Is 'objective' a 'quality' or an 'abstraction' existing only in 'mentation'?
Are you using 'objective' a synonym for 'real'?
For X to have objective existence is for X to exist independently of the concept of X in any brain. And yes, for me those things are real which have objective existence, and no other things. However it's not clear to me that everyone agrees.
Because for me 'objective' is not synonymous with 'real'.
This is why straight lines are not 'real', but mathematics is 'objective'.
It's true that arithmetic and its procedures arise out of human experience of reality, and have been constantly adjusted so as to conform with that. But this depends on human convenience and the way humans see the world. For there to be two sheep, you need a human to define the relevant physical region (let's call it the 'field') and the thing to be counted (let's call it the 'topic' and let's say 'sheep') and the test for relevance amongst the potential elements of the topic (eg 'all sheep I can see' or 'nearest sheep' or 'black sheep' or 'suitable for slaughter' &c). Same with pebbles, trees, parking police, and so on. And then from pebbles in a bag or notches on a stick on to abstractions like the numbers 1, 2, 3, and so on, concepts being derived from concepts, to build the edifice of maths.
I don't have a problem with mathematics not being 'real' in the sense that 'straight lines' are not 'real'. But to say there is no 'counterpart in reality' is starting to play loose with the language, imo.
We could argue that, I dare say. But there are no Euclidean points, lines, planes, no irrationals, infinities, outside of human thought. We have the concepts, defined with remarkable clarity, and the concepts have no real counterparts.
That said, how is 'validly derived in accordance with the rules of the relevant branch of maths' a matter of personal feeling or opinion?
It isn't. Applied maths is like turning a crank and getting a machine-made answer. Calculators could do useful arithmetic long before computers. Computers doing maths execute predetermined procedures analogous to the cranked machine or the Jacquard loom. What they do is done in reality.
The results remain conceptual though ─ 20,032.34 may be the week's takings, the number of Ruritanian vlads you can buy for $US100 today, the average number of rivets the factory uses in an hour, and so on ... in other words, the human has to provide the meaning of the calculated result. Otherwise it has no meaning.
In mathematics, we have a name for personal opinions... we call them 'conjectures' or 'hypotheses'. A 'conjecture' is someone's hypothesis: a mathematical statement imagined to be true, but not having proof. And it is often the goal of future mathematicians to prove or disprove conjectures.
True, but the Riemann hypothesis is about as abstract, as conceptual, as lacking a real counterpart, as you could wish for. And when it's replaced by ArtieE's Theorem (Fields Medal winner 2022) showing that the hypothesis holds for all values, it'll still be as abstract, as lacking a real counterpart, as ever.
Okay, I take this to mean that you regard things which exist 'only in mentation' to be things that we imagine but that do not have 'real counterparts'.
Just so.
So, in this sense, 'three' also may refer to something with real existence. If I say, 'these three chairs' referring to the three chairs I see gathered around my kitchen table, three has a 'real counterpart' in that the thing to which I refer is manifest (in fact, self-evident).
The three chairs are an instantiation of the concept 'three'. They aren't the concept three itself. That still is only found in brains. That's why, until a human comes along and takes notice of the chairs, ie chooses (makes relevant) the room as the field, chair as the topic, and remarks their quantity, there's no threeness there, any more than there's (say) tenness for the room's furniture or twoness for the room's carpets unless and until someone deems those relevant and notices their quantity.
Whereas, if I were to say 'some group of three chairs' where the chairs to which I am now referring lack substance, then they 'exist only in mentation'.
They lack real identity. Instead we're dealing with the abstraction 'something to sit on' or whatever.
And when I physically move 'this particular kitchen chair' taking it away and putting it in the living room, I have, in fact, done 'real mathematics' (that is to say 'real subtraction') as there are now two chairs in my kitchen
You've done mental mathematics on real things. That's the only way that anything mathematical can occur. As I said, without selection of relevant fields and topics, there can be no maths applied to reality, and only brains make those selections.
While your 'chair' may be 'real' to you, it exists 'only in mentation' to me. Is your 'chair' both 'objective' and 'subjective' at the same time? To wit: it is the mathematics of the chairs that is objective and the physical existence of the chairs that is subjective.
So for you I'm sitting on 'a chair' which is for me 'this chair', yes. But we both know that there are many chairs in the world, so it's a matter of particularity, not a matter of existence (at least in this case). It's the way the brain works by such abstractions that's interesting.
hmmm, it sounds like you are well on your way to a morality of some sort.
Why not? I'm genetically a social animal, with behavioral traits and attitudes built in.
I don't regard it as my aim to convince you otherwise. But I do find it burdensome to qualify morality as 'not influenced by personal feelings or opinions in considering and representing facts' vs 'based on or influenced by personal feelings, tastes, or opinions'. Instead of calling it 'objective' vs 'subjective'.
What's an example of a moral rule not influenced by personal feelings? Isn't the whole basis of morality about how the individual relates to others? And from there
by extension to how groups relate?