For example, is "a bachelor is an unmarried man" a definition or tautology? The context is this: "Some philosophers of science have argued that 'survival of the fittest' is a tautology (the fit are those who survive, and the survivors are those who are fit). How does this critique challenge the scientific testability of Darwin's mechanism?"
What is the difference between a tautology and a definition?
A tautology is a syntactic element: a statement that is always and invariably true by virtue of its structure. Usually we restrict this to simpler types of statements that are immediately apparent as always true — e.g., x=x; P⋁¬P — because otherwise we'd end up calling every proof an extended tautology.
A definition is a semantic element: the assignment of meaning to a given word or phrase. We rely on definitions to bridge lapses or lacks in language: e.g., if I want to talk about the beauty of a truss bridge near my home, I may have to give a definition for the word 'truss' (a word which isn't too commonly used).
As a rule, if we try to represent a semantic definition in symbolic logic, we will end up with something like a tautology: e.g., the definition 'bachelors are unmarried men' would look something like "B∧¬M" (B is bachelor, M is married, and this proposition always evaluates to true on inspection). This is because definitions in semantic contexts serve the role of specifying linguistic (a priori) truths. But logical tautologies don't need to have semantic meaning — P⋁¬P is always true, no matter what we take P to mean — and so we cannot necessarily create or recover a definition from a tautology.
A definition introduces a new word into the vocabulary; a tautology does not. In your example,
(1) A bachelor is an unmarried man.
there are two possibilities for how to interpret this. If we interpret (1) assuming that (1) is introducing a new word "bachelor", then it is a definition. If we interpret (1) assuming that we already know what a bachelor is, then it is a tautology (by an extremely broad understanding of what a tautology is). However, after you use (1) as definition, you can then use it as a tautology.
You are apparently using a very loose definition of "tautology", something like "a sentence that is true by definition". Just be warned that that is not how logicians usually understand the word, so if you use it that way, be prepared to be misunderstood.
We can define the predicate "___ is a bachelor" (intended to be applied to individuals of homo sapiens) as "___ is an unmarried man". Giving a (nominal) definition means you are making a statement about how you intend to use some word, phrase, or predicate. In this case, you are basically saying: "Every time that I will use the term 'bachelor', I mean 'unmarried man', and you are free to substitute the words 'unmarried man' for every one of my 'bachelor' usages."
Once you have given a (nominal) definition of the above form
The predicate __ is an F is equivalent to __ is a G
you are allowing yourself and others to make that substitution. That is, make a substitution without changing the truth-value of the actual proposition. So, any statement "x is an F" will then be true if and only if "x is a G" is true.
A tautology is a statement that is true by virtue of its logical form. For instance, if p is any proposition (a statement that has a truth-value), then
If p then p
is perhaps the most simple tautology. In this case, it doesn't matter what the content of proposition p is, the conditional "If p then p" will always be true.
Note, that when we say a proposition is true by virtue of its logical form, we mean that it is true by virtue of the accepted rules for the logical connectives and operators in the proposition. In propositional logic these are negation ("it is not so that ..."), and the connectives that join propositions: implication ("if ... then ..."), conjunction ("... and ...") and disjunction ("... or ..."). These rules themselves, if they can be expressed as propositions, will also be tautologies.
Now, once you have defined "bachelor" to have the same meaning as "unmarried man", but only once you have established that definition first, the proposition
A bachelor is an unmarried man
of (equivalently)
All bachelors are unmarried men
is true by virtue of that initial definition (by virtue of the meaning of the words alone). It's called an "analytical truth". This is not strictly speaking identical to a tautology (a purely logical truth) (though according to some it ultimately boils down to the same thing), but it's very similar to a tautological truth in sofar that it is true by virtue of the linguistial form or rather the linguistical conventions that are in play in that statement. This implies that, similar to a tautology, the statement is not informative about the empirical world; it doesn't tell us any new facts about what is the case, it merely exhibits a linguistic rule or convention.
An extremely well-written introduction to the uses of definitions and their role in debate is found in the first chapters of Arne Naess' Communication and Argument: Elements of Applied Semantics (1966). The book only presumes a high-school level background knowledge. For years, it had to be studied for the examen philosophicum, a preparatory examination compulsory for all students of the University of Oslo, with the exception of those studying dentistry or pharmacy.
In evolutionary theory, the statement that the fittest individuals will survive, means something more or less like "If two individuals differ in 'fitness', the probability that the fitter one will live longer (and have more opportunities to reproduce) is greater." In this case, if the criteria for determining which individuals are "fitter" are independent of the knowledge which individual live (or have lived) longer, the statement is not a tautology and not an analytical truth. Howewer, if "fitter" is initially defined as "will live longer", the statement would be an analytical truth. But, in fact, "__ is fitter" is not simply defined as "lives longer". It's much more complex than that - and even a common-sense notion of "fitter" involves more than the mere notion of "lives longer" (e.g. is not sick, is stronger, smarter, etc.)
