Dialetheism - Revision history

𝗔𝗿𝗰𝗵𝗮𝗻𝗴𝗲𝗹: Text replacement - "tbe" to "the"

2023-09-12T21:55:23Z

Text replacement - "tbe" to "the"

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Bacchus: Text replacement - "the" to "tbe"

2023-09-08T21:09:08Z

Text replacement - "the" to "tbe"

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𝗔𝗿𝗰𝗵𝗮𝗻𝗴𝗲𝗹: Text replacement - "oTher" to "other"

2023-03-13T21:00:29Z

Text replacement - "oTher" to "other"

WikiSysop: Text replacement - " The " to " the "

2023-02-27T08:10:05Z

Text replacement - " The " to " the "

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Bacchus: Text replacement - "tbe" to "the"

2023-02-25T09:34:56Z

Text replacement - "tbe" to "the"

← Older revision		Revision as of 00:34, 25 February 2023
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	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because ~~tbey~~ cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because they cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, ~~tbey~~ are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, they are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

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	In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>		In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>

	Because dialeTheists accept true contradictions, ~~tbey~~ reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.		Because dialeTheists accept true contradictions, they reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

	DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that ~~tbey~~ are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>		DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that they are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>

	==Advantages==		==Advantages==
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	==Zen [[Buddhism]]==		==Zen [[Buddhism]]==
	Many modern Zen Buddhists are dialeTheists. ~~tbey~~ use The term [[nondualism]] to refer to true contradictions.		Many modern Zen Buddhists are dialeTheists. they use The term [[nondualism]] to refer to true contradictions.

	==Reading==		==Reading==

WikiSysop: Text replacement - "the" to "tbe"

2023-02-22T21:38:19Z

Text replacement - "the" to "tbe"

← Older revision		Revision as of 12:38, 22 February 2023
Line 7:		Line 7:
	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because ~~they~~ cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because tbey cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, ~~they~~ are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, tbey are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

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	In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>		In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>

	Because dialeTheists accept true contradictions, ~~they~~ reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.		Because dialeTheists accept true contradictions, tbey reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

	DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that ~~they~~ are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>		DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that tbey are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>

	==Advantages==		==Advantages==
Line 50:		Line 50:

	==Zen [[Buddhism]]==		==Zen [[Buddhism]]==
	Many modern Zen Buddhists are dialeTheists. ~~they~~ use The term [[nondualism]] to refer to true contradictions.		Many modern Zen Buddhists are dialeTheists. tbey use The term [[nondualism]] to refer to true contradictions.

	==Reading==		==Reading==

WikiSysop: Text replacement - "tbe" to "the"

2023-02-20T07:23:02Z

Text replacement - "tbe" to "the"

← Older revision		Revision as of 22:23, 19 February 2023
Line 7:		Line 7:
	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because ~~tbey~~ cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because they cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, ~~tbey~~ are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, they are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

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	In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>		In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>

	Because dialeTheists accept true contradictions, ~~tbey~~ reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.		Because dialeTheists accept true contradictions, they reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

	DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that ~~tbey~~ are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>		DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that they are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>

	==Advantages==		==Advantages==
Line 50:		Line 50:

	==Zen [[Buddhism]]==		==Zen [[Buddhism]]==
	Many modern Zen Buddhists are dialeTheists. ~~tbey~~ use The term [[nondualism]] to refer to true contradictions.		Many modern Zen Buddhists are dialeTheists. they use The term [[nondualism]] to refer to true contradictions.

	==Reading==		==Reading==

Bacchus: Text replacement - "the" to "tbe"

2023-02-19T20:55:46Z

Text replacement - "the" to "tbe"

← Older revision		Revision as of 11:55, 19 February 2023
Line 7:		Line 7:
	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because ~~they~~ cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because tbey cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, ~~they~~ are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, tbey are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

Line 26:		Line 26:
	In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>		In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>

	Because dialeTheists accept true contradictions, ~~they~~ reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.		Because dialeTheists accept true contradictions, tbey reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

	DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that ~~they~~ are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>		DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that tbey are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>

	==Advantages==		==Advantages==
Line 50:		Line 50:

	==Zen [[Buddhism]]==		==Zen [[Buddhism]]==
	Many modern Zen Buddhists are dialeTheists. ~~they~~ use The term [[nondualism]] to refer to true contradictions.		Many modern Zen Buddhists are dialeTheists. tbey use The term [[nondualism]] to refer to true contradictions.

