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The Cosmological Argument (causal series version)

  1A series of causes exists
  2No infinite or circular series of causes can exist
3There is a start to a series of causes(from 1 and 2)
4Some thing has no cause(from 3)
  5Every non-necessarily existent thing has a cause
6Something is uncaused and exists necessarily(from 4 and 5)

Huemer's Argument for Non-Egalitarianism

Source: Michael Huemer
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  1An equal distribution of welfare across an individual's life is not intrinsically valuable (i.e. it does not make their life better)
2Worlds 1 and 2 have equal value(from 1)
  3The value of a state of affairs supervenes on its non-evaluative properties
4Worlds 2a and 3a have equal value(from 3)
5Worlds 3a and 3b have equal value(from 3)
6Worlds 2a and 2b have equal value(from 3)
7Worlds 2a and 2b have equal value(from 3)
8Worlds 2b and 3b have equal value(from 4, 5, 6 and 7)
9The summed value of World 2a and World 2b equals that of World 3a and World 3b(from 4 and 8)
10Worlds 2 and 3 have equal value(from 9)
11Worlds 1 and 3 have equal value(from 2 and 10)
  12If equal welfare were intrinsically valuable, Worlds 1 and 3 would not have equal value
13Equal welfare is not intrinsically valuable(from 11 and 12)

Huemer's Argument for Intrapersonal Non-Egalitarianism

Source: Michael Huemer, 'Non-Egalitarianism', Philosophical Studies 114 (2003), p141-171
  1It is never rational to choose a smaller increase in welfare over a greater increase
  2If an equal distribution of welfare across an individual's life were intrinsically valuable, it could be rational for them to choose a smaller increase in welfare in low-welfare periods of their lives over a greater increase in welfare in high-welfare periods
3An equal distribution of welfare across an individual's life is not intrinsically valuable (i.e. it does not make their life better)(from 1 and 2)

The Cartesian Argument for Scepticism about the External World (brain-in-vat version)

Source: Rene Descartes
2
  1If you were a brain in a vat, you would be having the same sensory experiences as you are actually having
  2If something would be the case if a proposition were true, it is not evidence against that proposition
3Your sensory experiences are not evidence that you are not a brain in a vat(from 1 and 2)
  4Your sensory experiences are the only evidence you have for propositions about the external world
  5The proposition that you are not a brain in a vat is a proposition about the external world
6You have no evidence that you are not a brain in a vat(from 3, 4 and 5)
  7For you to have justification for the proposition that you are not a brain in a vat, you must have evidence for it
8You have no justification for the proposition that you are not a brain in a vat(from 6 and 7)
  9For your beliefs about the external world to be justified, you must have justification for the proposition that you are not a brain in a vat
10Your beliefs about the external world are not justified(from 8 and 9)

Aquinas's First Way

Source: Thomas Aquinas, Summa Theologica
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  1Something is in motion
  2Everything in motion must have been moved by something else
  3An infinite regress of transfer of motion is impossible
4There is an Unmoved Mover ultimately responsible for the motion of something(from 1, 2 and 3)

Berkeley's P1-P3 argument against matter's comprehensibility (A)

Source: George Berkeley, Sections 1-3 of Berkeley's Principles of Human Knowledge
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  1The only comprehensible properties are those of which we are directly aware
  2The only properties of which we are directly aware are those of sensations and thoughts, or the property of 'being a mind'
  3The properties of sensations are all mind-dependent
  4The properties of thoughts and the property of 'being a mind' are all mind-dependent
5The only comprehensible properties are mind-dependent(from 1, 2, 3 and 4)
  6Matter is that which can exist mind-independently
  7Something cannot exist mind-independently if some of its properties are mind-dependent
8The concept of matter is incomprehensible(from 5, 6 and 7)

Berkeley's P1-P3 argument against matter's comprehensibility (B)

Source: George Berkeley, Sections 1-3 of Berkeley's Principles of Human Knowledge
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  1The only comprehensible properties are those of which we are directly aware
  2The only properties that material substance could have of which we are directly aware are properties of sensations
  3The properties of sensations are all mind-dependent
4The only comprehensible properties that material substance could have are mind-dependent(from 1, 2 and 3)
  5Matter is that which can exist mind-independently
  6Something cannot exist mind-independently if some of its properties are mind-dependent
7The concept of matter is incomprehensible(from 4, 5 and 6)

