Questions tagged [self-reference]
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Gödel's Incompleteness Theorem
I'll keep this short and sweet.
Construct Axiomatic System A in which we can do math.
Gödel Sentence G = G is unprovable in A.
Gödel's Argument (I)
If G is provable then there's proof that G has no ...
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In the liar/similar sentences, are the characteristic predicates being used more generally or more particularly, or neither?
Between (1) and (2), it seems like "is true" is more particular in the latter than the former:
The truth predicate ("is true") is a predicate attaching to (interpreted) sentences ...
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Conjunctive imperatives can be in-itself imperatives?
One of Hannah Arendt's claims about the more abstract side of totalitarianism was a resistance to doing things "for their own sakes," but so where everything was made to subserve an ever-...
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Would, "Don't run this program," pose a similar problem as, "Don't comply with this imperative"?
I was reading the SEP article on philosophy and computer science and there was this passage:
Suber (1988) goes even further, maintaining that hardware is a kind of software. Software is defined as ...
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Can, "This problem is unsolvable," be used to formulate the first incompleteness theorem in erotetic logic specifically?
Assumptions/definitions: the Gödel sentence is informally equivalent to, "This sentence can't be proved in system X," where X is appropriately specified. Since that sentence can itself be ...
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"Impredicative" definitions in mathematics
In this blog post, the following definition of an "impredicative definition" is offered:
A definition is said to be impredicative if it defines an object E by means of a quantification over a ...
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"I vow that this sentence 𝘸𝘪𝘭𝘭 be true," vs., "I vow that this sentence 𝘴𝘩𝘢𝘭𝘭 be true"
To try to "explain" why the liar sentence is "logically dangerous" whereas the Gödel sentence is "logically helpful," I tried out contrasting the differing "effect&...
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How can I optimize the attributes of God?
The Problem
The three traditional attributes of God (in whichever tradition it is) are omnipotence, omniscience, and omnibenevolence. Under the assumption that reasonable discussion of God is possible,...
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Is there some formal system of "first-person logic"?
The SEP article on indexicals mentions a lot of the seemingly logical complications that arise in connection with them. Indexicals are also comparable to variables and hence objects of schematism, so ...
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Kant's transcendental apperception and 'ipseity' in phenomenology
In the writings of various phenomenologists, the concept of 'ipseity' is widely discussed. As far as I can make out from various sources (e.g. Zahavi, Subjectivity and Selfhood, esp. chapter 5), ...
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Does the cardinal Yablo problem have the same solution as the ordinal one?
To quote Kant (as usual!):
A quantity is infinite, if a greater than itself cannot possibly exist. The quantity is measured by the number of given units- which are taken as a standard—contained in it....
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How should we characterize the logical structure of wishes?
The motivation for this question is extraordinarily stupid, but it requires just enough thought and specific knowledge of formal logic that I think it still falls within the broad scope of "...
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Is there a conflict between self-reference and ontology? (In relation to mathematics)
I am a total layman when it comes to math, but I promise at least to clearly spell out my thought process.
Some like Elaine Landry say "mathematics is not metaphysics" https://youtu.be/...
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What's (if anything) wrong with this argument for the non-existence of the self?
1: The self, if it exists, is a thing that receives and/or controls experience. Some aspects of experience it controls, other aspects it receives. But whether the experience is "controlled" ...
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The type of all types, the type of being a token
Do descriptions like those result in paradox or antinomy like "set of all sets" or (nLab seems to say at one point) "category of all categories" do? It seems that the type of types ...
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Are actions self-referential? [closed]
Someone recently told me that "actions are self-referential" (which means that we do not have to specify a particular actor to know whether an action is possible or not).
He made it sound as ...
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Assigning "self-awareness" to qualia as a necessary attribute [duplicate]
The teleportation question which I'm sure most of you have researched,
If I replicate you atom for atom, which one of them will be you?
The issue of materialistic basis for consciousness posits a ...
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Can these selfreferential statements be rewritten as such?
This statement is a paradox = this statement is both true and false
this statement is a hypodox = this statement is either true or false
this statement is a contradiction/always false = this ...
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always false vs necessarily false , is it the same?
according to the basic tenets of classical propositional logic, contradictions are 'always false' tautologies 'always true'.
When it is extended to modal logic we have the notions of 'necessarily ...
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Liars paradox towards a solution?
This statement is not true
2.This statement is true only if true and not true.
(1) and (2) are clearly different sentences, but do they express the same proposition?
If yes, then it becomes clear ...
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What is the self? [closed]
Let us accept that science has an answer. The self then would be a representation of one's own body in the context of the environment. However if that is true wouldn't it imply that something is aware ...
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SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC
Hello can someone explain me exacty how in this fragment of the paper (SELF-REFERENCE AND THE LANGUAGES OF ARITHMETIC, RICHARDG.HECK,JR.):
(9) Tr(x) ≡∃y(rhs(x,y)∧¬Tr(y)), where rhs(x,y) is a formula ...
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Can we create a paradox of self-consciousness?
On the theme of Russell's paradox:
Does the set of all sets that do not contain themselves contain itself?
And the Barber's paradox:
Does a barber who shaves all men who do not shave themselves ...
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The origin of a particular self-reference paradox
This is a simple reference request, for the origin of a particular type of paradoxical statement. The example I remember is
Roger Penrose can't consistently claim this statement to be true.
It's a ...
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