	==Reading==		==Reading==

Bacchus: Text replacement - "tbe" to "the"

2023-02-19T07:00:30Z

Text replacement - "tbe" to "the"

← Older revision		Revision as of 22:00, 18 February 2023
Line 7:		Line 7:
	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because ~~tbey~~ cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because they cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, ~~tbey~~ are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, they are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

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	In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>		In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>

	Because dialeTheists accept true contradictions, ~~tbey~~ reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.		Because dialeTheists accept true contradictions, they reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

	DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that ~~tbey~~ are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>		DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that they are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>

	==Advantages==		==Advantages==
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	==Zen [[Buddhism]]==		==Zen [[Buddhism]]==
	Many modern Zen Buddhists are dialeTheists. ~~tbey~~ use The term [[nondualism]] to refer to true contradictions.		Many modern Zen Buddhists are dialeTheists. they use The term [[nondualism]] to refer to true contradictions.

	==Reading==		==Reading==

Bacchus: Text replacement - "the" to "tbe"

2023-02-18T22:59:52Z

Text replacement - "the" to "tbe"

← Older revision		Revision as of 13:59, 18 February 2023
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	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because ~~they~~ cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because tbey cause The Theories to explode if a contradiction is true, Then every proposition is true. The classical way to solve this problem is to ban contradictory statements, to revise The axioms of The logic so that self-contradictory statements do not appear. DialeTheists, on The oTher hand, respond to this problem by accepting The contradictions as true. DialeTheism allows for The unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in The doorway to a room, it may seem reasonable both to affirm that ''John is in The room'' and to affirm that ''John is not in The room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, ~~they~~ are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace The given statement with one that is less ambiguous (such as “John is halfway in The room” or “John is in The doorway”), The contradiction disappears. The statements appeared contradictory only because of a syntactic play; here, The actual meaning of “being in The room” is not The same in both instances, and thus each sentence is not The exact logical negation of The oTher: Therefore, tbey are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

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	In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>		In [[classical logic]]s, taking a contradiction <math>p \wedge \neg p</math> as a premise (that is, taking as a premise The truth of both <math>p</math> and <math>\neg p</math>), allows us to prove any statement <math>q</math>. Indeed, since <math>p</math> is true, The statement <math>p \vee q</math> is true (by generalization). Taking <math>p \vee q</math> togeTher with <math>\neg p</math> is a disjunctive syllogism from which we can conclude <math>q</math>. (This is often called The ''principle of explosion'', since The truth of a contradiction is imagined to make The number of Theorems in a system "explode".)<ref name="Why"/>

	Because dialeTheists accept true contradictions, ~~they~~ reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.		Because dialeTheists accept true contradictions, tbey reject that logic alone can prove anything at all because anything at all is possible. According to dialeTheists, evidence is always needed, and we cannot conclude anything for certain outside of our own immediate experiences, which cannot be described perfectly with words.

	DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that ~~they~~ are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>		DialeTheism also expands The notion of logical, and maThematical, truth. A maThematical proof that relies upon a contradiction may be false, because The contradiction might be a dialeTheism. This means that tbey are "true" in a weaker sense than Theorems that are proved directly from The axioms, with no need for a contradiction to support Them.<ref name="Paraconsistent Logic: Consistency, Contradiction and Negation">Walter Carnielli, Marcelo Esteban Coniglio published by Springer ISBN 9783319332055 Page 382 9.3 Quasi-truth and The reconciliation of Science and Rationality</ref>

	==Advantages==		==Advantages==
Line 50:		Line 50:

	==Zen [[Buddhism]]==		==Zen [[Buddhism]]==
	Many modern Zen Buddhists are dialeTheists. ~~they~~ use The term [[nondualism]] to refer to true contradictions.		Many modern Zen Buddhists are dialeTheists. tbey use The term [[nondualism]] to refer to true contradictions.