Berkeley's assimilation argument

Source: George Berkeley, Section 4 of Berkeley's Principles of Human Knowledge
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  1You cannot form new concepts of properties by abstracting away aspects of properties you already understand - for example you cannot understand the property of being a colourless shape on the basis of having seen coloured shapes
  2All properties of sensations have phenomenal aspects could only belong to sensations (colours for visual experiences of shapes, etc.) {Berkeley's Likeness Principle}
3The properties of sensations are all mind-dependent(from 1 and 2)

Berkeley's P4 argument for the mind-dependence of sensible objects

Source: George Berkeley
4
  1Sensible objects, like houses, mountains and rivers, are perceived by sense
  2Only sensations are perceived by sense
3Sensible objects are sensations or collections thereof(from 1 and 2)
  4Sensations are mind-dependent
5Sensible objects] are [mind-dependent(from 3 and 4)

From the undeserved nature of unequal status to egalitarianism

  1If someone enjoys wealth due to having properties that they do not deserve, then they do not deserve that wealth.
  2All wealth that people enjoy is due to properties that they do not deserve to have (such as being born clever, or diligent, or to wealthy parents)
3All wealth is undeserved(from 1 and 2)
  4Unless someone deserves a greater-than-average share of wealth, they should not have it
5No one should have a greater-than-average share of wealth(from 3 and 4)

The physicalist argument for moral scepticism

  1Only claims in the best physics are true
  2No moral claims will feature in the best physics
3Some moral claims are true(from 1 and 2)

A reductio of physicalism

Source: Russ Shafer-Landau, Moral Realism: A Defence (OUP, 2003), p81
  1The best physics will not include the claim that only its claims are true
  2It cannot be the case both that only claims in the best physics are true and that the best physics will not include the claim that only its claims are true
3Some claims not in the best physics are true(from 1 and 2)

The natural embryo loss reductio of anti-abortionism

Source: Toby Ord, 'The Scourge: Moral Implications of Natural Embryo Loss', The American Journal of Bioethics 8 (2008), p12-19
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  1Vast numbers of embryos experience spontaneous, natural abortion
  2That vast numbers of embryos experience spontaneous, natural abortion is not an enormous problem demanding great efforts to solve
  3If embryos have the same moral status as adult human beings and vast numbers experience spontaneous, natural abortion, then this is an enormous problem demanding great efforts to solve
4Embryos do not have the same moral status as adult human beings(from 1, 2 and 3)

The physicalist attack on moral beliefs (abductive version)

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  1Moral truths are not the sort of thing that can figure in scientific explanations of physical phenomena
  2Our beliefs supervene on physical phenomena
3There is no plausible explanation of our belief in moral claims which relies on their truth(from 1 and 2)
4The explanation of our beliefs in moral claims does not rely on their truth(from 3)
  5If our holding of a belief that could be false is not explained by the belief's truth, then it is not probably true (COME BACK AND EDIT: HOW TO PHRASE THE PRINCIPLE IN MY THESIS?)
6Our beliefs in moral claims are true(from 4 and 5)

The abductive argument from our belief in moral claims to moral realism

  1There is a plausible explanation of our belief in moral claims which relies on their truth
  2There is no plausible error theory (explanation of our belief in moral claims which doesn't rely on their truth)
3The truth of some moral claims is the best explanation of our belief in them(from 1 and 2)
  4We believe in some moral claims
5Some moral claims are true(from 3 and 4)

The causal constraint on appropriate belief defended in terms of truth-reliant explanations

  1If something would not cause anything, then it would not cause our belief in it
  2If something would not cause our belief in it, then the explanation of that belief cannot rely on its truth
3If something would not cause anything, then the explanation of our belief in it cannot rely on that belief%u2019s truth(from 1 and 2)
  4If our holding of a belief that could be false is not explained by the belief's truth, then it is not probably true (COME BACK AND EDIT: HOW TO PHRASE THE PRINCIPLE IN MY THESIS?)
  5If a belief is not probably true then it is not appropriate
6If something would not cause anything, then it's not appropriate to believe in it if that belief could be false(from 3, 4 and 5)

The causal constraint on appropriate belief defended abductively in terms of truth-reliant explanati

