A question about logic. When symbolizing and making inferences in natural languages that contain such terms as "it is necessary that", "A ought to do X", "A knows X", and "it is always the case that", there are extensions of classical logic, respectively, modal, deontic, epistemic, and tense logic that attempt to deal with such natural language analogues.
My question is: What about propositions that contain a mixture of all the above terms? For example, there are sentences in natural language of the form “It is necessary that John ought to always know that 2+2=4." Is there a logic that can effectively handle (i.e. symbolize and correctly infer) such propositions? If so, is this logic both sound and complete? If there is no such logic, what is a logician to do with such propositions?
My intuition is that things get tricky when you mix these operators together and/or the classical quantifiers.
Thanks kindly for your reply,
A Concerned Thinker
How do formal logicians respond to Marxist/Leninist/Dialectical logic claims? For example, in "An Introduction to the Logic of Marxism", George Novack explains that the law of identity of formal logic, that "A is equal to A", is always falsified when we try to apply it to reality. Here is a quote from the book, in which he quotes from "In Defense of Marxism" (it is long, I apologize):
"... a pound of sugar is equal to itself. Neither is this true -- all bodies change uninterruptedly in size, weight, color, etc. They are never equal to themselves. A sophist will respond that a pound of sugar is equal to itself at 'any given moment.'
"Aside from the extremely dubious practical value of this 'axiom,' it does not withstand theoretical criticism either. How should we really conceive the word 'moment'? If it is an infinitesimal interval of time, then a pound of sugar is subjected during the course of that 'moment' to inevitable changes. Or is the 'moment' a purely mathematical abstraction, that is, a...
I once took a graduate course in education in which I was the only non-teacher. One day, I disagreed with something said by another student, and her response has always baffled me. She said: "Who are you? You can't question me until you've walked in my shoes." In other words, she felt that I was unqualified to question her, to cast doubt on anything she said. Who was I to say? Well of course her response was nonsense but how so? As a matter of logic or illogic, was her remark an example of an appeal to authority? She certainly felt that she was an authority.
I am having trouble understanding the difference between a 'necessary' and a 'sufficient' condition (in philosophical usage). Would I be right in thinking that the former is a condition that must be present in order for something to happen, while the latter is merely 'enough', i.e. that no other condition needs to be met (while with a necessary condition others can be met)?
A friend once had me consider this logic.
Because the Catholic Immaculate Conception doctrine is a cornerstone tenet of the church, but is essentially a dogmatic belief, any dogmatic doctrine canonized by the church must also be as worthy of faith as the Immaculate Conception doctrine.
However the doctrine of transfiguration is also a dogmatic belief. Yet even after a priest has blessed the sacramental wine and bread, in reality it does not literally transfigure into the blood and body of Christ even though the doctrine of transfiguration states that it does.
If the wine does not literally turn to blood, the doctrine of transfiguration is wrong and because the doctrine of transfiguration is equally as valid as the Immaculate Conception, it too is also wrong by association.
However, if the Christ were literally made of bread and wine, then all conflicts would be resolved. Can you please comment on this logic?
As a beginner in philosophy, I got the impression that philosophy is all about arguments. You put in statements (premises), use some rules of argumentation to manipulate these premises, and reach other statements (conclusions).
Is there a way to argue for the rules of argumentation themselves? I mean, we use them all the time but how do we know that they are true? What kind of rules would we use to prove the rules of argumentation? Can we use the same rules?