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STT
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Yes, I agree.It is pretty obvious that “[does not] have form independent of a thinker” should at least mean that the object ceases to exist when no one is thinking of it (there is no thinker), and that the thinker gets to decide what the form is going to be.
Numbers are abstract objects hence they are underlying of the reality. They don’t have form though independent of a thinker.Otherwise an object clearly has form somewhat independently of the thinker. Yet, apparently, that was not what you meant, since you do not think any “Little Johnny” can decide that 2+2=5, while claiming that numbers have form “not independently of thinker”.
I do agree with that definition. Why do you think like that?No, I do not agree with that definition. But that’s beside the point. The point is that you also do not really agree with that definition.
What has changed? The abstract objects mostly are not subject to time. Roman Empire existence however is subject to time as an abstract object.That completely misses the point. The point is that you cannot explain what changed when the Holy Roman Empire was disbanded. In your view, it was an abstract object and it stayed an abstract object. Thus, according to you, nothing has changed. And yet, it is clear that something has changed.
There is nothing mysterious about abstract objects. As I mentioned before they are underlying truth of reality without them our experiences become empty. You don’t need the God’s mind to find a place for abstract objects. Moreover I am not a disbeliever.If reality exists without a thinker, then so does any “underlying truth”. And thus you cannot keep all those claims - something has to go.
Actually, there is one argument for existence of God that points out that the only available place for abstract objects (like numbers) is God’s mind. But, since you deny God’s existence, abstract objects become mysterious to you…
That is true. They are all part of our experience. Experiencing something without shape is meaningless. I think we are lost on this part.That does not answer the question. In other places you have claimed that hearing and thinking also count as experiencing, so visibility shouldn’t be special here.
Angels are either abstract objects or they are real. Which one do you pick? Firs, it means that they just have form inside the mind of a thinker otherwise they have forms independent of thinker.That does not answer the question. You have also claimed that angels cannot be imagined and thus cannot be experienced. Are you taking that claim back?
Does the content of what you hear has a geometrical shape? No. But you can distinguish between different content. Why? Because they have forms.That does not answer the question. The question was not “Can you assert that something has form?”. We know that you can. In words of Hamlet, it is “as easy as lying”…No, the question was what those forms of aleph-zero, imaginary unit and quaternions actually are. You should give actual geometrical shapes, since that’s how you understand forms.
That is an obvious premise.Also, that begs the question - you haven’t shown that distinguishing objects requires difference of form yet.
Well, yes the content of a book can be represented as a set of characters or bits.That does not answer the question. (Are you beginning to see a pattern here?) You still are not giving meters, thus we only have bits and characters. And if something can be measured in bits and not in meters, then it has no definite geometrical shape - and all kinds of problems for your philosophy follow.
I just tried to explain that abstract objects have form inside a thinker’s mind as hearing has by providing some example. I think that the premise “Form is necessary for us to distinguish objects” is obvious.That does not answer the question. The question asked where do you get a premise like “Form is necessary for us to distinguish objects.”. Your answer does not address it in any way.
They could be simply a part of our experience.That does not answer the question (yes, neither here nor above). You haven’t explained how to imagine aleph-zero, imaginary unit or quaternions.
We cannot imagine/experience something which is not underlying of the reality.Neither have you taken back the claims that would seem to imply that imagining them is necessary.
A thing is an abstract object if it is the underlying of the reality and it could be experienced or imagined otherwise it does not exist.The obvious reason for that is that none of those objects can be imagined - and that’s fine. However, your philosophy demands that imagining them would be possible…
To be continued…