  1If something would not cause anything, then it would not cause our belief in it
  2If something would not cause our belief in it, then the explanation of that belief cannot rely on its truth
3If something would not cause anything, then there is no plausible explanation of our belief in it that relies on its truth(from 1 and 2)
4If something would not cause anything, then the explanation of our belief in it cannot rely on that belief%u2019s truth(from 3)
  5If our holding of a belief that could be false is not explained by the belief's truth, then it is not probably true (COME BACK AND EDIT: HOW TO PHRASE THE PRINCIPLE IN MY THESIS?)
  6If a belief is not probably true then it is not appropriate
7If something would not cause anything, then it's not appropriate to believe in it if that belief could be false(from 4, 5 and 6)

The argument against moral realism from the causal constraint on appropriate belief

Source: Russ Shafer-Landau, Moral Realism: A Defence (OUP, 2003), p106
  1Moral facts don't cause anything in the non-moral realm
  2Moral facts don't cause anything in the moral realm
3Moral facts don%u2019t cause anything(from 1 and 2)
  4If something would not cause anything, then it's not appropriate to believe in it if that belief could be false
5Some moral claims are true(from 3 and 4)

The physicalist attack on moral beliefs (non-abductive version)

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  1The explanation of our beliefs in moral claims relies on their truth
  2Our beliefs supervene on physical phenomena
3Moral truths are the sort of thing that can figure in scientific explanations of physical phenomena(from 1 and 2)
  4The explanation of our beliefs in moral claims does not rely on their truth
  5If our holding of a belief that could be false is not explained by the belief's truth, then it is not probably true (COME BACK AND EDIT: HOW TO PHRASE THE PRINCIPLE IN MY THESIS?)
6Our beliefs in moral claims are true(from 4 and 5)

The Humean argument against induction (version involving absence of reasons other than circular dedu

Source: David Hume
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  1A good reason for believing a proposition cannot rely on that proposition
2If we have a good reason for thinking observed regularities to hold universally, it cannot rely on this belief itself(from 1)
3Our reason for thinking observed regularities to hold universally cannot be that they have always done so so far as we%u2019ve observed, and such observed phenomena hold universally(from 2)
  4We have no good reason for thinking observed regularities to hold universally besides that they have always done so so far as we%u2019ve observed, and such observed phenomena hold universally (not meaning that this is a good reason)
5We have no good reason for thinking observed regularities to hold universally(from 3 and 4)

The Humean argument against induction (version involving absence of reasons other than induction's p

Source: David Hume
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  1A good reason for believing a proposition cannot rely on that proposition
2If we have a good reason for thinking observed regularities to hold universally, it cannot rely on this belief itself(from 1)
3Our reason for thinking observed regularities to hold universally cannot be that they have always done so so far as we%u2019ve observed, and such observed phenomena hold universally(from 2)
  4The fact that observed regularities have always held universally even after additional observation does not entail that they do so universally absent an extra premise equivalent to the proposition that observed regularities hold universally
5Our reason for thinking observed regularities to hold universally cannot be a deduction from the fact they have always done so so far, even after additional observation(from 3 and 4)
  6Any reason we have for thinking observed regularities to hold universally must involve the fact they have always done so so far, even after additional observation
7Any reason we have for thinking observed regularities to hold universally cannot be deductive(from 5 and 6)
8Any reason we have for thinking observed regularities to hold universally cannot be deductive(from 5 and 6)
  9Any reason we have for thinking observed regularities to hold universally must be deductive
10We have no good reason for thinking observed regularities to hold universally(from 7, 8 and 9)

Fitch%u2019s Paradox (simple phrasing)

Source: Frederic Fitch, 'A Logical Analysis of Some Value Concepts' (1963)
  1There is a proposition p (its contents not specified here) which is true, but not known to be true
  2No one can know that a proposition p (where p is a specified proposition, with a particular content they have in mind) is both true and not known to be true (rationale: if they know that it is true, then it is known to be true - by them)
  3If all truths are knowable and there is a proposition p (where p is a specified proposition) which is true, but not known to be true, then it is knowable that this is so
4Not all truths are knowable(from 1, 2 and 3)

Reductio ad absurdum of the proposition that someone can know that a proposition p is true and not k

Source: Frederic Fitch, 'A Logical Analysis of Some Value Concepts' (1963)
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  1Someone can know that a proposition p (where p is a specified proposition, with a particular content they have in mind) is both true and not known to be true (%u25CAK(p %u2227 ¬Kp))
2Someone can know that a proposition p (where p is a specified proposition, with a particular content they have in mind) is both true and know that it is not known to be true (%u25CA(Kp %u2227 K¬Kp))(from 1)
  3If someone knows something, then it must be true
4Someone can know that a proposition p (where p is a specified proposition, with a particular content they have in mind) is true and not know that it is true(%u25CA(Kp %u2227 ¬Kp))(from 2 and 3)

