Inconsistent theories do not mean that they are trivial, but they may be - for example in classical propositional logic, once a contradiction is admit the theory becomes trivial and essentially useless.

To adopt a non-classical logic may mean that one is simply playing games with the formal structure of the logic, which one adopts or tires to adopt an interpretation of what the logic means - its semantics. For example classical logic uses Tarksian semantics, the same semantics that Wittgenstein adpted in his Tractatus, which is that truth corresponds to existance, and falsity to non-existence.

The BHK semantics, first put forward by Brouwer, is to assign truth the semantics of proof. It turns out then that the most natural logic is intuitionistic where the excluded middle is denied, and it is a multi-valued logic. This is not a logic that allows contradictions, but its dual does.

One might adopt such a paraconsistent logic to model epistemological truth where what is known may be in conflict with each other, so boundaries between domains of knowledge need policing. One might then argue that this is knowledge as represented to us, not truth in itself. This leads us into the deeper waters that Feyerabend is pointing out. If one adopts the principle that the Jain philosophers expounded on, anekantevada, or more than one point of view as being absolute, in a similar sense that Wittgenstein said of the logic being the limits of our world and not the world, then inconsistent logic is inevitable; Feyerabend took his at least some of his cues from Hume and Kant who placed logic in the realm of human knowledge, as opposed to being a property of the world itself.

This is still different from dialethism or true contradictions - formally for example one solution of the liars paradox is to adopt a three-valued logic which allows a statement to be both true & false. One still of course has to explain quite what this means. The Dao begins with a famous line:

The Tao that is the Tao is not the True Tao

One can take a dialethist position on this statement, or an epistemological position, in that truth that can be grasped by the human mind is always partial, and 'true' truth always eludes us. The Catuskoti/tetralemma shows also that the formal consequences of considering dialethism was considered formally - and one possible consequence of this, in at least Buddhist logic, is that an atom can be both a point and not a point. This gives a new picture of the continuum, which as Aristotle argued against the Greek atomists must have cohesion; this is not far from the conception the intuitionistic continuum where a similar view is taken.

Hegel is probably the major philosopher in the West to have taken contradictions seriously - from Being & Non-Being comes Becoming is one of his early triads that sets his Geist in motion, or one might say is his Geist, for contradiction is "the root of all movement and vitality."

Inconsistent theories do not mean that they are trivial, but they may be. For example in classical propositional logic once a contradiction is admitted the theory becomes trivial and essentially useless.

To adopt a non-classical logic may mean that one is simply playing games with the formal structure of the logic where one adopts or tries to adopt an interpretation of what the logic means - its semantics. For example classical logic uses Tarskian semantics, the same semantics that Wittgenstein adopted in his Tractatus which is that truth corresponds to existence and falsity to non-existence.

The BHK semantics, first put forward by Brouwer, is to assign truth the semantics of proof. It turns out then that the most natural logic is intuitionistic where the excluded middle is denied, and it is a multi-valued logic. This is not a logic that allows contradictions, but its dual does.

One might adopt such a paraconsistent logic to model epistemological truth where what is known may be in conflict with each other. So boundaries between domains of knowledge need policing. One might then argue that this is knowledge as represented to us, not truth in itself. 

This leads us into the deeper waters that Feyerabend is pointing out. If one adopts the principle that the Jain philosophers expounded on anekantevada or more than one point of view as being absolute, in a similar sense that Wittgenstein said of logic being the limits of our world and not the world, then inconsistent logic is inevitable. Feyerabend took at least some of his cues from Hume and Kant who placed logic in the realm of human knowledge as opposed to being a property of the world itself.

This is still different from dialethism or true contradictions. Formally for example one solution of the liar's paradox is to adopt a three-valued logic which allows a statement to be both true and false. One still of course has to explain what this means. The Dao begins with a famous line:

The Tao that is the Tao is not the True Tao

One can take a dialethist position on this statement, or an epistemological position, in that truth that can be grasped by the human mind is always partial and 'true' truth always eludes us. The Catuskoti tetralemma shows also that the formal consequences of considering dialethism was considered formally - and one possible consequence of this, in at least Buddhist logic, is that an atom can be both a point and not a point. This gives a new picture of the continuum which as Aristotle argued against the Greek atomists must have cohesion. This is not far from the conception the intuitionistic continuum where a similar view is taken.

Hegel is probably the major philosopher in the West to have taken contradictions seriously. From Being and Non-Being comes Becoming is one of his early triads that sets his Geist in motion, or one might say is his Geist, for contradiction is "the root of all movement and vitality."

