They can be, I didn't mean to exclude this possibility; I was only explaining Frege's position on this. But yes, we could allow that fictional entitie...
An abstract object. In fact, for Frege it references as extension (of a second-level concept). To be a bit more modern: it would pick out a particular...
Hey Wayfarer, I do not have the time for a considered reply to this, but I can reply to the issue about imaginary or fictional objects, so I will do t...
Getting Clear on how to Formulate the Law of Identity, and why we need to be logically precise In logic, it is important to note that arbitrary refere...
Typically, we say that rules or, rather, norms are constitutive. If we think that mathematics is logic (logicist position), then we still have the pro...
All things are identical to themselves. Which is exactly the formulation I discussed and exactly the principle that implies nothing with respect to th...
I guess I pressed for more explanation on these claims. I am not sure that they simply don't amount to the mere assertion that there is a difference b...
This is the view that logic is constitutively normative for thought. That is, the norms themselves make thinking possible, just as the rules of a game...
Hi Mephist, I am very curious about this. Doesn't the vector's length follow from the Pythagorean theorem? If so, then it seems it isn't a simple logi...
Why empiricist or naturalist? They would at least want to deny that there are abstract objects. One route to do this is to say that mathematical langu...
? I am not sure where you are getting this and why you think it is true. Could you clarify? In no suitable formulation of the law of identity would it...
This is an extremely interesting claim, and if we could make it precise, it would be very helpful in the debate on Consciousness. I am not well versed...
This pretty much sums up the appropriate response to the OP as well. The entire claim is a conditional claim of this sort, which is why it is not cont...
That is not a suitable definition for 'object' in philosophy at all. An object is whatever can be the semantic reference of a term. This includes abst...
But this is my point: you are misusing "objective validation". Arithmetical propositions are necessarily true and deductively certain. They are object...
But the variable need not refer in certain models, since certain models may be empty. But it is true nonetheless since it is a quantified statement. C...
Hi MU, I apologize: I should not have assumed you were familiar with this; that is completely on me. I am employing standard first-order logic notatio...
But we know now, because of mathematical advances in logic, that this principle does not assume the existence of anything. The statement (\forall x) (...
My apologies if this other conception of necessity was being deployed. I know very little of it. I was using the contemporary idea of necessity (as it...
The law of identity is a law of logic; it is not an ontological principle. Perhaps you mean Leibniz's law of indiscernibles? There is a notable and im...
This has no bearing on whether or not a proposition is objective or whether or not it is true (or false). A proposition can be objective even if a per...
Thanks Wayfarer for your response! Indeed, I would say that the symbol "7" refers to the object 7. I do not use the term "object" metaphorically at al...
Hi Leo, Thanks for the reply, but I have to admit that as it stands this does not seem to be a defensible position. I used that sentence as an example...
I have to admit I was not able to read through all the posts carefully here, but I believe there is something we all seem to be conflating: truth and ...
(Thanks for the reply!) Of course it can. While it is still an open dispute in the philosophy of mathematics, ontological realists argue for the exist...
Hi Tim, Thanks for the response. I am not quite sure I know exactly what you intend to mean by your first sentence. That is, I am not sure what exactl...
The law of identity should stated as: \forall x (x=x). However, when you write: I believe you are importing metaphysical claims into the law of identi...
Hey Tim, It is absolutely true that there is the possibility for there to exist multiple, distinct necessary beings. However, neither claims (1) or (2...
Hey fresco, you are right to point out that @CurlyHairedCobbler presented an argument that seems to take the form: {P\rightarrow Q, \neg Q}\vdash \neg...
Hey Gilbert, I think this question has already been answered quite well by fdrake and ssu. I thought I would offer a less technical answer (though hop...
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