1. ## Aristotle's Logic

Aristotle: Logic. Aristotle does not believe that the purpose of logic is to prove that human beings can have knowledge. (He dismisses excessive scepticism.) The aim of logic is the elaboration of a coherent system that allows us to investigate, classify, and evaluate good and bad forms of reasoning.

What is the logical basis of AL.

We all intuitively accept 'if a equals b and b equals c then a equals c' . What is the basis or proof of such a belief? These kinds of logical snippets are the basis of daily reasoning and we learn then informally growing up. How are these apparent truths known to be valid.

This not a thread on syllogisms, it is on the basis of reasoning.

https://en.wikipedia.org/wiki/Term_logic

In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century. This entry is an introduction to the term logic needed to understand philosophy texts written before it was replaced as a formal logic system by predicate logic. Readers lacking a grasp of the basic terminology and ideas of term logic can have difficulty understanding such texts, because their authors typically assumed an acquaintance with term logic.

https://oregonstate.edu/instruct/phl...f_thought.html

Law Of Identity A = A, is this provable? Or is it a definition?

2. Originally Posted by steve_bank
What is the logical basis of AL.
???

It's, er, logical?

So what? What we want to care about is whether it's true or not.

And Aristotelian logic is true. Unlike mathematical logic, it is correct. It is a correct formal model of the logic human beings use in deductive reasoning.

Not one mistake. Done 2,500 years ago! And here you are not even able to articulate a question that would make sense.

Aristotle's syllogistic is a formal model of a very limited part of logic, but it's all good.

Mathematicians, however, have proposed several generalised methods, but they are all without relation to human logic except to say that some of them may be regarded as crude approximations of it, in the same sense that a square inscribed in a circle is an approximation of the circle..

Originally Posted by steve_bank
We all intuitively accept 'if a equals b and b equals c then a equals c' . What is the basis or proof of such a belief?
There is no proof outside your own intuitive certainty that it's always true and the fact that we all agree it's true.

Once we realised we agreed on this property of equality, we made up the formal definition, as used in mathematics.

The definition says that transitivity, expressed by the implication that if a = b and b = c, then a = c is a property of equality.

But this is only one part of the definition of equality.

There is also the reflexive property: a = a ......

And the symmetric property: If a = c, then c = a.

Thus, the formal definition, as used in mathematics, is only a model of the way most people think without even realising that they do it.

Originally Posted by steve_bank
These kinds of logical snippets are the basis of daily reasoning and we learn then informally growing up.
We only learn the formal expression of it. Any moron knows without having to think about it that a = a.

Originally Posted by steve_bank
How are these apparent truths known to be valid.
There is no other proof that if a = b and b = c, then a = c is true. It's just the way our mind works. How the mind of everybody works. Which explains why we get to agree on this.

Originally Posted by steve_bank
This not a thread on syllogisms, it is on the basis of reasoning.
Syllogisms are based on human reasoning, too.

Funny how you're always giving lessons and making all sorts of claims about logic, as if you were an experienced and savvy practitioner ... and yet, it is clear you understand next to nothing about it. You don't even understand the basics.

It's perfectly OK to know nothing about logic. Most people don't. But most people don't go about making extravagant claims about it and posturing as expert.
EB

3. Then considering your ongoing critique that math logic is not on a logical foundation. how is that any different than Aristotle?

You criticized mathematical proofs for seemingly being based on assumptions. How was Aristotle any different?

You side step the point. If he 'invented' logic how did he logically deduce logic? A fair question. That he did it locally as you say is rather silly.

A = A is an unprovable assumption.

'if a = b and b = c then a = c' is an unprovable assumption logically.

In your view how is AL any more sound than mathematical logic and proofs?

4. Originally Posted by steve_bank
Then considering your ongoing critique that math logic is not on a logical foundation. how is that any different than Aristotle?

You criticized mathematical proofs for seemingly being based on assumptions. How was Aristotle any different?

You side step the point. If he 'invented' logic how did he logically deduce logic? A fair question. That he did it locally as you say is rather silly.

A = A is an unprovable assumption.

'if a = b and b = c then a = c' is an unprovable assumption logically.

In your view how is AL any more sound than mathematical logic and proofs?
I already replied to that but you didn't understand because you don't understand much at all.

I certainly didn't say Aristotle "invented" logic. You're a triple idiot. You're making stuff up and then asking me to justify your own idiotic assertions. Sorry, no, I won't do that.

______________________________

To everybody else,

Aristotle merely realised humans did something we now call deductive logic and explained what he understood of it as best he could and he did a great job. However, his work obviously doesn't explain anything and indeed is not properly justified. But precisely, that's the job he left for us to do and so far we've shown ourselves not up to the job. It is probably our most monumental failure for that kind of theoretical question. Think that we did General Relativity and Quantum Physic and it took only a few decades to do it once the problem had been identified. Deductive logic? Well, 2,500 years after Aristotle, we still haven't solved it at all, and this even though there are more mathematicians (and philosophers for that matter, not to mention computer scientists) alive today than ever before, and that's something of the order of millions of mathematicians alive today!

Not only we didn't do it, but mathematicians pretend to have done it and they don't even understand what the problem is to begin with. Humanity had 2,500 years to think about it and still hasn't come up with the good. You can't charge Aristotle with 2,500 years of failure when he was no longer there.

He pointed his finger at what we now call deductive logic. He identified it. Without him probably we would still live in caves metaphorically speaking.

Yes, mathematicians are idiots but no more so than all human beings. I'm just pointing out the obvious problem that people don't wan't to see because that's how humanity works, as demonstrated by Fascist regimes, Stalinist regimes, Maoist regimes, as demonstrated by the Catholic Church and by the cheer stupidity of most comments on most Internet forums. People don't like to be made to look at their failures. It's just human and I am myself just like that too, but that doesn't mean there is no failure to begin with.
EB

5. Originally Posted by Speakpigeon
[Aristotle] pointed his finger at what we now call deductive logic. He identified it. Without him probably we would still live in caves metaphorically speaking
According to Plato, we do.

6. A non answer to the issue of claiming math proofs are not on a sound logical foundation.

As yiu said with Aristotle, they think logically...

7. Originally Posted by steve_bank
A non answer to the issue of claiming math proofs are not on a sound logical foundation.
I don't know of any good reason to accept that mathematical logic is correct.

I've been trying to find one for the last three years without any result.

If you know one, your welcome to put it here.

Please, just don't tell me mathematicians should be trusted because they are ... mathematicians.

Originally Posted by steve_bank
As yiu said with Aristotle, they think logically...
Yes and no. Sometimes they do, I hope most of the time, but apparently they are now capable of not thinking logically, since they now have the option of thinking using mathematical logic. Choose your own poison, that sort of thing.

Initially, it is clear that people like Russell in particular reasoned logically, absolutely. However, they reasoned logically on unproven premises, and obviously unproven premises since based on an unjustified assumption. Sorry I can't go into the detail of that but it's publicly available material and for all to see in book on logic.