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 13:19, olcott wrote: > On 7/7/2026 1:46 PM, André G. Isaak wrote: >> 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' >> > > To do with with minimal simplicity the axioms of > PA are construed as semantic entailment thus when > there is no sequence of inference steps between G > and PA then G is Kripke undefined in PA. So why don't you illustrate this with an actual proof? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.