A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can then be built up from a few initial values and a small number of rules. The Fibonacci numbers are most commonly defined recursively. Care, however, must be taken to avoid self-recursion, in which an object is defined in terms of itself, leading to an infinite nesting.
.Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress.
No.You're equivocating between two different definitions of "self". The first is the conscious experience we're having right now; the traditional "self"(1). This is the context in which someone says "look at that orange tree". The second definition, which comes from solipsism, is "the source of everything that exists"(2.1) or "the only real mind"(2.2). So when a solipsist encounters a tree they could think/say: "look at that tree which does not exist in any reality external to some conscious or unconscious part of my mind" . — VagabondSpectre
My second point is that solipsism is and always has been presented as a possible explanation for phenomenon, not a rejection of the existence of phenomenon. Saying that if solipsism were true there would be no trees blatantly misrepresents the inherent thrust of solipsism. The single object universe you describe as "self-referential" isn't solipsism because it says nothing about the nature of the phenomenon we perceive as solipsism does; it depends on their non-existence to be an apt objection. — VagabondSpectre
My mind all the way back is no more problematic than turtles all the way down... — VagabondSpectre
I am saying that if solipsism was true then the only thing it would be possible to reference would be the self which is self recursive and leads to an ill defined infinite regress.
I don't care what definition of self you use, if there exists only one object and that object includes a reference to something, it will be a referencing only of itself.
That simply cannot be avoided. — m-theory
Because we reach conclusions all the time within a finite amount of steps and without any issue this means we can be logically certain that solipsism is not really what is going on ontologically or epistemologically. — m-theory
So saying turtles all the way down never gets you to the bottom, just like saying only the self exists would never allow you to reach a conclusion about the existence of self or anything else. — m-theory
The self cannot be logically equivalent in reality to the non-self without infinite regress of self recursion. — m-theory
Under metaphysical solipsism ("the world and other minds do not have objective "existence"."), everything that exists is presumed to be a part of one's own mind, but not equivalent to one's own mind (that's kinda the whole ontological point of solipsism). The "Mind" ("self"(2)) encompasses everything that exists, including "self"(1). Everything that exists, as a whole, is "the mind". The "self"(1) is a part of this whole, and the stimuli the self(1) experiences (like trees and animals) is also a part of the greater "mind" (the whole), but it (a tree) is neither equivalent to self(1) or self(2). It is a thing generated by self(2) and perceived by self(1) (under metaphysical solipsism). — VagabondSpectre
If I say things such as "That tree is actually just my own mental phenomena," and "You are just my own mental phenomena." "Only my mental phenomena exist," would you say that that is sufficient for me to be a solipsist? If not, why not? — Terrapin Station
And if it is, I'm asking you where, in this specific example, some infinite regress comes into play with my hypothetical views there.) — Terrapin Station
Note that when defining objects with recursion objects are treated as though they exist independently from each other, even if they are considered the same object each one must exist independently.A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of recurrence relation, the entire class of objects can then be built up from a few initial values and a small number of rules.
This will apply in the case where objects do not have any independent existence.Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress.
So this will mean to formally/logically apply properties.A definition assigns properties to some sort of mathematical object.
Again this is not a semantic issue that I raise it is syntactical one.I'm not asking you with respect to things you'd need me to say in order for there to be an infinite regress. (And regarding that, by the way, I might very well say, for example, that there is no such thing as perception in reality; I could say that perception is a non-solpsistic concept, a fictional interpretation of my solipsistic mental phenomena. So it's not the case that everything is "subjective perception" because a fortiori it's not the case that anything is perception. But this is an aside, please address the other part instead.) — Terrapin Station
Re my request, I'm also asking for a specific example of what you think I'd need to say (that is, the sort of thing I'd need to say) that would be an infinite regress given "That tree is actually just my own mental phenomena" etc. In other words, give me a quote, not an abstract description as you did above. I want to examine how a hypothetical conversation would go, as if we were writing a Socratic dialogue. — Terrapin Station
https://en.wikipedia.org/wiki/Curry's_paradox#Language_capabilities_for_expressing_the_paradoxCurry's paradox can be formulated in any language supporting basic logic operations that also allows a self-recursive function to be constructed as an expression. The following list gives some mechanisms that support the construction of the paradox but the list is not exhaustive....
...The self-recursive function can then be used to define a non terminating computation whose value is solution to an equation. In Curry's Paradox we use implication to construct a negation, that constructs an equation with no solution.
How can you really define the distinction between objective and subjective if we only ever are subjective.
The objective world remains only ever an inference at best. — intrapersona
Curry's paradox can be formulated in any language supporting basic logic operations that also allows a self-recursive function to be constructed as an expression. The following list gives some mechanisms that support the construction of the paradox but the list is not exhaustive.
1. Self-reference; "this sentence".
2. Through naming of an expression which includes the name.
2. Apply naive set theory (Unrestricted comprehension).
The logic rules used in the construction of the proof are,
1. rule of assumption for conditional proof
2. contraction
3. modus ponens
The self-recursive function can then be used to define a non-terminating computation whose value is solution to an equation. In Curry's Paradox we use implication to construct a negation, that constructs an equation with no solution.
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