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 2026-07-06 19:24, olcott wrote: > On 7/6/2026 7:47 PM, André G. Isaak wrote: >> On 2026-07-06 17:40, olcott wrote: >>> On 7/6/2026 6:37 PM, André G. Isaak wrote: >>>> On 2026-07-06 16:53, olcott wrote: >>>>> On 7/6/2026 5:50 PM, André G. Isaak wrote: >>>>>> On 2026-07-06 16:36, olcott wrote: >>>>>>> On 7/6/2026 5:15 PM, André G. Isaak wrote: >>>>>>>> On 2026-07-06 15:54, olcott wrote: >>>>>>>>> On 7/6/2026 3:20 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-07-06 14:04, olcott wrote: >>>>>>>>>> >>>>>>>>>>> ⊥ ⊢ ⊥ no explosion. >>>>>>>>>> >>>>>>>>>> Of course that's an explosion. It says that ⊥ demonstrates >>>>>>>>>> that ⊥ is true. >>>>>>>>>> >>>>>>>>> >>>>>>>>> That you do not know what explosion is is not my mistake. >>>>>>>>> I thought that one of you two guys had a PhD in math >>>>>>>>> is that you or Alan? >>>>>>>> >>>>>>>> I do know what explosion is in the context of logic. Apparently >>>>>>>> you do not. And I've never claimed to have a doctoracte in >>>>>>>> maths. My background is in linguistics. >>>>>>>> >>>>>>>> André >>>>>>>> >>>>>>> >>>>>>> You are flat our wrong about explosion. >>>>>> >>>>>> No. You claim that ⊥ ⊢ ⊥ which is to say that ⊥ can be derived >>>>>> from ⊥. But in a consistent logic, ⊥ shouldn't be derivable from >>>>>> *anything*. The >>>>> >>>>> >>>>> It is not explosive, full stop you are wrong. >>>> >>>> You're really not qualified to make such a claim. >>>> >>>> André >>>> >>> >>> Define in your own words what you think that deductive >>> explosion means. >> >> Odd that you should ask such a thing since you rarely if ever respond >> to requests for you to explain things in your own words and instead >> post links to wikipedia pages. >> >> deductive explosion occurs when contradictory premises are introduced >> into an argument therefore allowing anything, including false >> statements to be derived. >> >> You offered ⊥ ⊢ ⊥ >> >> ⊥ is the logical symbol representing a falsehood or contradiction. You >> are therefore deriving a falsehood or contradiction which shouldn't >> happen. The only reason you were able to do this is because your >> premise was ⊥. That's explosion. >> >> André >> > > OK good. I am stipulating that from contradiction only > falsum follows and from falsum only falsum follows > cutting off the legs of explosion. > > ∀x (x ∧ ¬x) ⊢ ⊥ Which is simply a way of stating that (x ∧ ¬x) proves that ⊥ is true. How is that not an explosion? I don't think you grasp what ⊢ or ⊥ mean. 'X follows' means that the truth of X is entailed by the premise. 'falsum follows' means that falsum is true. That's explosion. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.