Questions tagged [propositional-logic]
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Using the Universal Quantifier, Existential Quantifier, and logical connectives, write a description of a time when somthing bad for you was not bad
The following is an exercise in ethics, logic, the use of the universal quantifier and the the use of the existential quantifier.
In the following context, the syntax for the universal quantifier is ...
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What's the difference between "iff" and "=df"?
Just a quick question I stumbled upon from my readings.
When some philosophers write A ↔ B and others write A =df B, is there supposed to be a difference?
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Is affirmation of the consequent always invalid?
Examples that I've seen usually go something like
"If the lamp is off, then the room is dark. The room is dark, therefore the lamp must be off."
However, what about the following example
&...
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Propositional Logic: Truth table for a certain argument form
I'm confused about evaluating a certain argument form with the truth table approach.
I think below argument matches the corresponding truth table I made, but if my truth table is right it means the ...
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Missing two syntactical expressions of rules of inference in sentential logic
I have a table of the rules of inference in propositional logic. Among the entries are an Associative and a Commutative. The Associative rule is expressed with disjunction, but the commutative is ...
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Implicature justification for translating "P unless Q" as (¬Q → P)
In The Laws of Truth, Smith translates utterances of the form "P unless Q" as (¬Q → P) and takes the further suggestion that (Q → ¬P) to be an implicature of the utterance. The justification ...
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Confused On The Definition Of A Proposition
One definition I encountered was something that is either true or false.
(for example, I ate vegetables yesterday is a proposition).
Another definition I encountered is the meaning of a sentence
(for ...
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Propositions vs sentence types and tokens and the context insensitivity of PL
I came across the following explanation for the context insensitivity of the language of propositiional logic (PL) on page 34 of The Laws of Truth by Nicholas Smith:
Because glossary entries pair ...
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Can a valid argument be said to be unsound if the set of premises is unsatisfiable (inconsistent)?
I'm asking in a strict propositional logic sense. Suppose that I have a set of premises that is logically unsatisfiable (or inconsistent), i.e. they can not be all True simultaneously, that argument ...
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Difference between Propositions and Statements
I have read the answers to many questions like mine I reached these two definitions of propositions (I don't know which one is correct)
A proposition is a statement that can be true or false.
If this ...
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If the modern understanding of the categorical/hypothetical distinction is better than Kant's, does this undermine the categorical imperative?
In first-order logic (FOL), we have dedicated connectives for conditionals and disjunctions. Again in FOL, we can turn a conditional into a disjunction, though. Frege's logic has a judgment stroke, or ...
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Trivialism vs Alethic Nihlism
What are the similiarities and differences between the two theories (as well as arguments for and counterarguments against).
From what I know, trivialism states that everything is true (and I believe ...
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Proof of A & B from ¬(A → ¬B) using rules of inference
I have been tasked with proving A & B from −(A → −B). However, I'm only allowed to use the following rules:
ModusPonens,
ModusTollens,
ConditionalProof,
DoubleNegation,
AndIntroduction,
...
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Natural language into logic and proof
I'm working through Logic by Paul Tomassi, and there is one particular problem I'm stumped with. The problem is on pg 186 and involves representing an argument in English as a sequent and then ...
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Are these formulas correct in modal logics?
I'm looking to try to simplify 2 different formulas to be easier to say but i'm not sure on the exact rules of propositional calculus. I am starting with the two formulas (1) and (2) and i'm ...
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What is the relationship between possible worlds and a valuations?
A propositional formula is something like this, A&~B, which uses letters to represent propositions. The letters are called propositional variables.
Compare the following two sets of terminologies ...
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How does "if p, then q" compare to "p only if q"?
How do the statements if p then q and p only if q compare
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What is the difference between a tautological corresponding conditional and (P v ~P)?
The Wikipedia article on the corresponding conditional contains the following sentence:
An argument is valid if and only if its corresponding conditional is a logical truth.
Some sources use "...
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How to show DeMorgan Law in intuitionistic logic using weak excluded middle?
I am trying to show in intuitionistic logic that ~(A & B) > (~A v ~B) using the deduction theorem and weak excluded middle (~A v ~~A). I already proved (~~A & ~~B) > ~~(A&B) and ~(A &...
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Help reconstructing argument
I saw the following argument in Paul Guyer's text "Kant" (Routledge). I am trying to reconstruct it, yet am not sure the of the form of the argument. Can anyone provide help?
If whenever ...
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Justification of the material conditional truth function in Introduction to Formal Logic
Pages 150-151 of §18.3 of Introduction to Formal Logic by Peter Smith provide two justifications for the truth table of the material conditional.
In the first justification (paragraph (a) - (c) on pg. ...
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First use of exportation/importation in formal logic?
Who is the logician who first used exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r))?
Gödel used it in his 1939 Logic lecture, but it doesn’t seem to have been known from the Aristotelian ...
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Is there a proof of exportation/importation from more obviously true implications such as Modus ponens?
Is there a proof of exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r)), from more obviously true implications such as the Modus ponens, Transposition, de Morgan etc.
I don’t believe that ...
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Truth-functional vs non-truth functional conditionals
I'm struggling to understand truth functionality.
I know that a connective is truth-functional if the truth value of a compound statement formed with that connective is completely determined by the ...
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Translating English statements to logical expressions
this is my first questions so I apologize for any formatting mistakes.
Given the following propositions:
c: I will return to college.
j: I will get a job.
and given the sentence:
"There is no ...
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Intersection of the Gettier problem and knowing-what or knowing-how
From what I can tell, it seems like the Gettier problem comes down to Smith not knowing that the man who has ten coins in his pocket is going to get the job. What about Smith knowing what the ...
