I was a little flippant in my previous remark, Blue - and I apologize for that.
Accepted thanks.
But yes, either way would be fine.
It isn’t in my book.
If one’s logic and later syllogisms are to be consistent one cannot mix these two different understandings of what the terms/words refer to.
Take number.
We are not dealing with “reality” - we are dealing with one small conceptualised aspect of that bigger reality. You call it an “abstraction”.
This is the world of apriori “truth” then.
And any “logic” or self-evident principles would therefore seem to flow from the number abstractions as a matter of the arbitrary number definitions themselves. Much like the “truths” about unicorns.
If we allow our conceptual numbers to be further abstracted/symbolised by 10 different written digits or combinations thereof then **by definition **0 is not 1 and so on.
If we then invent/define operations like addition or division (which in maths is also an abstraction from a far richer and arbitrary way of regarding unity/place/separation in time/space) we are also “abstracting” from the real world by limiting the real world with a strict definition.
In the real world what we symbolise as “1” and what we symbolise as “2” can in fact be the very same thing. Take a blob of matter and imagine it “cut in half” (a very specific, arbitrary and narrow abstraction). 1 becomes 2.
But you say this is a contradiction of logic perhaps? Well yes, in terms of the defined concepts of number and operation then of course it is. If we understand what the arbitrary and abstract definition of “division” is then you are right.
But then we are simply back to the unicorn again.
Apriori knowledge whose certitude comes from the definition of the mental terms used.
But in the “real world” a blob of something can be any number you want it to be without contradiction. You just need imagination and a mental knife.
While most of us might say that even a blob of something is a single unity and therefore “1” objectively “in itself” is that really so?
Not really. We see it as “1” because we sensibly perceive it to be spatially or temporally separate from another blob perhaps behind us or yet to appear in the future (another apple on the tree).
Its our very words that imply a set of pre-existing conditions and ways of conceptualising what we want to see or do in “the real world”. We always have a narrow purpose built into our words and statements such that “the real world” is always shaped and “spun” in some way according to what we preconceive by our approach.
Which is why I am unable to agree with you that we may talk about “truth” in the same way when we deal with concepts as opposed to the bigger sensible realities that these concepts represent.
One is a truth of consistency (“concepts”) the other is a truth of “existence” or “adequation”.
The symbol “2” is a concept, it can refer to something in physical/material reality, or as an idea.
So it should be clear I find this assumed univocal predication of idea and material reality problematic when we want to start speaking of “truth” “logic” or “self evident”.
But “true” in this case would be a positive accord with what is meant by the idea or the physical reality - either way. False would be not in accord.
And what if we said that ideas (ie abstractions or symbols) are never wholly in accord with physical reality? Does that mean all ideas/symbols are false…or just somewhat “adequate”. And then what of “logic” and “self evident”?
A syllogism is true or false. A mathematical formula calculates a true or false result.
Yes, just like a unicorn having one horn. But its only a word game where the certitude of the truth flows from the narrow definitions imposed. It says nothing about whether a unicorn concept is a sensible reality…or even if the possible reality it refers to could ever coherently self-exist or be created by God if he wanted to.
For example we all believe that Newton’s Laws state that an object moving in space without friction will move forever. Yet there is no place in the universe completely without friction. So how do we actually know if that is true, logically and absolutely certain? We don’t really.
Why do we say that 2+2 - 4 is not the same as 2+2 = 5?
This is universal. If I insisted that those were both the same, we would say “that is false” - but why do all humans accept that?
For the same reason that we say an immovable object can never be shaken - not even by the most powerful of forces. Its a definition word game. Nothing necessarily to do with any nature or “thing” inherent the sensible world.
Could I say that I just use different rules? In my rules, a false answer is better than a true one?
That would be strange, but obviously nobody does that.
So, the idea that true is correct and good, is part of that idea that is embedded in human nature.
There are no exceptions to that.
In fact, there can be no exceptions to that.
Given the word/concept definitions it must be true or language and communication breaks down.
But that doesn’t mean this sort of “truth” is transferable to relations between “sensible realities” which defy our desire to encapsulate and tame them with symbols, definitions, concepts and abstractions that strangle “sensible reality” in attempting to bend it to the same sort of word definition games.
Like the riddle says: “what is the difference between truth and fiction…?”
Answer: “Only fiction has to make sense.”