# Questions tagged [symbolic-logic]

For questions related to symbolic logic, also known as mathematical logic. Topics might range from philosophical implications of metamathematical results to technical questions.

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### Philosophers or philosophical traditions that reject symbolic reasoning

I'm most familiar with philosophy in the context of discussing various flavors of logic, such as independence-friendly logic, various extensions of first-order logic with plurals, relevant logic, and ...
101 views

### Symbolization and Evaluation of Some Simple Sentences

Here are some sentences, and I want to know whether I'm thinking about them correctly: (1) The tooth fairy is not real. Symbolization: (-R)t Truth Value: False (2) It is not the case that the tooth ...
132 views

### Can you give me some concrete example, so that I could understand these modal logic sentences

So there is these simple modal logic sentences: □(a → b) and a → □b Can anyone help me with some real-life examples, because I have troubles grasping the difference? edit The simpler question is this: ...
51 views

### Fitch proofs help?

I'm new to logic and can see how to write these out informally, but need some help seeing how they should be translated into formal proofs in Fitch.
201 views

### How do we arrive at stronger theories in mathematics/logic?

A reasonable aim of formal mathematics/logic is to build systems which can "interpret" many things. As an example, ZFC can interpret a number of things. Incompleteness Theorems provide us ...
155 views

### How to model “forget about” in first order logic?

The other day, my housemate said "Don't forget to not leave the spoon at the bottom of the container". I understood what he meant: "Do not leave the spoon at the bottom of the ...
37 views

### How to represent “apart from” formally?

While working on an argument over the last few days, I came to a point where I needed to formally render an "even if" sentence. Here and here, I found some good options, but I'm not sure I ...
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### Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)

Does ∃x(Nx & ~Nx) contradiction itself? Is there an error in my proof? Thank you
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### Prove (-A=-A) = [-(-A => A) = (A=>-A)]

This is not homework I do this for fun. I tried using prover. The result is quite confusing. I use the Logic Book This is the last problem I want to do in this section. I have to it mostly in SD+ . |- ...
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I think I got it, could you take a look, please.
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### Prove the following theorem: Need hints to finish it

This is not homework. I do it for fun and learning. I use the Logic Book. Problem has to be done in SD+. How to prove the following argument : |- [~A =>(~B=>C)]=>[(A v B) v (~~B v C )] I ...
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### How do I symbolise this statement with a definite description in first order logic?

"If there is exactly one present King of France, then the present King of France is a present King of France" The part I am confused about is the consequent of the conditional which equals ...
376 views

### How did symbolic logic show that Heidegger's assertions about the nothing were illogical?

In his inaugural address at Freiburg University in 1929, Heidegger explicitly challenged the central place given to logical principles in neo-Kantianism, on the basis of a radical account of ‘the ...
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### Need help to convert the following semantic tableau to Fitch style proof

Derive ~M 1.~R & ~W. 2.[(R=W)v(Mv G)]=>(W=M). As you see, the tableaux is valid.So l want to translate it an SL derivation(Fitch style) Here is my understanding 1 ~R. 1 => E 2 ~W. 1 =...
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### Need to check to if my SL is correct for following problem

This is not homework . l do this for fun. I am 58. I graduated Concordia University in 1993 Problem comes from the Logic Book by Bergman pg 217 (17)c I want to see if my SL is correct. If civil ...
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### Need help to inconsistency problem

I am using theThe Logic Book) I need help to find the inconsistencies. using SD 1.(E V F)=>(G & -I) 2.(G V F)=>I 3 -F=> E I tried everything to show it I think showing -I and I might do ...
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### What is the smallest theory formulated in a given first-order language? [closed]

I received an exercise question in my meta-logic course, which asks: "What is the smallest theory formulated in a given first-order language L? Provide an axiomatisation of this theory. What is ...
90 views

Consider an example A A V ~B (addition) B > A It seems logically vaild . Now assume A is being apple and B is banana . So its equivalent **It's Apple It's apple or not banana If it's Banana ...
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### In symbolic logic why (p->q) and (p->~q) don't contradict each other?

I am a beginner in symbolic logic and still mostly using intution to solve the problems. After spending some time trying to figure out why (p -> q) is true if p is false I've realized that this ...
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### Understanding [(a→b).(c→d)] formula in section 36 of The Logic of Scientific Discovery

Excerpt from footnote 1 in section 36 of Popper's "The Logic of Scientific Discovery": In the present section, the arrow is used to express a conditional rather than the entailment relation....
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### What is 'expendable' in logic and how to explain 'tautology' given this image?

This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
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### Is the material implication the correct model of conditional reasoning in mathematics?

Question: Do you believe that the material implication correctly models the kind of conditional reasoning necessary in mathematics to prove a theorem? Example: If x > y and y > 0, then x > ...
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### Is there a symbol for what a logic gate yields?

Is there a logic symbol for what output a logic gate yields? For instance, for an AND gate: A B A ^ B T T T T F F F T F F F F I want to propagate A ^ B into output C, but I wouldn't want to use ...
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### an argument that is clearly valid but invalid in a sentence logic

I was reading these paper(dont really remember the title) it stated that there are simple arguments that are clearly valid but would be counted as invalid in the sentence logic system it was using. i ...
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### What relationship exists between logical and. material Implication (Conditional)? Can you please represent both conditionals in a truth table?