The argument for non-cognitivism from Humeanism about moral motivation

Source: Russ Shafer-Landau, Moral Realism: A Defence (OUP, 2003), p121
  1The acceptance of a moral statement provides an effective motive for action by itself
  2Beliefs do not provide effective motive for action by themselves Comments icon
3Moral statements do not express beliefs(from 1 and 2)

The argument from direction of fit to Humeanism

Source: Michael Smith, The Moral Problem (Blackwell, 1994), p116
  1Having a motivating reason involves having a goal
  2Having a goal is being in a state which the world must fit, as opposed to believing which is being in a state which must fit the world
  3Being in a state which the world must fit is having a desire
4Having a motivating reason involves having a desire(from 1, 2 and 3)

Argument for motivational judgement externalism from the imaginability of amoralists

Source: Russ Shafer-Landau, Moral Realism: A Defence (OUP, 2003), p146
  1If we can imagine something, then it is conceptually possible
  2We can imagine an amoralist
3An amoralist is conceptually possible(from 1 and 2)
  4If an amoralist is conceptually possible, then motivational judgement internalism is false
5Motivational judgement internalism (the position that judging an action to be right involves being defeasibly motivated to do it) is false(from 3 and 4)

The argument from dualism to epiphenomenalism by rejection of causal overdetermination

Source: Jaegwon Kim, Mind in a Physical World (MIT Press, 1998)
  1Every physical event has a physical cause
  2Mental states are not physical states
3If mental events cause physical events, then there is causal overdetermination(from 1 and 2)
  4There is no causal overdetermination
5Mental events do not cause physical events(from 3 and 4)

The argument from dualism to epiphenomenalism by rejection of the Causal Inheritance Principle

  1Mental states are not physical states
  2When states supervene on other states which cause certain events, the supervening states do not inherit this property of being the causes of these events
3If mental events caused physical events, then physical events could be caused without any physical cause(from 1 and 2)
  4Physical events cannot be caused without any physical cause
5Mental events do not cause physical events(from 3 and 4)

The argument for physicalism from the causal closure of the physical

  1Physical events cannot have non-physical causes Comments icon
  2Mental events cause physical events
3Mental events are physical events(from 1 and 2)

The conceivability argument for the possibility of zombies

  1God does not exist
  2The only being to whom our feelings of conscience could reflect responsibility, shame and fear is God
3With regards to our feelings of conscience, there is no one %u201Cto whom we are responsible, before whom we are ashamed, whose claims upon us we fear%u201D(from 1 and 2)

The Chinese Room argument (simple version)

Source: John Searle, 'Minds, Brains and Programs' in Behavioral and Brain Sciences 3 (1980), p417%u201357
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  1A man in a Chinese Room cannot understand Chinese
  2If following procedures which let an agent respond to Chinese questions with Chinese answers indistinguishable from those of a Chinese-speaker were sufficient for understanding Chinese, a man in a Chinese Room would understand Chinese
3Following procedures which let an agent respond to Chinese questions with Chinese answers indistinguishable from those of a Chinese-speaker is not sufficient for understanding Chinese(from 1 and 2)

The Chinese Room argument (covering the Systems Reply)

Source: John Searle, 'Minds, Brains and Programs' in Behavioral and Brain Sciences 3 (1980), p417%u201357
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  1The complete system of the Chinese Room cannot understand Chinese
  2If instantiating a complete system which responds to Chinese questions with Chinese answers indistinguishable from those of a Chinese-speaker were sufficient for understanding Chinese, the Chinese Room system would understand Chinese
3Instantiating a complete system which responds to Chinese questions with Chinese answers indistinguishable from those of a Chinese-speaker is not sufficient for understanding Chinese(from 1 and 2)

The Chinese Room argument (covering the Robot Reply)

Source: John Searle, 'Minds, Brains and Programs' in Behavioral and Brain Sciences 3 (1980), p417%u201357
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  1A Chinese Robot cannot understand Chinese
  2If instantiating a system which responds to both external objects and Chinese questions with Chinese conversation indistinguishable from that of a Chinese-speaker were sufficient for understanding Chinese, a Chinese Robot would understand Chinese
3Instantiating a system which responds to both external objects and Chinese questions with Chinese conversation indistinguishable from that of a Chinese-speaker is not sufficient for understanding Chinese(from 1 and 2)