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How do you prove that a logic system is sound?
I am aware of the fact that a logic system must be sound, in order to be useful. However, I am not sure, about how, after setting up or coming up with the basic logic axioms that make up my system, I ...
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Sentential Interpretation in P. Suppes (1957)
Patrick Suppes gives a working definition of sentential interpretation, based on a sentence maintaining its form. By working definition, I mean an incomplete definition that is needed for someone to ...
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Hi! I'm 99% sure my formal argument is valid, but can you check? [closed]
I wrote this argument, and while i'm sure it is valid, it has been awhile since I've done basic logic.Thanks!
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How understand abstraction when some cases can’t be abstracted?
Like the liar sentence “this sentence is false” is said not to be a proposition.
So not all sentences can be abstracted into props. Can infinite sentences be abstracted into propositions. Can infinite ...
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Philosophy book written using logic statements
I would like to translate a philosophy text into logic axioms and propositions. Then, I would like to use prolog to check if the text is logically consistent.
However, I find it difficult to translate ...
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Translation of Arguments from Propositional Logic to Predicate Logic
How exactly does this work? What can we assume stays the same, what changes?
Take for an example this (valid) argument:
A & ~C
~C > ~D
~D > B
∴ B
Now let us take rewrite it according to ...
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Semantic consequence and Sound Argument
Is that correct to say that semantic consequence is equivalent to the concept of sound argument in classical propositional logic?
If it is the case, arguments or theories with contradictory premises ...
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Proof for "⊢ (A → ¬¬A)"
I've spent 4.5 hours on this, with no exaggeration. I clearly have no idea what I'm doing here, and it's become a serious time sink. If any of you could help in proving this, I would be eternally ...
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Help with proving: P, ¬(Q ∧ P) ⊢ ¬Q
Here's the issue, there's no usage of derived rules allowed. So no DeMorgan's Law. All that's allowed is the basic TFL elimination/introduction rules, IP, (e)X(plosion), and ⊥. I'm absolutely lost on ...
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What does it mean, intuitively and then also precisely, that a particular English word is not truth functional?
What does it mean, intuitively and then also precisely, when we say that a particular English word is not truth functional? Let me present some examples.
Example 1
As far as I can tell from a book I ...
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Proofs of propositional logic truth tree rules in natural deduction?
It is a great irony of natural deduction that some of the most seemingly obvious inferences are also some of the trickiest to prove! So far, I haven't been able to prove the following, and I'd greatly ...
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How to interpret "P ⟺ Q is true if and only if the first-order logic sentence P ↔ Q is logically necessary"?
I'm learning about the two truth-functional connectives "material conditional" and "material biconditional".
I came across this particular snippet in a book:
An important fact ...
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Prove that if S tautological consequence of P, S tautological consequence of Q, then S tautological consequence of P | Q
Consider the following argument:
S is a tautological consequence of P.
S is a tautological consequence of Q.
Therefore, S is a tautological consequence of P | Q.
I wish to give an informal proof of ...
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Why is any sentence a logical consequence of a set of inconsistent premises?
If a set of premises is inconsistent, there is no situation that makes all the premises true simultaneously.
Given a sentence S, there is no situation in which a conjunction of a set of inconsistent ...
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How to understand a proof by contradiction in minute detail?
I am following the course "Language, Proof, and Logic" from Stanford on EdX. I am trying to understand proof by contradiction specifically. I understand the gist of this type of proof, and I ...
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If A entails C, and B entails C, why doesn’t (A and B) necessarily entail C?
The original question is in Greek letters Γ and Δ, each representing a set of sentences, and φ representing an individual sentence (atomic proposition). The question is from Introduction to Logic by ...
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Is Propositional Logic (or Zeroth-order logic) the most basic form of logic?
Could all systems of logic (not only classical logic 1, but also non-classical logics like intuitionistic logic 2, quantum logic 3, many-valued logic 4, modal logic 5, paraconsistent logic 6...etc) be ...
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Is "Not all S are P", ambiguous?
I read Kelley's book (the art of reasoning: An Introduction to Logic and Critical Thinking 4th edition). On page 150, I found this statement:
"A special problem arises with statements that have ...
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Am I correct that tautologies and contradictions are NOT truth-functional?
We call a statement truth functional if its truth value depends on truth value of its parts. Like A⊃B can be true or false, depending on truth values of A and B.
But, it's not the case with ...
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How to define ‘impossible’ using propositional modal logic?
I am trying to define impossibility using the symbols we have in propositional modal logic. I got ‘negation diamond alpha’ in mind as equivalent to ‘it is impossible that alpha’. It that correct and ...
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Understanding David Deutsch's assertion about the laws of physics as emerging from those of biology
In the Chapter 1 of the Fabric of Reality, David Deutsch says the following:
There is no reason to regard high-level theories as in any way 'second-class citizens'.
Each of them has implications for ...
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so im arranging these arguments from strongest to weakest, and am confused?
Either reublocrats are uninformed, or democrans or independents are uninformed
it is not true that republocrats are uninformed
someone is uninformed
either republocrats are informed or they are not ...
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Issue with the interpretation of Propositional Logic
I’m having an issue with the terminology and perception authors use. Some authors perceive PL as a branch of logic “with subsets” with classical or truth-functional PL as these subsets. Other perceive ...
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i don't understand modus ponens
I'm learning about modus ponens in propositional logic but it doesn't makes sense to me
I can think of an examples where a true premises leads to a false
conclusion:
p -> q
p
Therefore q
If the kid ...
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