Now, there may still be a worry that there is some circularity here. For instance, if "fitness" in practice is operationalized ( measured) in terms of "survival rate", then the statement that the fittest survive would be an analytical truth - true by virtue of the operational definition. But do evolutionary biologists do this? Not really. Fitness does not need to be interpreted as actual reproductive success (the actual outcome of the process), but can be see as the propensity to have more offspring - which is a probability measure depending also on the environment. Fitness is not an intrinsic property of individual organisms but can only be seen in relation to an environment (that may change and is itself changed by those organisms). (See: Susan K. Mills and John H. Beatty, The Propensity Interpretation of Fitness, 1979).
You also have to see that the statement "the fittest survive" is a huge simplification that doesn't do justice to evolutionary theory. It's a caricature. Afterall, sometimes a not-so-fit individual will survive and have offspring; sometimes a very fit individual gets destroyed by a meteor. Evolutionary biology does not deny this.
Tautology applies to propositional logic:
a formula that is always true regardless of which valuation is used for the propositional variables.
The corresponding terms for predicate logic is that of Valid formula:
a formula that is true under every possible interpretation.
According to the definitions, a tautology is a valid formula of propositional logic.
In natural language, it has little sense to say that a statement S is a tautology (in the formal sense) because it is not very useful to apply the condition of the definition: "true in every possible interpretation."
From a formal point of view, a tautology is a theorem of propositional calculus.
A valid first order formula is a theorem of predicate calculus.
In both cases, they are logically true sentences, that remain true no matter what the interpretation of the nonlogical constants.
An analytically true sentence is true in virtue of the meanings of its words.
The paradigmatic example of the second one is: "All bachelors are unmarried", whose logical form is "for every x (if B(x) then U(x))" which is not a tautology.
A definition is used in the context of a theory (a collection of axioms), and it is like an axiom: it is not a logical law. A definition is true in every model of the axioms (an interpretation that satisfies the axioms).
You ask:
What is the difference between a tautology and a definition?
Ted Wrigley's answer is succinct and accurate. Tautologies must be true because they have a syntactic form that does not allow them to be interpreted in a way where they are ever false. For instance, "2+2 = (y+4)-y" is a tautology because no matter what value of y you introduce into the formula it will always be true. But, imagine that the symbol "4" requires a definition. If we say "4 =def 1+1+1+1", then we have a definition. Traditionally, definitions are neither true nor false. See Bumble's answer here for an explanation.
You say:
Some philosophers of science have argued that 'survival of the fittest' is a tautology (the fit are those who survive, and the survivors are those who are fit). How does this critique challenge the scientific testability of Darwin's mechanism?
This is an example of a circular definition which is tautological in the sense that both definienda serve as mutual definientia. Here, no substantial information is introduced because references for each term merely point to each other. This is sometimes referred to as pleonasm.
A definition explains what a word means to aid in and facilitate communication.
There are 2 meanings of tautology:
In formal logic, a tautology is a formula or statement that's always true regardless of the truth value of any variables or premises. As an example, for a truth statement X, either X is true or X is false*.
* In reality, a statement might also be partially true or a paradox. But formal logic tends to avoid those complexities.
In language, a tautology is roughly saying the same thing twice, such as by using an adjective that's already implied by the corresponding noun, e.g. "convicted felon". There can however be some rhetorical use to such tautologies, like to emphasise ideas.
X is Y:
Definitions are typically in the form "X is Y", or can be written in that form.
"X is Y" could also be a language tautology (among other things). For example, "it is what it is".
"X is Y" wouldn't generally be a logical tautology, except if Y = X or if one adds clauses to the statement, e.g. "X is Y and Y is not (not X)".
To tell the difference, one may need to consider the context and intent of what's being said.
"A bachelor is an unmarried man" could either be a definition or a tautology, depending on context. If I hear someone say it in everyday speech, I'd be inclined to consider it a definition, since casually-spoken tautologies tend to either be not so obvious or serve some rhetorical use, neither of which seems to apply here.
Note that "is" statements could also describe belonging to a set or possessing some trait or traits, e.g. "Jane is a woman" - this could also be phrased as: Jane is part of the set of women or possesses the trait of being a woman. That's the sense in which "A bachelor is an unmarried man" would be a tautology: it would be saying a bachelor is someone who possesses the trait of being an unmarried man, but that's already implied by the use of the term "bachelor".
It doesn't really make sense to ask whether "survival of the fittest" is a definition or tautology (in the sense described above), because it's not defining anything. Someone might (dubiously) say "evolution [or natural selection] is survival of the fittest" and one could ask whether that's a definition or a tautology, but that's a different question. Something's definition itself may contain a tautology, while providing that definition may not be a tautology. It's somewhat just confusing the matter to ask whether it's a definition or tautology.
Is the phrase a tautology? It depends on definitions.