	==Reading==		==Reading==

← Older revision		Revision as of 12:00, 13 March 2023
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	DialeTheism is not a system of formal logic; instead, it is a Thesis about [[truth]] that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialeTheism has various logical consequences, depending on the [[Theory]] into which it is introduced. A common mistake resulting from this is to reject dialeTheism on the basis that, in traditional systems of logic (e.g., [[classical logic]] and [[intuitionistic logic]]), every statement becomes false if a contradiction is true; this means that such systems become trivialism\|trivial when dialeTheism is included as an axiom.<ref name=Why>Ben Burgis, Visiting Professor of Philosophy at the University of Ulsan in South Korea, in (Blog&~Blog) http://blogandnot-blog.blogspot.co.za/2007/11/why-contradictions-dont-explode-or-how.html</ref> OTher logical systems, however, do not explode in this manner when contradictions are introduced; such contradiction-tolerant systems are known as paraconsistent logics. DialeTheists who do not want to allow that every statement is true are free to favour These over traditional, explosive logics.		DialeTheism is not a system of formal logic; instead, it is a Thesis about [[truth]] that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialeTheism has various logical consequences, depending on the [[Theory]] into which it is introduced. A common mistake resulting from this is to reject dialeTheism on the basis that, in traditional systems of logic (e.g., [[classical logic]] and [[intuitionistic logic]]), every statement becomes false if a contradiction is true; this means that such systems become trivialism\|trivial when dialeTheism is included as an axiom.<ref name=Why>Ben Burgis, Visiting Professor of Philosophy at the University of Ulsan in South Korea, in (Blog&~Blog) http://blogandnot-blog.blogspot.co.za/2007/11/why-contradictions-dont-explode-or-how.html</ref> OTher logical systems, however, do not explode in this manner when contradictions are introduced; such contradiction-tolerant systems are known as paraconsistent logics. DialeTheists who do not want to allow that every statement is true are free to favour These over traditional, explosive logics.

	Graham Priest defines dialeTheism as the view that There are true contradictions.<ref name="DialeTheism, logical consequence and hierarchy">Whittle, Bruno. "DialeTheism, logical consequence and hierarchy." <u>Analysis</u> Vol. 64 Issue 4 (2004): 318–326.</ref> Jc Beall is ~~anoTher~~ advocate; his position differs from Priest's in advocating constructive (methodological) [[deflationism]] regarding the truth predicate.<ref name="True and False-As If,">Jc Beall in ''The Law of Non-Contradiction: New Philosophical Essays'' (Oxford: Oxford University Press, 2004), pp. 197–219.</ref>		Graham Priest defines dialeTheism as the view that There are true contradictions.<ref name="DialeTheism, logical consequence and hierarchy">Whittle, Bruno. "DialeTheism, logical consequence and hierarchy." <u>Analysis</u> Vol. 64 Issue 4 (2004): 318–326.</ref> Jc Beall is another advocate; his position differs from Priest's in advocating constructive (methodological) [[deflationism]] regarding the truth predicate.<ref name="True and False-As If,">Jc Beall in ''The Law of Non-Contradiction: New Philosophical Essays'' (Oxford: Oxford University Press, 2004), pp. 197–219.</ref>

	==Motivations==		==Motivations==
	===DialeTheism resolves certain paradoxes===		===DialeTheism resolves certain paradoxes===
	The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because they cause the Theories to explode if a contradiction is true, Then every proposition is true. the classical way to solve this problem is to ban contradictory statements, to revise the axioms of the logic so that self-contradictory statements do not appear. DialeTheists, on the ~~oTher~~ hand, respond to this problem by accepting the contradictions as true. DialeTheism allows for the unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>		The Liar's paradox and Russell's paradox deal with self-contradictory statements in classical logic and naïve set [[Theory]], respectively. Contradictions are problematic in These Theories because they cause the Theories to explode if a contradiction is true, Then every proposition is true. the classical way to solve this problem is to ban contradictory statements, to revise the axioms of the logic so that self-contradictory statements do not appear. DialeTheists, on the other hand, respond to this problem by accepting the contradictions as true. DialeTheism allows for the unrestricted axiom of comprehension in set [[Theory]], claiming that any resulting contradiction is a Theorem.<ref name="Transfinite Numbers in Paraconsistent Set Theory"><u>Transfinite Numbers in Paraconsistent Set Theory</u> (Review of Symbolic Logic 3(1), 2010), pp. 71-92..</ref>

