Gary, List,
sorry for my suggestion, I only wanted to show, where logic-pluralism might lead to, not to accuse anybody here. Anyway, I have misunderstood it, because it is called this or that "logic", though it is just this or that kind of symbolizing logic.
The point in the abstract was exactly my point: Substitution, making a proposition an object by substituting it with a singular term. But now I see, that this is making a metaphor, as you wrote. Ok, I see, that this way is probably not good for a formal system. Why, I don´t know, I would have to be a mathematician, to know, when substitutiton is allowed, and when not.
Best regards, Helmut
31. Oktober 2024 um 23:11
"Gary Richmond" <[email protected]>
wrote:Helmut, Jerry, Jon, List,
I too am sure that there is only one logic. But note that there is this one significant difference between classical propositional/predicate logic and modal logic:
"The only difference between the symbolic languages of modal logics and those of classical propositional or predicate logic is that the former have two additional symbols – the modal operators □ and ◊. (In temporal modal logic, the operators are four). https://formallogic.eu/EN/4.1.ModalLogics.html#:~:text=Syntax%20of%20modal%20logic,%2C%20the%20operators%20are%20four).
And, as I earlier wrote: While " a predicate in logic typically applies to an object or a subject and conveys a property or attribute of that object. . . Modal operators. . . apply to propositions rather than individual objects and express the mode of truth of a proposition, that is, whether the statement is necessarily true, possibly true, or conditionally true" (emphasis added).
This seems to me to be not at all to be an _expression_ of "logical-relativism" as you suggested, Helmut, but a useful extension of classical logic quite unlike your 'analogy' of politicians making up "alternate facts."
There has, however, "always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators." This "temptation" is taken up in "Modal Predicates" by Andrea Iocana. Here's the abstract of the paper:
Abstract: Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates. The model is built by enriching the language of standard modal logic with a quantificational apparatus that is “substitutional” rather than “objectual”, and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions.
I found the paper's argument -- that there is "plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates" -- interesting, but a bit too caught up in 'metaphor' (see especially the conclusion), and ultimately unconvincing. But I'd be interested in what you and others think.
Best,
Gary R
On Thu, Oct 31, 2024 at 5:22 PM Helmut Raulien <[email protected]> wrote:
Gary, Jerry, Jon, Edwina, List,I am sure, that there can only be one logic. To accept logic-relativism would make me feel totally unsafe, like a paranoid or psychotic. There are politicians, who exploit logic-pluralism´s possibility to lie, to manipulate people by blurring their minds, e,g. say, that they have access to "alternative facts". But not with me. Formal and modal "logic" are only different ways of symbolizing this one logic. In "modal logic" (which is not another logic, but just another way to write logic), possibility , existence, necessity are modalities, and in "formal logic", they are predicates. In "formal logic" a proposition is either true or false, and a proposition is not forbidden, just because it contains one of these here-predicates. A proposition is either true or false too, if it contains the predicate "possible". Different symbolic systems are merely different, because they allow different calculi, and different mathematicians use different symbolic systems, because they can better calculate either with the one or the other in different task situations. Whether something is a predicate or not, is a matter of linguistics, but not of logic. Sapir-Whorf is ad acta, isn´t it?Best regards, Helmut31. Oktober 2024 um 19:36"Gary Richmond" <[email protected]>wrote:Jerry, Jon, List,Note: I missed this post until now, Jerry, since it went into my spam folder (I mentioned that this was happening to your posts some months ago and it continues to be the case; there is one other List member whose posts also go into my spam folder).JAS wrote: In logic, possibility and necessity are not predicates any more than existence/actuality.And JLRC asked: ???Why?I'm not exactly sure to what extent this applies to Peirce's modal logic, but in the logic classes I've been exposed to and the logic texts I've read, in modal logic possibility and necessity are not treated as predicates. Instead, they are considered modal operators that modify statements rather than describing properties of objects.
As I understand it, a predicate in logic typically applies to an object or a subject and conveys a property or attribute of that object (e.g., 'x is blue' or 'x is a horse'). In other words, predicates express qualities that can be true or false of specific entities.
Modal operators, on the other hand, apply to propositions rather than individual objects and express the mode of truth of a proposition, that is, whether the statement is necessarily true, possibly true, or conditionally true.
In sum: Modal operators modify the proposition itself rather than describing a property of an object. Thus, in formal logic, they are treated differently from predicates.
I really don't see why you questioned this.Best,Gary R
On Thu, Oct 31, 2024 at 5:46 AM Jerry LR Chandler <[email protected]> wrote:List, Jon:_ _ _ _ _ _ _ _ _ _
On Oct 26, 2024, at 7:17 PM, Jon Alan Schmidt <[email protected]> wrote:
In logic, possibility and necessity are not predicates any more than existence/actuality.???Why?What forms of logic are you referring to?Which grammar of which logic informs your assertion?How is it plausible that this assertion is meaningful?[This statement directly contradicts chemical, biochemical and biological equilibrium processes as was well described by A. N. Whitehead.]CheersJerry
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