The regress argument for scepticism

  1For a belief to be justified, we must have another justified belief which is our reason for it
2For any justified belief we have, we must have a justified belief which is our reason for it, and a justified belief which is our reason for that, and so on in an endless chain(from 1)
  3The chain of reasons required for a justified belief cannot involved the repetition of any beliefs (such as a belief that the world is flat being the reason for thinking it has edges and a belief that it has edges being a reason for thinking it is flat)
4For any justified belief we have, we must have a justified belief which is our reason for it, and a justified belief which is our reason for that, and so on in an endless chain involving no repetition of beliefs(from 2 and 3)
5If we have any justified beliefs, we must have infinitely many different beliefs(from 4)
  6We cannot have infinitely many different beliefs
7We do not have any justified beliefs(from 5 and 6)
8We do not have any justified beliefs(from 5 and 6)

The problem of the criterion

Source: This formulation comes from Michael Huemer's Skepticism and the Veil of Perception (Rowman and Littlefield, 2001), p13. The classic ancient presentation of the problem comes from Sextus Empiricus was an ancient source of the problem (see Scepticism, Man, and God, edited by Peter Hallie (Wesleyan University Press, 1964), p145-146
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  1All our beliefs are formed by some method
  2We do not have an infinite series of belief-forming methods
3All our beliefs must rest on beliefs formed by methods whose reliability has not first been established(from 1 and 2)
  4We are justified in accepting beliefs formed by method M only if we are already justified in thinking that M is reliable
5We do not have any justified beliefs(from 3 and 4)

Voltaire’s immutability argument against the possibility of miracles

Source: Voltaire, Philosophical Dictionary, in The Works of Voltaire (E. R. DuMont, 1901), volume 11, p272
  1A miracle is a violation of immutable natural laws by God
  2Immutable natural laws cannot be violated
3Miracles are impossible(from 1 and 2)

The deist argument against miracles

Source: Voltaire, Philosophical Dictionary, in The Works of Voltaire (E. R. DuMont, 1901), volume 11, p273
  1A miracle is a violation of the laws of nature by God
  2If a law of nature would be violated by God, He would not have created it Comments icon
3Miracles are impossible(from 1 and 2)

Hume’s argument against believing in miracles

Source: Hume, 'Of Miracles'. (This reconstruction is similar to that in Alan Hájek’s 'Are Miracles Chimerical?', in Oxford Studies in Philosophy of Religion 1, edited by Jonathan Kvanvig (OUP), p88. It is modified to avoid an invalidity Hájek points out.)
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  1We only believe in laws of nature when we%u2019ve experienced an overwhelming number of instances of them, with no exceptions
2We have the strongest possible experiential reason to believe laws of nature are not violated(from 1)
3Our experiential reason to believe in a miracle (be it from testimony or our own observation) cannot be stronger than our experiential reason to believe laws of nature are not violated, since we sometimes experience testimony and observation to be wrong(from 2)
  4Our only reason to believe in miracles is experiential
  5A miracle is a violation of the laws of nature by God
6Our reason to believe in miracles is at least counterbalanced by our reason to believe laws of nature are not violated(from 3, 4 and 5)
7We have no reason to believe in miracles(from 6)

Hume’s argument for disbelieving in miracles

Source: Hume, 'Of Miracles'. (This reconstruction is similar to that in Alan Hájek’s 'Are Miracles Chimerical?', in Oxford Studies in Philosophy of Religion 1, edited by Jonathan Kvanvig (OUP), p88. It is modified to avoid an invalidity Hájek points out.)
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  1We only believe in laws of nature when we%u2019ve experienced an overwhelming number of instances of them, with no exceptions
  2We sometimes experience testimony and observation to be wrong
3Our experiential reason to believe in a miracle (be it from testimony or our own observation) cannot be as strong as our experiential reason to believe laws of nature are not violated(from 1 and 2)
  4Our only reason to believe in miracles is experiential
  5A miracle is a violation of the laws of nature by God
6Our reason to believe in miracles is outweighed by our reason to believe laws of nature are not violated(from 3, 4 and 5)
7We have reason to believe miracles do not occur(from 6)

The argument for theism as a basis for morality (divine commandment version)

  1Some moral claims are true
  2Moral claims are commandments
  3Commandments require a commander
4There is a commander whose commands are the basis of moral truths(from 1, 2 and 3)
  5The only commander whose commands could be the basis of moral truths is God
6God exists(from 4 and 5)