Inconsistent theories do not mean that they are trivial, but they may be - for example in classical propositional logic, once a contradiction is admit the theory becomes trivial and essentially useless.

To adopt a non-classical logic may mean that one is simply playing games with the formal structure of the logic, which one adopts or tires to adopt an interpretation of what the logic means - its semantics. For example classical logic uses Tarksian semantics, the same semantics that Wittgenstein adpted in his Tractatus, which is that truth corresponds to existance, and falsity to non-existence.

The BHK semantics, first put forward by Brouwer, is to assign truth the semantics of proof. It turns out then that the most natural logic is intuitionistic where the excluded middle is denied, and it is a multi-valued logic. This is not a logic that allows contradictions, but its dual does.

One might adopt such a paraconsistent logic to model epistemological truth where what is known may be in conflict with each other, so boundaries between domains of knowledge need policing. One might then argue that this is knowledge as represented to us, not truth in itself. This leads us into the deeper waters that Feyerabend is pointing out. If one adopts the principle that the Jain philosophers expounded on, anekantevada, or more than one point of view as being absolute, in a similar sense that Wittgenstein said of the logic being the limits of our world and not the world, then inconsistent logic is inevitable; Feyerabend took his at least some of his cues from Hume and Kant who placed logic in the realm of human knowledge, as opposed to being a property of the world itself.

This is still different from dialethism or true contradictions - formally for example one solution of the liars paradox is to adopt a three-valued logic which allows a statement to be both true & false. One still of course has to explain quite what this means. The Dao begins with a famous line:

The Tao that is the Tao is not the True Tao

One can take a dialethist position on this statement, or an epistemological position, in that truth that can be grasped by the human mind is always partial, and 'true' truth always eludes us. The Catuskoti/tetralemma shows also that the formal consequences of considering dialethism was considered formally - and one possible consequence of this, in at least Buddhist logic, is that an atom can be both a point and not a point. This gives a new picture of the continuum, which as Aristotle argued against the Greek atomists must have cohesion; this is not far from the conception the intuitionistic continuum where a similar view is taken.

Hegel is probably the major philosopher in the West to have taken contradictions seriously - from Being & Non-Being comes Becoming is one of his early triads that sets his Geist in motion, or one might say is his Geist, for contradiction is "the root of all movement and vitality."

Inconsistent theories do not mean that they are trivial, but they may be - for example in classical propositional logic, once a contradiction is admit the theory becomes trivial and essentially useless.

To adopt a non-classical logic may mean that one is simply playing games with the formal structure of the logic, which one adopts or tires to adopt an interpretation of what the logic means - its semantics. For example classical logic uses Tarksian semantics, the same semantics that Wittgenstein adpted in his Tractatus, which is that truth corresponds to existance, and falsity to non-existence.

The BHK semantics, first put forward by Brouwer, is to assign truth the semantics of proof. It turns out then that the most natural logic is intuitionistic where the excluded middle is denied, and it is a multi-valued logic. This is not a logic that allows contradictions, but its dual does.

One might adopt such a paraconsistent logic to model epistemological truth where what is known may be in conflict with each other, so boundaries between domains of knowledge need policing. One might then argue that this is knowledge as represented to us, not truth in itself. This leads us into the deeper waters that Feyerabend is pointing out. If one adopts the principle that the Jain philosophers expounded on, anekantevada, or more than one point of view as being absolute, in a similar sense that Wittgenstein said of the logic being the limits of our world and not the world, then inconsistent logic is inevitable; Feyerabend took his at least some of his cues from Hume and Kant who placed logic in the realm of human knowledge, as opposed to being a property of the world itself.

This is still different from dialethism or true contradictions - formally for example one solution of the liars paradox is to adopt a three-valued logic which allows a statement to be both true & false. One still of course has to explain quite what this means. The Dao begins with a famous line:

The Tao that is the Tao is not the True Tao

One can take a dialethist position on this statement, or an epistemological position, in that truth that can be grasped by the human mind is always partial, and 'true' truth always eludes us. The Catuskoti/tetralemma shows also that the formal consequences of considering dialethism was considered formally - and one possible consequence of this, in at least Buddhist logic, is that an atom can be both a point and not a point. This gives a new picture of the continuum, which as Aristotle argued against the Greek atomists must have cohesion; this is not far from the conception the intuitionistic continuum where a similar view is taken.

Hegel is probably the major philosopher in the West to have taken contradictions seriously - from Being & Non-Being comes Becoming is one of his early triads that sets his Geist in motion, or one might say is his Geist, for contradiction is "the root of all movement and vitality."