Can someone help me derive the truth table of the logical conditional from the material conditional? Here are three statements about logical implication from my logic professor: Given the argument: S:...
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### Is there a non-transitive frame in which schema 4 is true? Or an irreflexive frame in which schema T is true?

So, I know that I can construct a frame {W, R, I} which is not transitive and in which schema 4 is not true (more specifically, Axiom Schema K and Axiom Schema 4 are not both true). I also know that I ...
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### Formal versions of exotic logical connectives in natural language

Formal logic tends to be concerned with minimal or at least almost-minimal sets of logical connectives. The standard logical connectives are and, or, implies, iff, neg (I couldn't use Latex for their ...
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### Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) [closed]

Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) How do I prove this using statement logic? I know I need to start with a supposition ...
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### What does the symbol “:=” mean in formal logic?

:= What does the "colon-equal symbol" mean, and how is it used?
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### A thought experiment: will the following observations lead you to question Aristotle's syllogism?

Many philosophers think that logic are "inherently right" and cannot be refuted by empirical observations. Below is a thought experiment that questions this view. Let's take Aristotle's ...
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### How do you express the following in symbolic logic?

If P is true, then Q is true. P being false or unknown says nothing about Q. Instead of a truth table like this: P : Q 0 : 0 = 1 0 : 1 = 1 1 : 0 = 0 1 : 1 = 1 You have a truth table like this: P : Q ...
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### When can I discharge an assumption? or better put, When can I not discharge an assumption?

It's homework, so I won't give the example, but when is it legal for me to discharge an assumption? Basically, I'm introducing a conditional to prove a theorem that does not rest on any assumptions, ...
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### Tautology of p implies q and not p or q [duplicate]

I'm learning about tautologies right now. I see that a tautology is when two propositional statements have the same truth values. But I'm struggle with the truth table my professor provided about the ...
227 views

### How to reconcile the fact that mathematical proofs are logical implications with the lack of a formal calculus equivalent to the logical implication? [closed]

Theorems follow from axioms. That is, theorems are the logical consequence of axioms. Thus, mathematical proofs are essentially deductive. Proofs are all essentially logical implications. There is ...
101 views

### how to translate the following sentence

Either it is not the case that Gonzolo play music and does not go to concert,or it is not the case that he does not read book and does not play football. P:Gonzolo play music , Q: Gonzolo go to ...
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### if [if (if P then Q) then (if P then R)] then [if P then (if Q then R)]

i am new in logic course, i saw an question in my book. it says that show the following argument is valid by using natural derivation rules. if [if (if P then Q) then (if P then R)] then [if P then (...
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### Truth function question

Is there a truth function connective for the phrase “after all” I know “all” can be done in finite cases I am using the Logic Book 4th ed I am trying to find a paraphrase for it.
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### Why does Gensler's Star Test not work on some syllogisms? [duplicate]

All teachers are intelligent. All teachers are well-paid. From the Star Test, we can deduce that the argument must be invalid with whatever conclusion (according to the classical syllogism figures), ...
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### Are there famous unsolved problems in logic akin to the Millenium Prize problems?

Are there major theorems that logicians have yet to tackle? And I don't mean any problems that pertain to the philosophy of logic (i.e. logical pluralism, the nature of logical consequence, etc), but ...
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### Equivalence Thesis

What is, if any, the canonical justification accepted in mathematical logic for the Equivalence Thesis, asserting (1) that indicative conditionals are truth-functional logical expressions and (2) that ...
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### Why is Turing claiming that a complete and computable axiomatization of arithmetic would imply the decidability of first-order logic?

So I'm reading the famous paper of Turing "On Computable Numbers, with an Application to the Entscheidungsproblem". At the beginning of his proof of the undecidability of first-order logic (FOL), he ...
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### The form of elementary propositions in TLF

In Tractatus Wittgenstein states that: 4.22 An elementary proposition consists of names. It is a nexus, a concatenation, of names. Suppose now that L is a first order language. As far as I ...
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### fitch proof. P v Q Q→ ¬ R ¬ P ¬ R → ¬ S GOAL: ¬ S

Need help exercise using the FITCH program format. I'm stuck on where to start. The following 4 steps must be used to prove the goal. P v Q Q→ ¬ R ¬ P ¬ R → ¬ S GOAL: ¬ S Now I know: ¬ P and P v Q ...
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### Solving a proof with Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. B ^ D (B^¬A) → ¬C B → ¬A (D^E)→ (A v C) GOAL: ¬E
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### Is ¬(a = b) the same as (a ≠ b) in logic

Are these the same in predicate logic with identity: ¬ (a = b) a ≠ b I'm not quite sure whether they can be used interchangeably in proofs. Any help would be great!
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### What is (∃!e) in Davidson 1967?

Davidson proposes a causal law for singular event causation. Here is one example of a backward-looking part of such a law (changed slightly for clarity and to avoid copyright infringement): (e)(u)((...
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### Alphabetic Substitution, Barcan, and Strict Implication

Context: I'm stuck on Axiom 8 from the introduction to Barcan 1946, "A Functional Calculus of First Order Based on Strict Implication." My instinct is that I'm missing a basic, perhaps obvious concept-...
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### Is Classical Logic the proper model of the deductive logic of human reasoning?

Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it? The expression "Classical ...