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Jul
27
comment What is $0\div0\cdot0$?
You didn't tell us what the set of numbers was. If you keep the set of numbers in mind, it becomes clearer that there is no such thing, since division on the natural numbers is VERY unlike division on the real numbers, especially in comparison to multiplication on the natural numbers and real numbers respectively.
Jul
27
revised What is $0\div0\cdot0$?
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Jul
27
answered What is $0\div0\cdot0$?
Jul
27
comment Max/Min to logical operator transformation and viceversa
What set of numbers are those inequalities supposed to apply to?
Jul
26
revised Law of Clavius explained
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Jul
26
revised Law of Clavius explained
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Jul
26
comment Law of Clavius explained
@skyfire I've added a link to an entry on Polish notation.
Jul
26
revised Law of Clavius explained
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Jul
26
revised Law of Clavius explained
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Jul
26
comment Law of Clavius explained
@skyfire I'm not sure what you mean by "more general". My understanding goes that a formula "Prop1" is more general than a formula " Prop2 " if and only if given Prop1 we can derive Prop2, but given Prop2 we can't derive Prop1. If you have the deduction meta-theorem and the law of Clavius, you can't derive the formula CCNpqCCNpNqp, which embodies proof by contradiction. I found a model which indicates this using Mace4. Just consider the model where C00 = 1, C01 = 1, C10 = 0, C11 = 1, N0 = 1 and N1 = 1. Suppose that p = 1 and q = 1 to find how CCNpqCCNpNqp fails.
Jul
26
comment Law of Clavius explained
@lodrik There do exist cases where you can use the law of Clavius without using the contradiction rule. See my answer and the theorem that Euclid proved.
Jul
26
revised Law of Clavius explained
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Jul
26
answered Law of Clavius explained
Jul
26
comment Law of Clavius explained
I don't understand how you can have a contradiction without a conjunction, or without having some proposition "p" and another "not p". You don't have either of those in the law of Clavius.
Jul
25
comment What is the Viewpoint of Modern Logic?
@Nagase No, I didn't think that. I thought there existed rather widespread agreement that propositional logic precedes all other logical systems. Thanks for the information.
Jul
25
comment What is the Viewpoint of Modern Logic?
@Nagase Conceptually.
Jul
25
comment What is the Viewpoint of Modern Logic?
@MaliceVidrine How their term logic fits into the viewpoint of modern logic. From my understanding the viewpoint of formal logic goes that propositional logic precedes predicate logic, and propositional logic precedes traditional Aritsotelian term logic even (Lukasiewicz's work basically established this). But, Sommers claimed to have reduced conditionals like "if p, then q" to term based sentences such as "every p is a q." I don't see how those viewpoints fit together. Also, Sommers indicates that his logic is systematically ambiguous. Other logics don't seem to work that way.
Jul
25
comment What is the Viewpoint of Modern Logic?
@Nagase What's DRT?
Jul
25
comment What is the Viewpoint of Modern Logic?
@MaliceVidrine How does the work of Fred Sommers, Lorne Szabolcsi and other 20th/21st century logicians fit into viewpoint of modern logic?
Jul
25
comment Is there any commonality between Math induction and Logic induction?
@AlanU.Kennington Is the omission of Frege's "Concept Script" in your list deliberate? Also, there's Jan Lukasiewicz's Elements of Mathematical Logic, and Arthur Prior's Formal Logic. Prior's book has an appendix with several axiom sets. Nicod's proof for the completeness of his axiom was incorrect. For more details see this paper: projecteuclid.org/download/pdf_1/euclid.ndjfl/1093958259 C. A. Meredith's paper didn't establish that a single axiom could suffice for propositional calculus. If I recall correctly, Tarski did so. See the papers in the volume "Polish Logic" for details.