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By century-old arguments due to Russell, this "existence of existence" is incoherent. For example, as an imagined counterargument, imagine that there is a set o

By century-old arguments due to Russell, this "existence of existence" is incoherent. For example, as an imagined counterargument, imagine that there is a set of all things which exist, are sets, and do not contain themselves. By your axiom, this set exists. By definition, this set does not contain itself. Therefore, and by definition, this set contains itself. Formal proofs are syntactic. As a result, they do not need consciousness to be verified; verification is algorithmic and can be done by a machine. Proofs can also be searched for by machines, although such proof search does not run at practical speeds on existing hardware yet. Nonetheless, to take your claim at face value is to claim that computing machines are conscious; are you prepared to embrace this result? (I don't personally have a problem with it, but many people do.) This sort of word salad, more generally, is why Objectivism has such a poor reputation: It doesn't make sense when examined with even basic critical thinking.

psychoslave 7y ago
Russell's paradox deals with self-referencing logically unconstructible objects, not with the impossibility of proving anything as existing. >Formal proofs are syntactic. […] This confuses means of formal proof with meanings attached to them. A proof, whatever the means used to perform it, only matter to conscious beings. A computer can help to solve a logical problem, but so far none have been catched wondering which logical problem would be interesting to solve as its next challenge – as far as I know.
- lidHanteyk 7y ago
  In mathematics, we do actually take logically self-defeating objects to be non-existent, as a matter of classical reasoning: If they don't exist, then they must not-exist; otherwise, they would exist, and immediately defeat themselves in a puff of logic [5]. Such classical reasoning can reject a large number of similarly-shaped objects [2], and Russell's antimony is actually only the tip of the iceberg of a bundle of formal results, notably Tarski's [3] and Lawvere's [4]. The Gödel Machine algorithm [0][1] is only a few years old, and it cannot yet be tested due to practical hardware constraints, but it provably implements a system which wonders, specifically, about which direction of proof search will speed up its ability to search for proofs, to consider directions, or to wonder. [0] https://en.wikipedia.org/wiki/G%C3%B6del_machine https://en.wikipedia.org/wiki/G%C3%B6del_machine [1] http://people.idsia.ch/~juergen/goedelmachine.html http://people.idsia.ch/~juergen/goedelmachine.html [2] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeating-object-argument/ https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat... [3] https://en.wikipedia.org/wiki/Tarski's_undefinability_theorem https://en.wikipedia.org/wiki/Tarski's_undefinability_theore... [4] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem [5] https://tvtropes.org/pmwiki/pmwiki.php/Main/PuffOfLogic https://tvtropes.org/pmwiki/pmwiki.php/Main/PuffOfLogic

psychoslave 7y ago

Russell's paradox deals with self-referencing logically unconstructible objects, not with the impossibility of proving anything as existing. >Formal proofs are syntactic. […] This confuses means of formal proof with meanings attached to them. A proof, whatever the means used to perform it, only matter to conscious beings. A computer can help to solve a logical problem, but so far none have been catched wondering which logical problem would be interesting to solve as its next challenge – as far as I know.

lidHanteyk 7y ago
In mathematics, we do actually take logically self-defeating objects to be non-existent, as a matter of classical reasoning: If they don't exist, then they must not-exist; otherwise, they would exist, and immediately defeat themselves in a puff of logic [5]. Such classical reasoning can reject a large number of similarly-shaped objects [2], and Russell's antimony is actually only the tip of the iceberg of a bundle of formal results, notably Tarski's [3] and Lawvere's [4]. The Gödel Machine algorithm [0][1] is only a few years old, and it cannot yet be tested due to practical hardware constraints, but it provably implements a system which wonders, specifically, about which direction of proof search will speed up its ability to search for proofs, to consider directions, or to wonder. [0] https://en.wikipedia.org/wiki/G%C3%B6del_machine https://en.wikipedia.org/wiki/G%C3%B6del_machine [1] http://people.idsia.ch/~juergen/goedelmachine.html http://people.idsia.ch/~juergen/goedelmachine.html [2] https://terrytao.wordpress.com/2009/11/05/the-no-self-defeating-object-argument/ https://terrytao.wordpress.com/2009/11/05/the-no-self-defeat... [3] https://en.wikipedia.org/wiki/Tarski's_undefinability_theorem https://en.wikipedia.org/wiki/Tarski's_undefinability_theore... [4] https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem https://ncatlab.org/nlab/show/Lawvere's+fixed+point+theorem [5] https://tvtropes.org/pmwiki/pmwiki.php/Main/PuffOfLogic https://tvtropes.org/pmwiki/pmwiki.php/Main/PuffOfLogic