Help please -- Seeking clear definition of fundamental terms

[Zacarias Nason]

I've tried repeatedly to get clear, succinct definitions of the following terms over and over again, but invariably the definitions provided clash, and I'd like to put an end to that. The terms I am trying to define clearly are:

- Relation
- Definition (Mathematical definition)
- Function
- Law (Not the concept, but a mathematically expressed law like PV=nRT, if it can be treated as a separate entity from the idea of a scientific law itself)
- Equation
- Derivation
- Formula

I see some of these often used interchangeably (function, relation, equation, formula) unless it happens that someone is actively debating this question, and it confuses the hell out of me. I'm aware there are huge amounts of overlap among some of these, but still having that overlap strictly defined would be very helpful.

 

[anorlunda]

What good does it do to have clear and succinct definitions of any word unless those definitions are widely known and used? It is part of natural language that users of words may have somewhat different definitions in their minds. That is why dictionary definitions are clear and succinct enough in most cases.

 

[Zacarias Nason]

But sometimes they aren't. Just because good definitions aren't prolific enough doesn't mean they shouldn't be. It's unavoidable that people will have somewhat different definitions in their minds, but entirely not preferential as opposed to having clarity. I feel like your response amounted to, "Yeah, but no".

 

[fresh_42]

I've tried repeatedly to get clear, succinct definitions of the following terms over and over again, but invariably the definitions provided clash, and I'd like to put an end to that. The terms I am trying to define clearly are:

- Relation
- Definition (Mathematical definition)
- Function
- Law (Not the concept, but a mathematically expressed law like PV=nRT, if it can be treated as a separate entity from the idea of a scientific law itself)
- Equation
- Derivation
- Formula

I see some of these often used interchangeably (function, relation, equation, formula) unless it happens that someone is actively debating this question, and it confuses the hell out of me. I'm aware there are huge amounts of overlap among some of these, but still having that overlap strictly defined would be very helpful.

Well, to provide them all would lead too far. Wikipedia should be a good reference to look them up. At least relation and function are rigorously defined (set theory). The others might be context sensitive, for I would consult a textbook on logic here.

 

[Zacarias Nason]

The main reason I'm making this is in response to what I view as two god-awful definitions of law and definition I came across in a textbook.

Definition
Law (1)
Law (2)

Maybe it's just me, but I just take these as being deeply unsatisfactory for how much the book just browbeat the reader with, "It's really important you understand the distinction between these, okay?". I don't know if I'm just imagining it but the two provided definitions seem rife with really poorly defined phrases like, "a relationship that already exists in nature", or, "all the variables in this law existed before its discovery".

It seems simple and stupid and easy to take for granted, but I fail to see how the reading speed example isn't composed of a bunch of variables that existed (in concept, at least) before its discovery. Even if it's clunky, not very useful and self-evident, I don't get how, "the reading speed is the quotient of the number of words read and the time passed" doesn't qualify as a law. For how totally unimpressive that statement is, it's always been true. That relationship, as simple as it is, "already exists in nature", just like Coulomb's law.

I feel like the authors got caught up trying to emphasize how scientifically rigorous a law is that they just made the difference sound like it's based on impact rather than some firm conceptual difference.

 

[fresh_42]

This is the usage of the term "law" in physics (context!). If I'd try to explain it in my words, I only added another explanation, and I don't think this is helpful in the context you gave. There is probably no one and only definition of it. In general it's simply a formula that describes a behavior of - usually fundamental - physical quantities. Counter-question: Why do you want to define it rigorously? The usage of it comes by adaption anyway. Since we are talking about "ordinary" language here, @anorlunda's answer in post #2 says it all. Each attempt to "define" it, must necessarily begin with: "Most physicists ..."

 

[Jehannum]

It's good to get a clear definition of terms such as these.

What good does it do to have clear and succinct definitions of any word unless those definitions are widely known and used? It is part of natural language that users of words may have somewhat different definitions in their minds. That is why dictionary definitions are clear and succinct enough in most cases.

It is a good thing for a writer to be self-consistent with technical terms, however loosely they may be employed in general use.

For example, I do not use "formula" and "equation" interchangeably. "Formula" implies a numerical / algebraic method for obtaining a well-understood quantity (e.g. A = π r²), whereas "equation" is used to signify equality between two general expressions.

 

[fresh_42]

... whereas "equation" is used to signify equality ...

Isn't this a circular reasoning? To me equations are simply a certain (context sensitive) relation.

 

[gmax137]

The main reason I'm making this is in response to what I view as two god-awful definitions of law and definition I came across in a textbook.

Definition
Law (1)
Law (2)

Maybe it's just me, but I just take these as being deeply unsatisfactory for how much the book just browbeat the reader with, "It's really important you understand the distinction between these, okay?". I don't know if I'm just imagining it but the two provided definitions seem rife with really poorly defined phrases like, "a relationship that already exists in nature", or, "all the variables in this law existed before its discovery".

I agree with your assessment of whatever this text is you're trying to get through.

It seems simple and stupid and easy to take for granted, but I fail to see how the reading speed example isn't composed of a bunch of variables that existed (in concept, at least) before its discovery. Even if it's clunky, not very useful and self-evident, I don't get how, "the reading speed is the quotient of the number of words read and the time passed" doesn't qualify as a law. For how totally unimpressive that statement is, it's always been true. That relationship, as simple as it is, "already exists in nature", just like Coulomb's law.

I feel like the authors got caught up trying to emphasize how scientifically rigorous a law is that they just made the difference sound like it's based on impact rather than some firm conceptual difference.

Again, I agree. If possible, just let all this go and get on with the real point of the text... I don't see how these fine distinctions can possibly matter, nor how (as you have noticed), they can even hold up to critical scrutiny.

 

[Nugatory]

If possible, just let all this go and get on with the real point of the text... I don't see how these fine distinctions can possibly matter, nor how (as you have noticed), they can even hold up to critical scrutiny.

This is really quite good advice. In fact, it's such good advice that we can use it to close the thread.