Yes, but the question was if (a description of) a set of relationships is interchangeable with logic. You said it it's interchangeable with anything. See how I'm describing a set of relationships regarding your argument. It's your logic.
Yes. But I never said that logic was a set of definitions.
Logic is a set of
rules that restrict combinations of statements about relationships between different entities.
Because you literally said you wouldn't cooperate in our conversation. Calling my claims "silly" and then hiding what you wrote in spoiler tags. My reponse that I was just going to restate what I wrote was in response to that.
You have misinterpreted consideration of other people's feelings as avoidance.
I broke my post into spoiler tags, so I would not be writing walls of text, as I've been accused of that before, and told that it results in TL;DR. So then you and others could read as much or as little as you wanted.
If I had wanted to hide what I wrote, I could have simply left all of that out.
So you see how argumentation can be logical yes?
That's going to depend on your definition of "argumentation".
This idea of "rigorous" anything is redundant in this context. It's like, is writing in C# vs C++. Syntax and semantics are less precise in one. Does the computer understand the same message. No, but functionally the same thing happens.
I've coded for years in both, on projects with real-world outcomes for actual people, where I got significant feedback on the real-world results.
I worked in C# for several years, and then worked with C++. There was a significant learning curve, not in terms of the syntax or the libraries, but in terms of understanding the things you have to pay attention to, which are completely different.
If you're not paying attention to the right things in each, the computer keeps crashing. Even if you're trying to apply both sets of rules, you'll also get a system crash.
If I had to compare them to something, it would be like comparing dating a left-wing lawyer (C#) to dating a right-wing fitness freak (C++).
E.G. if you invite them both to a party, the C# woman will turn up in a little black cocktail dress expecting to be taken to a swanky hotel/mansion. The C++ woman will turn up in a mini-skirt expecting to go to a rave.
You just cannot treat them the same way, not unless you want your systems to fail repeatedly.
It is shorthand for a much more expanded argument. If either interlocutor needs elaboration, then we give it to them.
That doesn't work for logic. People don't always ask all the questions they need answers to when you are there, or they forget some of the answers. Then they look back at the logic and can't make head or tail of it. So in logic, you have to write your entire working out, or you'll just end up inventing things that have no basis, and that's something that is not allowed in logic (one of the rules).
I never defined argumentation.
Then define it.
Because it seems like you are applying human reasoning to logic.
People get confused between the 2. Logic is a particular type of human reasoning, one in which we take a particular approach.
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Principia Mathematica is a very intense work. It's not for lightweights. It takes over 200 pages for Russell and Whitehead to prove that "1 + 1 = 2", because they're not assuming all the basic rules of arithmetic that we usually treat as axioms (premises), and trying to prove them from scratch.
It's quite important, because Euclid had 5 axioms of geometry, rules that we take for granted in human life. Mathematicians were able to prove 4 of them. But the 5th remained unproved. Eventually, Einstein showed that our universe is inconsistent with the 5th axiom, which means our universe is not Euclidean, which means all of Euclidean geometry is assuming a universe that we do not live in.
Turns out you need to know that the universe is non-Euclidean in order to make things like reliable GPS and reliable global mobile phone communications.
If we'd stuck to avoiding using logic, everyone would have assumed Euclid's axioms were all true, would have rejected Einstein's theories, and right now, you wouldn't have a working SatNav or a working mobile phone.
I said this before, but you keep stating the obvious.
P1. Unicorns do not exist.
C. All unicorns are tigers.
1. -∃xUx A
2. ∀x-Ux 1 QE
3. -∀x(Ux→Tx) IP
4. ∃x-(Ux→Tx) 3 QE
5. -(Ua→Ta) 4 ∃O
6. -(-UavTa) 5 Imp
7. --Ua&-Ta 6 DM
8. --Ua 7 Simp
9. -Ua 2 ∀O
10. --Ua&-Ua 8,9 Conj
11. ∀x(Ux→Tx) 3-10 IP
Ux = x is a unicorn, Tx = x is a tiger
P1: Unicorns don't exist.
P2: No reasoning exists to suggest that any unicorns are or are not tigers.
C: There is insufficient evidence and logic to conclude that all unicorns are tigers, or even that any unicorns are tigers, or even that no unicorns are tigers.
1) Suppose that unicorns don't exist, and that not all unicorns are tigers.
2) You can't prove that not all unicorns are tigers, when you have no reason to think that unicorns would be tigers or not be tigers, unless you can prove that at least one unicorn exists that is not a tiger.
3) By (1), since you assumed that unicorns do not exist, you have no proof that at least one unicorn exists that is not a tiger.
4) By (3), if unicorns don't exist, you have no proof that "not all unicorns are tigers" is true or false. "not all unicorns are tigers" remains indeterminate.
5) Therefore, by (4), if unicorns don't exist, you have not proved your argument that "all unicorns are tigers" is true, and thus have not proved that all unicorns are tigers.
You jumped to this:
If unicorns don't exist, and you cannot prove that not all unicorns are tigers, then all unicorns must be tigers (WRONG).
Would you use a hammer to cure cancer? Does that mean hammers are flawed? Or does that mean that if someone uses a hammer in a situation in which it would not work properly, that such a person does not understand the tool they are using?
I'm saying the opposite. Anything can be justified with logic.
I understand you believe that. You made a flawed argument. See above.
Argumentation is a much more loftier ideal, that is made from logic.
You'll have to define "argumentation" then, before I can make any claims about it.
I would prefer to be skeptical about my tools and what they can do, then to fantasize that they alone can solve my problems.
Now you're starting to sound like a logician.