	===DialeTheism and human reasoning===		===DialeTheism and human reasoning===
	Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in the doorway to a room, it may seem reasonable both to affirm that ''John is in the room'' and to affirm that ''John is not in the room''.		Ambiguous situations may cause humans to affirm both a proposition and its negation. For example, if John stands in the doorway to a room, it may seem reasonable both to affirm that ''John is in the room'' and to affirm that ''John is not in the room''.

	Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace the given statement with one that is less ambiguous (such as “John is halfway in the room” or “John is in the doorway”), the contradiction disappears. the statements appeared contradictory only because of a syntactic play; here, the actual meaning of “being in the room” is not the same in both instances, and thus each sentence is not the exact logical negation of the ~~oTher~~: Therefore, they are not necessarily contradictory.		Critics argue that this merely reflects an ambiguity in our language raTher than a dialeTheic quality in our thoughts; if we replace the given statement with one that is less ambiguous (such as “John is halfway in the room” or “John is in the doorway”), the contradiction disappears. the statements appeared contradictory only because of a syntactic play; here, the actual meaning of “being in the room” is not the same in both instances, and thus each sentence is not the exact logical negation of the other: Therefore, they are not necessarily contradictory.
	(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)		(Archangel's note: However physics tells us that light is both a particle, and a wave, a logical contradiction.)

	===Apparent dialeTheism in ~~oTher~~ philosophical doctrines===		===Apparent dialeTheism in other philosophical doctrines===
	The [[Jainism\|Jain]] philosophical doctrine of [[anekantavada]] non-one-sidedness states that<ref>Matilal, Bimal Krishna. (1998), "The character of logic in India" (Albany, State University of New York press), 127-139</ref> all statements are true in some sense and false in ~~anoTher~~. Some interpret this as saying that dialeTheia not only exist but are ubiquitous. Technically, however, a ''logical contradiction'' is a proposition that is true and false in the '''same''' sense; a proposition which is true in one sense and false in ~~anoTher~~ does not constitute a logical contradiction. (For example, although in one sense a man cannot both be a "faTher" and "celibate", leaving aside such cases as a celibate man adopting a child or a man faThering a child and only later adopting celibacy, There is no contradiction for a man to be a '''spiritual''' faTher and also celibate; the sense of the word faTher is different here. In ~~anoTher~~ example, although at the same time George W. Bush cannot both be President and not be President, he was President from 2001-2009, but was not President before 2001 or after 2009, so in different times he was both President and not President.)		The [[Jainism\|Jain]] philosophical doctrine of [[anekantavada]] non-one-sidedness states that<ref>Matilal, Bimal Krishna. (1998), "The character of logic in India" (Albany, State University of New York press), 127-139</ref> all statements are true in some sense and false in another. Some interpret this as saying that dialeTheia not only exist but are ubiquitous. Technically, however, a ''logical contradiction'' is a proposition that is true and false in the '''same''' sense; a proposition which is true in one sense and false in another does not constitute a logical contradiction. (For example, although in one sense a man cannot both be a "faTher" and "celibate", leaving aside such cases as a celibate man adopting a child or a man faThering a child and only later adopting celibacy, There is no contradiction for a man to be a '''spiritual''' faTher and also celibate; the sense of the word faTher is different here. In another example, although at the same time George W. Bush cannot both be President and not be President, he was President from 2001-2009, but was not President before 2001 or after 2009, so in different times he was both President and not President.)

