I was attempting to distinguish between the common usage of "define" and the logic/mathematical usage of "define". Basically, the common usage of define is ambiguous and imprecise. The definition used in logic is not. Basically, there are (at least) two possibilities of the meaning of your statement "x is 3". In one case you are reporting a fact or making a claim. This is not a defining in the formal sense. A claim can be contested and even disproved.
The other possibility is defining in the formal sense. I'll get back to this in a minute.
I can't prove to you the definition of gender. It is a intensional definition, meaning it describes a meaning to which a thing may be checked against (like a category.) You cannot prove such a definition any more than you can prove the definition of a square or of whole numbers or of 3. There is nothing to prove.
As for why the terms sex and gender were decided on for their respective definitions, hell if I know. I didn't come up with it.
Well that is sort of my point. Someone(s) came up with the definition(s) either indirectly or directly. Regardless, when you make "any" claim, you should back it up.
But it is not a claim. This is where you seem to be hung up. Defining something is not a claim in any way. Think of it as purposing a symbol that encompasses an idea. "9" is the symbol that we have defined to mean the idea of the number 9, but you cannot back up that "9" is the correct symbol to represent the idea. People may or may not accept it for various reasons, but it's essential "correctness" as a symbol is not something that can be debated in the same way the correctness of a claim can be.
And is there not a definition of a square? There are trigonometry proofs for all types of shapes. Yes I understand Math revolves around axioms, but there is still proofs one can do to determine what is a square, even if we defined it. It is the reliability of those proofs on the definitions we make that in my opinion, makes the definition really hold any weight.
For example, if I were to come up with a shape, and it had 10 sides, according to my definition of square( 4 sides, right angles) it would not be one.
There absolutely is a definition of a square. But try to separate in your mind the symbol, the definition, and any proofs or tests that might determine if a shape is a square.
Consider it like this:
First we recognize a useful idea. "This shape seems like it has special significance."
Then we assign a the idea to a symbol. "We will call this shape a 'square'. It is defined as [formal definition of a square]."
Then we come up with the proofs and tests that allow us to test a given shape against the definition. "Check the number of sides, the length of the sides, and the angles of the connecting sides."
You cannot create a test to check against a definition until the definition has been created.
Now, creating a reliable test that checks if a shape is a square is a fairly trivial problem. Determining if a trait is gender or sexual or a combination of both is many, many orders of magnitude more complex. We are working on creating those tests now. Insisting the validity of a definition relies on the test that determine if a thing fits that definition is essentially demanding that scientists have all the answers before they begin their research.
There is research being done on the biological origins of gender, there is research being done on the social origins of gender. The quality of both I do not know.
I know that there are social effects on sex, I certainly know that there are biological effects on sex.
This of course depends on what you mean by "gender", "social effects", "sex" and "biological effects", and several other terms I am not going to bother enumerating. Just because gender and sex are often used interchangeably does not mean they are interchangeable in formal definition.
What you might consider "research being done on the biological origins of gender" might be better described as "research being done on the possible biological origins of traits suspected to be gender traits". Language is not precise, and even if it were people might mislabel or misspeak because people are not perfect.
I am not being intentionally obtuse, but how are the statements: "research being done on the biological origins of gender" versus "research being done on the possible biological origins of traits suspected to be gender traits" any different in effect? They both state the possibility of gender having biological origins. Does affixing the qualifier "traits" after gender somehow change it?
They are very different in effect, but the difference is subtle unless you are used to thinking about things like this in highly precise language. They can mean the same thing, but the first statement is ambiguous. It can mean several things.
In particular, the second does not state the possibility of gender having biological origins. This is vastly oversimplifying it, but think of all traits that might be gender or sex traits being sorted into two different columns based on our best experiments. Again, to be clear, this is a massive oversimplification just to illustrate the idea. It is not a binary question.
The second statement suggests that some trait might have been categorized as primarily gender and and research is being done to determine if this is the case. The suggestion is not that gender might have biological origins, but that something thought of as a gender trait is not a gender trait.
On the other hand the first statement can mean all sorts of things, it is ambiguous. But in particular it does suggest that gender might have biological origins, which is counter to the formal definition of gender. Gender, by formal definition, cannot have biological origins because it is defined as having social origins. Anything that has biological origins is by definition not gender.
Again, for the sake of simplicity I ignored the possibility of a non binary answer to the question.
I feel that we just should not limit any discussion of any term to one science. If researchers want to investigate the possible biological causes of homosexuality, why should they not?
They totally should? No one is saying that.
I am not saying psychologists cant define their own terms, but what makes it "their" terms in the first place? Sciences are connected. Psychology is a wide field, it involves the study of the brain to a degree, which intersects with biology. There are people from all of these fields studying gender, why is one more right than the other?
The distinction between what we might call biological traits and social traits between the observed sexes was first seriously considered by psychologists (specifically psychologists that studied the effect of biology on sexual behavior.) They were the first ones doing the research, they made definitions and names for things so they could talk about it and study it properly.
Turns out the distinction had far reaching implications across several major disciplines. Everyone else who later also studied the topic used the established terms and definitions so they too could talk about it and everyone involved would understand.
Psychologists defined the terms because it was first considered as a problem of psychology. That is the only reason.
A key part of the scientific method is asking questions. So if either sociologists or biologist ask the right questions and gather the right data in the right scope, I do not see fault in saying that "gender could be either biological or sociological" in origin.
Nothing is stopping a biologist or sociologist from studying the sex/gender distinction. In fact, many, many biologists and sociologists do study it. But they use the language decided on by the people who studied it first because it wouldn't make sense to rename it.
And as to your last part, I would say "stuff about definitions" is more philosophy than math
Not in the formal sense. Logic and mathematics have nailed down what it means to define something because without formal definitions language is ambiguous and cannot be used in logical discussion. Defining something has a very specific meaning in logic and mathematics. It has nothing to do with philosophy. And what we are discussing here are formal definitions.
Regardless the "hard" vs "soft" was my error in assuming one would be better than the other. As I stated above, we should just investigate the origins of gender by whatever field, and when the questions stop being asked, then we can say gender originates from "a" or "b" or both. To assume one over the other would be bad logic no?
Again, the problem is that you are not divorcing the idea of gender and gender traits in your mind.
A trait may be influenced by biological or social factors.
If the trait is primarily influenced by biological factors it is a sex trait, falling under the category of sex.
If the trait is primarily influenced by social factors it is a gender trait, falling under the category of gender.
Now, assuming one over the other in relation to specific traits would be bad logic, as would not using every tool at our disposal to study it (meaning different scientific disciplines and the relevant tools and perspective they bring to the table.)