Re: William T. Parry gets rid of Disjunction introduction
André G. Isaak <[email protected]>
| Newsgroups | sci.logic,comp.theory,comp.ai.philosophy,sci.math |
|---|---|
| Organization | Christians and Atheists United Against Creeping Agnosticism |
| Message-ID | <[email protected]> |
On 2026-07-07 10:04, olcott wrote: > On 7/7/2026 10:31 AM, André G. Isaak wrote: >> On 2026-07-06 21:40, olcott wrote: >>> On 7/6/2026 10:28 PM, André G. Isaak wrote: >>>> On 2026-07-06 21:12, olcott wrote: >>>>> On 7/6/2026 10:03 PM, André G. Isaak wrote: >>>>>> On 2026-07-06 20:44, olcott wrote: >>>>>>> On 7/6/2026 9:41 PM, André G. Isaak wrote: >>>>>>>> On 2026-07-06 20:24, olcott wrote: >>>>>>>> >>>>>>>>> ∀x(φ(x) ∧ ¬φ(x)) ⊢ ⊥ >>>>>>>>> and >>>>>>>>> Γ ⊢ ⊥ >>>>>>>>> -------------------- >>>>>>>>> derivation terminated >>>>>>>> >>>>>>>> That's simply gibberish. >>>>>>>> >>>>>>>> André >>>>>>>> >>>>>>> >>>>>>> How do you think that: >>>>>>> From a contradiction nothing follows >>>>>>> should be encoded? >>>>>> >>>>>> Since you don't understand the formalism you're trying to use, why >>>>>> bother trying to formalize it? >>>>> >>>>> Both LLMs agree that I am already correct. >>>> >>>> LLMs carry no weight in my opinion. >>> >>> This is also your own error. >>> >>>> And since you can't clearly express yourself, it wouldn't be clear >>>> exactly what they were agreeing with anyways. >>>> >>> >>> How do we formalize: "from a contradiction nothing follows?" >> >> You really ought to take an introductory course in formal logic, or >> simply give up on trying to formalize things. If you really wanted to >> you could write something like >> >> ∀Φ ¬∃Ψ (Φ ∧ ¬Φ) → Ψ >> >> But simply looking at the truth table for → would reveal that this >> statement is false. >> > > P ⊢ Q means syntactic derivation implements semantic > entailment encoded in syntactically the language. > This is the only inference steps allowed. The entailment > rules depend on the represented domain. That really doesn't seem to say anything. Why don't you illustrate this with a simple mathematical proof which shows exactly what you mean by 'semantic entailments encoded syntactically in the language' André > I am going with this in terms of > > The Definitional View of Atomic Systems in Proof-Theoretic > Semantics Thomas Piecha and Peter Schroeder-Heister > > When you actually look at the meaning of the English > words of the sentences then it becomes obvious that > the principle of explosion can only occur when you > ignore this underlying semantics. > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.