Yes, but you haven't explained what kind of existence such purported objects might have, beyond being concrete (would be able to be sensed if the appropriately equipped percipient were present) or ideal (actually thought). It's true that we can all think numbers, but it does not seem to follow from this that numbers exist as objects, independently of being thought as objects. Our idea of concrete objects, on the other hands, is an idea of objects that exist independently of being sensed.

Objects that can be sensed are parts of spacetime. But what is spacetime? Theory of relativity treats spacetime as a mathematical structure, a kind of metric space where the dimension of time is a special kind of spatial dimension. And there are many other possible mathematical structures, for example pure spaces, without a time dimension. So objects that are parts of such spaces cannot be sensed, yet they are not in our heads either. And then there are mathematical structures that are not even metric or topological spaces, for example functions.

Existence, in its most general sense, is identity: any object that is identical to itself, exists. And it exists in the way in which it is defined. (note however that it must be defined consistently in relation to everything, otherwise its identity would be violated)

I'm not interested in considering Relativity theory in the context of this discussion. Spacetime is a theoretical construct; the question of its mind independent existence encounters exactly the same problems as that of mathematical objects as far I can tell.

It can - it is the reversed order to "smaller prior to bigger". Magnitude defines both orders. — litewave

So magnitude allows for opposite orders. It also allows for any other order that one might like to use, counting by tens by twenties, odd numbers, even numbers, Fibonacci order, subtracting magnitudes, dividing or multiplying magnitudes, any possible order. Since it allows for the possibility of opposite orders, and any other order, it really doesn't define order at all.

Some of those groups do. — litewave

Your condition was "all possible groups of points". If you restrict this to some groups, then we no longer have that initial condition. And if you restrict the group of points, to the definition of a line, then clearly we are not talking about all possible groups of points in a given space, we are talking about a defined line.

So magnitude allows for opposite orders. It also allows for any other order that one might like to use, counting by tens by twenties, odd numbers, even numbers, Fibonacci order, subtracting magnitudes, dividing or multiplying magnitudes, any possible order. Since it allows for the possibility of opposite orders, and any other order, it really doesn't define order at all. — Metaphysician Undercover

No, it defines all those orders you mentioned.

Your condition was "all possible groups of points". If you restrict this to some groups, then we no longer have that initial condition. And if you restrict the group of points, to the definition of a line, then clearly we are not talking about all possible groups of points in a given space, we are talking about a defined line. — Metaphysician Undercover

But the group of points that define a line is contained in the group of all possible groups of points, which is the space itself. So the line exists in the space, together with other lines and curves.

No, it defines all those orders you mentioned. — litewave

Obviously that's wrong, just like your claim that all the possible points in a space define al the lines, curves and angles. For an order to be defined, it must be defined, just like for a line, curve, or angle to be defined, it must be defined. The possibility of infinite different orders does not define those orders.

So if your objection want to be coherent, you must now admit that thoughts and ideas are not existentially dependent upon sensory perception.
— creativesoul

No, I gave thoughts and ideas, as examples of connections and correlations which are carried out completely within the living being, to support my premise that connections, correlations and associations are carried out completely within the being. Sensations are of things external to the living being and are therefore not a necessary part of such processes. — Metaphysician Undercover

:yikes:

No... and then explain why the correct answer is "yes"...

So, you admit that thoughts and ideas are not existentially dependent upon physiological sensory perception...

Right, so meaning does not require sensations, it appears like we now agree. So making connections, correlations and associations whereby a being establishes meaning, could be carried out by a being which does not sense. And in the evolution of living beings it is possible that they evolved so as to develop the capacity to make connections correlations and associations prior to being able to sense.

Where we disagree is whether sensation requires meaning. If it does, then meaning is prior to sensation and those primitive living beings which do not sense actually do establish meaning. Don't you see that sensation necessarily involves making connections, correlations and associations, through memory, and therefore sensation does requires meaning? Without these connections and associations and correlations to the past, each sensation would be like an entirely new experience to the being, and the being would be lost in the apparent randomness of it all, having completely new experiences at every moment of its life. This is not the case though as sensation is a useful thing to the being. It is useful because the being is drawing connections, correlations, etc., and therefore sensation itself is meaningful.