Justification of the mathematical definition of logical validity?

[Speakpigeon]

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

[surreptitious57]

There must be some examples where it is true or else the definition itself would be not only invalid but irrelevant too
Though I would have thought that in any deductive argument both the premises and conclusion would have to be true

[Speakpigeon]

There must be some examples where it is true

I don't understand. Examples of what?

There must be some examples where it is true or else the definition itself would be not only invalid but irrelevant too

I don't understand. It's a definition, not an argument. A definition is never logically valid. So, what do you mean by a definition being "invalid"?

Though I would have thought that in any deductive argument both the premises and conclusion would have to be true

No. For example: A and B implies A. That's always true so that's definitely valid. Yet, A and B are not true and they are not even false. They stand for any proposition whatsoever and some of those will true, presumably, and some will be false.
EB

[Scott Mayers]

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

"Validity" is about expressing that logic is a type of machine that doesn't literally express the necessary truth of the data it uses with respect to the outside world of that machine, but that it only "lets pass" output data dependent upon the input data in a strict way. As such, 'validity' by that definition suffices to express that the conclusions that get through the machines we call 'logical' are those that have fixed unique conclusions such that IF the inputs exist as 'true' of the outside world, the unique output(s) are expected to be 'true' as a conclusion when reinterpreted to be about the outside world.

For example, a hand-held calculator is a 'logic' system itself. The 'input' we use is artificial data with respect to the calculator but has a strict output dependent on it such that IF the data we put into it is 'fit' to the reality we are using that calculator for, the output, when translated back into a reference to reality, is true. As an instance, if the reality I am using the calculator for is about trying to add two real prices and determine the total with any added taxes, the machine is only as trustworthy to be useful to the real world if that calculator's outputs 'fit' to the reality of its inputs.

The old adage, "garbage in/garbage out" [GIGO] for computers is identical to this meaning. In other words, once we design the calculator and determine its means to add and multiply, etc, we have to assume the machine itself is not what can make any errors if it 'functions' as it is expected to but that any errors that exist, must lie in the user only.

"Validity" IS 'truth' about the process (the calculator or computer or devices' function).

We CAN and DO try to find machines that can determine the truth of the data too. But when we think of nature, EACH datum is itself its own machine. In this way, as I interpret it, reality operates as both data and machines relative to each other. But we want the term, "logic" to represent only the 'ordered' patterns that define a determinate "function". We can use these functions to express relationships that are more complex. But we want to distinguish those mechanisms of thought that are 'ordered' versus the totality of all thought, which can be of any possible machine whether fixed or random. That is, we want to eliminate those machines/mechanisms of thought that lack a consistent pattern, even though those machines DO exist.

An example of this within math is to think of the 'function' of some unique input to the variables to provide a strictly unique outcome. We can then use functions to describe complex realities (relations) 'piece-wise' or in parallel. For example, a circle in the Cartesian plane is defined BY two functions:

y = square-root-function of (x^2 - r^2) AND the separate function, the negative-square-root-function of (x^2 - r^2).

These are two functions that collectively define the real concept of a circle. In essence, each function is its own 'logic' machine and alone cannot answer all of the reality we desire. We can define the collection of the two 'functions' (two logics) as a machine but then specify that this machine is a 'relation' but not a 'function'.

In the same way, we can have any process of thought that takes any number of inputs that provides one specific outcome, as a "logic". Since there are real mechanisms of thought that are more complexly able to output MORE THAN ONE output, we want 'determinate' outcomes for that regardless. These can still be defined using multiple logic functions. But if we use machines of thought for ANY number of outputs indeterminately, while 'true' of nature, we cannot make use of it to ORDER our thoughts.

So the definition of 'validity' IS the defining meaning of the logic, and represents the VALUE of the expected output as being meaningful or not for us using this machine.

[Speakpigeon]

Derail.
Your answer is entirely irrelevant to y question.
You are merely confusing two very, very different senses of the word "logic":

Logic
3. Valid reasoning
4. The relationship between elements and between an element and the whole in a set of objects, individuals, principles, or events.

This topic is about sense 3. Your comment is about sense 4. It's a derail.

Yeah, of course I know that there is bound to be a logic to each of the machines we build and that we can analyse and represent this logic in terms of the relation between some inputs and some outputs. And, yes, there is obviously a close similarity between the logic of human reasoning and the logic of all the machines we build because the human brain can be usefully considered, broadly, as a machine itself. And more to the point, we make sure we understand the machines we build, computers included. Big deal. That's not the topic of this thread. I'm talking about the logic of human reasoning and whether the mathematical definition of validity is correct in that respect.
EB

[Scott Mayers]

Derail.
Your answer is entirely irrelevant to y question.
You are merely confusing two very, very different senses of the word "logic":

Logic
3. Valid reasoning
4. The relationship between elements and between an element and the whole in a set of objects, individuals, principles, or events.

This topic is about sense 3. Your comment is about sense 4. It's a derail.

Yeah, of course I know that there is bound to be a logic to each of the machines we build and that we can analyse and represent this logic in terms of the relation between some inputs and some outputs. And, yes, there is obviously a close similarity between the logic of human reasoning and the logic of all the machines we build because the human brain can be usefully considered, broadly, as a machine itself. And more to the point, we make sure we understand the machines we build, computers included. Big deal. That's not the topic of this thread. I'm talking about the logic of human reasoning and whether the mathematical definition of validity is correct in that respect.
EB

?

If you were speaking to me, please at least acknowledge this. I contextually inferred this but would normally overlook something that doesn't directly either quote me or respond with my name.

I don't know what you mean of me 'derailing' anything. I 'justified' the definition of "logic" as 'valid' as per your question very precisely. "Validity" is absolutely THE necessary minimal meaning of "mathematical" logic. This term was specific to its precision and NOT about some colloquial use of the term as it is used non-mathematically. Older texts used to call formal studies of logic, "mathematical", but dropped it now that we don't deny math as rooted in logic as was once uncertain.

You chose the term. If you don't like my contribution, I'll leave. But I assure you that I did not derail the discussion. I'm guessing that you just don't like what I have to say as 'valid' per your own preference to broaden the meaning of what is 'mathematical' or for some other personal reason. Definition '4.' above is just about classification perspective but still implicit in '3.' It is also MORE about what you may prefer given it can include informal logic.

(A is a subset of B) == (If A then B) == (not-A or B) using different forms of logical expressions but all related to systems that require defining rule of 'validity'.

If you are including informal/non-mathematical logic, then you want to discuss inductive forms which treat general arguments as 'cogent' rather than 'valid' for reference to the "strength" in the arguments.

[Speakpigeon]

This thread is not about mathematical logic. It is about logical validity. Read again.
The question is whether the mathematical definition is correct. That is, whether the definition used in mathematical logic is correct of logical validity, i.e. validity of logical reasoning.
Your first post is about the logic of machines, which has nothing to do with truth and falsehood since machines don't know of such notions, computers included, and therefore your post is not at all about logic understood as the logic of valid reasoning. So, it's a derail.
EB