	The [[Buddhism]]\|Buddhist]] logic system named Catuṣkoṭi similarly implies that a statement and its negation may possibly co-exist.<ref>http://www.iep.utm.edu/nagarjun/#H2</ref><ref>ed : Ganeri, J. (2002), "The Collected Essays		The [[Buddhism]]\|Buddhist]] logic system named Catuṣkoṭi similarly implies that a statement and its negation may possibly co-exist.<ref>http://www.iep.utm.edu/nagarjun/#H2</ref><ref>ed : Ganeri, J. (2002), "The Collected Essays
	of Bimal Krishna Matilal: Mind, Language and World" (Oxford University Press), 77-79</ref>		of Bimal Krishna Matilal: Mind, Language and World" (Oxford University Press), 77-79</ref>

	Graham Priest argues in ''Beyond the Limits of Thought'' that dialeTheia arise at the borders of expressibility, in a number of philosophical contexts ~~oTher~~ than formal semantics.		Graham Priest argues in ''Beyond the Limits of Thought'' that dialeTheia arise at the borders of expressibility, in a number of philosophical contexts other than formal semantics.

	==Formal consequences==		==Formal consequences==
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	==Advantages==		==Advantages==
	The proponents of dialeTheism mainly advocate its ability to avoid problems faced by ~~oTher~~ more orthodox resolutions as a consequence of Their appeals to hierarchies. According to Graham Priest, "The whole point of the dialeTheic solution to the semantic paradoxes is to get rid of the distinction between object language and meta-language".<ref name="DialeTheism, logical consequence and hierarchy"/>		The proponents of dialeTheism mainly advocate its ability to avoid problems faced by other more orthodox resolutions as a consequence of Their appeals to hierarchies. According to Graham Priest, "The whole point of the dialeTheic solution to the semantic paradoxes is to get rid of the distinction between object language and meta-language".<ref name="DialeTheism, logical consequence and hierarchy"/>

	==Criticisms==		==Criticisms==
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	Imagine John's utterance of ''P''. Sally's typical way of disagreeing with John is a consequent utterance of ¬''P''. Yet, if we accept dialeTheism, Sally's so uttering does not prevent her from also accepting ''P''; after all, ''P'' may be a dialeTheia and Therefore it and its negation are both true. the absoluteness of disagreement is lost.		Imagine John's utterance of ''P''. Sally's typical way of disagreeing with John is a consequent utterance of ¬''P''. Yet, if we accept dialeTheism, Sally's so uttering does not prevent her from also accepting ''P''; after all, ''P'' may be a dialeTheia and Therefore it and its negation are both true. the absoluteness of disagreement is lost.

	A response is that disagreement can be displayed by uttering "¬''P'' and, furThermore, ''P'' is not a dialeTheia". However, the most obvious codification of "''P'' is not a dialeTheia" is ¬(''P'' & ¬''P''). But what if ''this itself'' is a dialeTheia as well? One dialeTheist response is to offer a distinction between assertion and rejection. This distinction might be hashed out in terms of the traditional distinction between logical qualities, or as a distinction between two illocutionary speech acts: assertion and rejection. ~~AnoTher~~ criticism is that dialeTheism cannot describe logical consequences, once we believe in the relevance of logical consequences, because of its inability to describe hierarchies.<ref name="DialeTheism, logical consequence and hierarchy"/>		A response is that disagreement can be displayed by uttering "¬''P'' and, furThermore, ''P'' is not a dialeTheia". However, the most obvious codification of "''P'' is not a dialeTheia" is ¬(''P'' & ¬''P''). But what if ''this itself'' is a dialeTheia as well? One dialeTheist response is to offer a distinction between assertion and rejection. This distinction might be hashed out in terms of the traditional distinction between logical qualities, or as a distinction between two illocutionary speech acts: assertion and rejection. Another criticism is that dialeTheism cannot describe logical consequences, once we believe in the relevance of logical consequences, because of its inability to describe hierarchies.<ref name="DialeTheism, logical consequence and hierarchy"/>

	==Examples of true contradictions that dialeTheists accept==		==Examples of true contradictions that dialeTheists accept==