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The Brain-in-a-vat argument is a skeptical challenge that questions the possibility of human knowledge, specifically regarding whether one can truly know they have hands [1] or that they are not a brain-in-a-vat [2]. The argument explores the conditions required for knowledge, such as the ability to discriminate between alternatives [3] and the application of the closure principle [4], while contextualists argue that the standards for what constitutes knowledge shift depending on the context {fact:12, fact:15}.

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Epistemology - Stanford Encyclopedia of Philosophy plato.stanford.edu Matthias Steup, Ram Neta · Stanford Encyclopedia of Philosophy 22 facts
claimWhen the possibility of being a Brain in a Vat (BIV) becomes salient, an individual's standards of knowledge rise, requiring the individual to be able to eliminate the error possibility of being a BIV to claim knowledge of having hands.
claimThe Brain-in-a-Vat (BIV) argument posits that if an individual cannot distinguish between being a brain-in-a-vat and not being one, they cannot distinguish between having hands and not having hands, leading to the conclusion that one cannot know they have hands.
claimThe Brain-in-a-Vat (BIV) argument posits that a person knows they have hands only if they can discriminate between the state of actually having hands and the alternative state of being a handless brain in a vat.
claimWhen the meaning of 'know' is fixed by high standards, humans know neither that they have hands nor that they are not Brains in a Vat (BIVs).
claimThe Moorean response to the Brain in a Vat (BIV) argument is considered insufficient by many philosophers because it merely asserts knowledge of not being a BIV based on knowledge of one's hands, rather than explaining how such knowledge is possible.
formulaThe application of the closure principle to the BIV argument is: If I know that I have hands, and I know that my having hands entails my not being a brain-in-a-vat, then I know that I'm not a brain-in-a-vat.
claimThe skeptical conclusion that one does not know they have hands is reached by applying the closure principle to the BIV argument, where the antecedent of the closure principle is considered false because the individual cannot know they are not a brain-in-a-vat.
claimRelevant alternatives theorists are committed to the claim that the closure principle is false because they assert that one can know they have hands and know that having hands entails not being a BIV, while simultaneously not knowing that they are not a BIV.
formulaThe BIV Argument is structured as follows: (1) I don't know that I'm not a brain-in-a-vat. (2) If I don't know that I'm not a brain-in-a-vat, then I don't know that I have hands. Therefore: (3) I don't know that I have hands.
claimContextualists resolve the paradox of the Brain in a Vat (BIV) argument by asserting that in low-standard contexts, the first premise and the conclusion of the BIV argument are false because we meet low standards of knowledge, whereas in high-standard contexts, the first premise and the conclusion are true because our epistemic position is not strong enough to meet high standards.
claimThe 'Counter BIV' argument proposed as a Moorean response consists of three parts: (1) I know that I have hands. (2) If I don't know that I'm not a BIV, then I don't know that I have hands. Therefore: (3) I know that I am not a BIV.
claimAmbiguity theorists assert that in the fallibilist sense of the word 'know', an individual can know that they are not a Brain in a Vat.
claimAn 'abominable conjunction' is a statement generated by denying the closure principle, exemplified by the assertion: 'I know that I have hands but I do not know that I am not a (handless) BIV.'
claimIn a low-standard context, the condition for knowing one has hands is simply the ability to discriminate between having hands and having stumps, hooks, or prosthetic hands, as the possibility of being a Brain in a Vat (BIV) is ignored.
claimThe 'semantic ascent' element of contextualism posits that a satisfactory response to skepticism and the Brain in a Vat (BIV) argument requires distinguishing between high-standards and low-standards meanings of 'knowledge'.
claimThe ambiguity response to the BIV (Brain in a Vat) argument posits that a 'knowledge'-attributing sentence expresses a proposition that depends on whether the speaker is using a high-standards or low-standards concept of knowledge.
claimThe ambiguity response to the BIV argument identifies three versions of the argument based on how the word 'know' is interpreted: the mixed version (infallible in premises, fallible in conclusion), the high-standards version (infallible in both), and the low-standards version (fallible in both).
claimMany epistemologists argue that the conjunction of knowing one has hands while not knowing one is not a Brain in a Vat (BIV) is abominable because it violates the intuition that one cannot know they have hands without knowing they are not a BIV.
claimContextualists assert that relative to the standards of knowledge operational in low-standards contexts, an individual can know that they are not a Brain in a Vat.
perspectiveRelevant alternatives theorists argue that an inability to discriminate between having hands and being a brain in a vat (BIV) does not prevent knowledge of having hands, because being a BIV is not a relevant alternative to having hands.
claimBecause the evidence available to a normal person and a brain-in-a-vat is identical, skeptics argue that a person cannot know they are not a brain-in-a-vat.
claimWhen the meaning of 'know' is fixed by low standards, humans know both that they have hands and that they are not Brains in a Vat (BIVs).
Epistemology (Stanford Encyclopedia of Philosophy/Fall 2019 Edition) plato.stanford.edu Stanford Encyclopedia of Philosophy 2 facts
claimIn an ordinary, low-standard context, the possibility of being a 'Brain in a Vat' (BIV) is ignored, allowing individuals to claim knowledge of having hands by simply discriminating between having hands and having stumps, hooks, or prosthetic hands.
claimThe 'low-standards' version of the Brain in a Vat (BIV) argument concludes that humans do not have even fallible knowledge of their hands, which is considered unsound and disturbing because it implies a radical mistake in what humans think they know.