If one defines fitness as likelihood to survive, then you have something like "survival of those most likely to survive". This is arguably language tautology. One could potentially make it a logical tautology through some modifications or additions, but it wouldn't be one as it stands.
But one could also e.g. define fitness as possessing traits making individuals likely to live until a fertile age, to produce offspring, to have that offspring be fertile, and to have that offspring be sufficiently fed and protected for them to continue on. And one could define survival as a population having a sustained or increasing size across many generations. If we define our terms as such, it would be hard to argue that it's a tautology.
One could debate whether this is close enough to the commonly understood meanings of these words. But if we're talking about evolution, the better question is what the theory of evolution actually is, rather than debating the semantics of this highly oversimplified phrase.
Maybe one could say that the second meaning is obviously true, but something being obvious and something being a tautology is not the same thing. Also, try to tell the people before Darwin how obvious it is. It's obvious to us, given our understanding of evolution, even among people who have a wildly incorrect understanding of the actual theory of evolution, based on a lot of false beliefs about the supporting evidence.
Also, calling something obvious wouldn't be a great strategy if one is trying to challenge it.
The Wikipedia article on the topic has an entire section dedicated to the question of whether it's a tautology.
Not really.
A better definition of evolution is:
Evolution is the change in the heritable characteristics of biological populations over successive generations, generally through mutation and natural selection.
And a better definition of natural selection is:
Natural selection is the natural process by which heritable traits increase or decrease in frequency in a population [based on how well those traits aid individuals' survival and reproduction].
Note the similarity between this and the non-tautological interpretation of "survival of the fittest" given above.
The definitions themselves wouldn't be tautologies, and as such, the question of tautologies doesn't "challenge the scientific testability of Darwin's* mechanism" at all.
* Darwin died almost 150 years ago. Yes, he provided pivotal contributions to our understanding, but our modern understanding of evolution has evolved since then, in light of the evidence. It's not really "Darwin's" anything at this point. It's mostly creationists who try to drag things back to Darwin, to try to paint science as dogmatically following some authority from long ago, when that just isn't factually true (that is what creationists do, though...). Darwin had to make the case for the theory of evolution, based on the evidence, and against significant pushback. It was accepted, and remains accepted, because of how well it explains the evidence. It's been verified by countless experiments and accurate predictions.
Creationists need to paint the scientific community as dogmatic, because that's the only way they can really make sense of why practically all scientists, especially biologists, accept evolution. But the reality is that the scientific community is very open to (sincere, well-evidenced and testable or verified) challenges to scientific theories. Most scientists are scientists precisely because they want to learn new things. If anyone could falsify evolution (in as far as you can falsify something with so many accurate predictions), there'd probably be a Nobel prize in it for you. The simple reality is that scientists don't accept creationism because creationism isn't science. Creationism rests on presupposition about specific actions of a deity, and it doesn't produce correct predictions (never mind that a lot of it is actively falsified by the evidence).
As your evolution example suggests, the word 'tautology' is often used derogatively for something so trivially true that it adds no information. For example, "the secret to winning is to get more points than the other team". That's merely rephrasing the rules for who wins. It's for-sure true, and that's good, right? But it's so trivially true that it's useless. Compare with "we'll win by wearing them out with fast play". That may not be true, but it communicates something. Of course context matters -- if the sport is roller-derby then "...more points..." may be communicating to newcomers who were not aware roller-derby has a score.
I've also heard 'tautology' used to describe something barely useful. For example, someone seeing pV!p=true might comment "isn't that a tautology?" They're saying that of course all derived rules aren't technically adding anything, but p->q == !q->!p is a useful shortcut, while pV!p=true -- seriously? Do we even have to write that down? We're still using 'tautology' in a derogative sense, but "less useful" instead of "useless".
On to evolution. If a kid doing a report on "survival of the fittest" got up and said "survival of the fittest is when the fittest survive" and sat down, they haven't said anything. Would the teacher write down '0pts, tautology'? Would a philosopher of science in the audience mutter that to his fellow? The student communicated nothing, while technically being 100% correct, so using the T-word seems fine. Does that poor performance disprove evolution? I'm going to say ... no?
For further reading, a "survival of the fittest tautology" search led to a Reddit post containing a link to a paper from "The Nature Institute". That's as far as I went, but my guess would be that looking up names (authors, institute members) and checking other places they appear would lead to Creationist and Intelligent Design groups, possibly Young Earth Creationism. Maybe they have a fuller explanation of what they mean by "evolution is a tautology".
The definition of a word is the specification of the words that comprised the meaning of this word.
When the otherwise meaningless finite string Bachelor(x) is stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
then Bachelor(x) meets this definition:
tautology, in logic, a statement so framed that it cannot be denied without inconsistency. Thus, “All humans are mammals” is held to assert with regard to anything whatsoever that either it is not a human or it is a mammal. https://www.britannica.com/topic/tautology
Also Quine's
Two Dogmas of Empiricism
https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf
Objection's to the analytic/synthetic distinction based on synonymity dissolves.
