ultra-logics and its implications for theories about the origins of the universe and how we should interpret nuclear decay rates. (In Gravity Past the author reasons that dinosaurs wouldn't have been able to breath in a gravitational force as strong as ours, it had to be less. )
Use of an extra word in a phrase or sentence which unnecessarily repeats an idea, eg the annual poetry festival is staged every year but if used in a colloquial sense for its stylistic effect is a tautological2 expression or pleonasm and not a fallacy.
Comment on this part when time allows
But he insists that we view scientific theories as consisting of an “elaborate collection of statements,” some of which are not falsifiable, and others – what he calls “auxiliary hypotheses,” which are. According to Kitcher, good scientific theories must have three features – unity, fecundity, and independent testability of auxiliary hypotheses:
Unity “A science should be unified .... Good theories consist of just one problem-solving strategy, or a small family of problem-solving strategies, that can be applied to a wide range of problems” (1982: 47).
Fecundity A great scientific theory, like Newton’s, opens up new areas of research... Because a theory presents a new way of looking at the world, it can lead us to ask new questions, and so to embark on new and fruitful lines of inquiry... Typically, a flourishing science is incomplete. At any time, it raises more questions than it can currently answer. But incompleteness is no vice. On the contrary, incompleteness is the mother of fecundity... A good theory should be productive; it should raise new questions and presume that those questions can be answered without giving up its problem-solving strategies (1982: 47–48).
Auxiliary hypotheses that are independently testable “An auxiliary hypothesis ought to be testable independently of the particular problem it is introduced to solve, independently of the theory it is designed to save” (1982: 46) (e.g. the evidence for the existence of Neptune is independent of the anomalies in Uranus’s orbit).
Like other definitions of theories, including Popper’s, Kitcher makes it clear that a good theory includes statements that have (in his terms) “observational consequences.” But, like the observation of irregularities in Uranus’s orbit, falsification is only one possible consequence of an observation. The production of new hypotheses is another possible – and equally important – observational consequence. Kitcher’s account of a good theory is based not only on his understanding of how physical sciences work. He is also taking into account the way the life sciences work.
From Kitcher’s point of view, Darwinian theory not only meets the three conditions for a good scientific theory; it is without question an extraordinarily successful theory: The heart of Darwinian evolutionary theory is a family of problem-solving strategies, related by their common employment of a particular style of historical narrative. A Darwinian history is a piece of reasoning of the following general form. The first step consists in a description of an ancestral population of organisms. The reasoning proceeds by tracing the modification of the population through subsequent generations, showing how characteristics were selected, inherited, and became prevalent. Reasoning like this can be used to answer a host of biological questions.
The same kind of story can be told again and again to answer all sorts of questions about all sorts of living things. Evolutionary theory is unified because so many diverse questions ... can be addressed by advancing Darwinian histories. Moreover, these narratives constantly make claims that are subject to independent check. Darwin not only provided a scheme for unifying the diversity of life. He also gave a structure to our ignorance. After Darwin, it was important to resolve general issues about the presuppositions of Darwinian histories. The way in which biology should proceed had been made admirably plain, and it was clear that biologists had to tackle questions for which they had, as yet, no answers.