Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the ...

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Truth Value of Sentences Containing Logical Contradictions

Do propositions containing logical contradictions have truth values, or are they meaningless? For example: A) Some married bachelors exist. B) 95% of married bachelors live in Maryland. C) ...
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Self-referring propositions

This proposition is false As you can see in the proposition above, there is a problem. This sentence can't be true, but it can't be false either. I believe that this issue comes from the fact that ...
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46 views

To Check or not to Check? [on hold]

Samuel and Paul make a wager. They want to know if a certain professor held class the day prior when they were absent. The professor is unreachable, though, so they have to ask students from class. If ...
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63 views

How to prove that what we will know isn't true isn't true?

My apologies for the convoluted question. I'm still (kinda) arguing with someone that if we have knowledge then there are facts. One way I've argued for this, is by saying that what we will know ...
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35 views

A and ~A in logical proof

In my logic class last semester, we went over proofs with the rules of induction and replacement. In a couple of the exercises, I noticed something. In each of the exercises in question, all of the ...
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3answers
151 views

A Critcism of the Ontological Argument for God

Allow me to present the argument: (1) By definition God is that being which possesses every perfection. (2) Existence is a perfection. (3) Therefore, God exists. Whether you agree is not ...
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Why it is impossible to find a Pythagoras triangle (in integers), where two sides are powerful numbers? [on hold]

It is too elementary to prove this simple conjecture for primitive triplets, but this might had been a strong reason behind many unsolved problems in the history of mathematics, especially the most ...
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58 views

What do you call the output of a truth table?

I know that the value of said output can be either True of False, but what is the actual output called? Another way of phrasing the question is, is what do you call the resolution of a complex ...
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95 views

Thieves are they who do theft [closed]

Thieves are they who do theft. Theft is when A takes from B what belongs to B without B's consent. Gov't takes from B what belongs to B without B's consent. What is Gov't then?
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42 views

Can one be a Modal Realist without also having to incorporate the existence of impossible worlds?

I know Modal Realism well enough itself, and have read many of the objections (and subsequent responses) that David Lewis himself took up in relation to the philosophical position. My question is, do ...
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61 views

Difference between Tautology and Circular Reasoning

Often it is considered that a tautology is the same as a circular reasoning. However, in the Wikipedia entry of Tautology, it is mentioned that circular reasoning and tautology are different. Can ...
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43 views

Omnipotence Paradox Defense and Meinongianism/Neo-Meinongianism

I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could ...
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30 views

What are some active areas of research in proof theory?

Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out ...
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How do I figure out how to program a program that will figure out how nothingness couldn't exist and thus created the first event? [closed]

Assume that there was a first event and before the first event there was nothingness. I already have an idea of how it would work and proof that there was nothing before the first event here
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3answers
58 views

Can all mathematical reasoning be translated into traditional logic?

Can all mathematical reasoning be translated into traditional (Aristotelian, syllogistic) logic? It would seem not ∵ one cannot syllogistically establish the validity of the reasoning in the ...
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1answer
39 views

Probability and logic

Is probability theory (using Kolmogorov's axioms) an extension of the propositional calculus, or an extension of first order logic?
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107 views

What does the term “mathematical logic” mean?

What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical? Also, is "quantificational logic" a particular type of ...
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68 views

Within philosophy, is “reason” a broader concept than “logic”?

Within philosophy, is "reason" a broader concept than "logic"? In a comment under this question Jon Ericson suggested a case could be made for "reason" to include "logic" but not vice-versa. I had ...
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2answers
47 views

Is a social construction a social construction?

I've been thinking a bit about the core argument of social constructionism. Whenever I see the argument being employed, it seems that it means that if something is a social construction, then this ...
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89 views

Why does what I've written fail to define truth?

(Also posted in mathstackexchange prior to this). I stumbled across a set of axioms for first order logic a bit ago. Intrigued, I decided to try to write it all down and organise what I read. After I ...
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26 views

Nominalist views and contradictions

Given a flavor of nominalism which denies that simple sentences and existential quantifiers referring to mathematical objects are literally true (pretense theory, fictionalism, figuralism, etc.), ...
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1answer
45 views

What is the name of this fallacy: “You don't have an explanation for x but I do, so I'm correct and you are wrong”?

I hope this is the most correct stack exchange to ask this question. What is the name of the logical fallacy that follows: "You don't have an explanation for x but I do, so I'm correct and you are ...
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42 views

how to solve this proof ¬A ∨ ¬(¬B ∧ (¬A ∨ B)) without premises [closed]

How do you solve a proof given ¬A ∨ ¬(¬B ∧ (¬A ∨ B)) without any premises?
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168 views

Valid arguments as tautologies

I don't quite understand this : "As it turns out, all valid arguments can be restated as tautologies - that is, hypothetical statements in which the antecedent is the conjunction of the ...
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1answer
180 views

What does this definition of Cardinal Number mean?

Definition: The cardinal number of a class K is the class of all classes equinumerous with K. I understand that cardinal numbers represent the number of elements in a class, and I understand that ...
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27 views

What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
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75 views

Did Wittgenstein consider the possibility of a language that was token-private?

Wittgenstein criticized the idea that there could be a meaningful language that was only known in principle by one person. His insights have often been used to disregard the idea of private mental ...
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62 views

What motivated Gödel to arithmetize syntax?

What were the benefits of arithmetizing syntax for Gödel? What did the arithmetization of syntax allow for Gödel that was otherwise not possible?
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56 views

Tarski's semantic conception of truth

Does Tarski's semantic conception of truth X is true if and only if p (where X is the name of a sentence, and p is the sentence itself) apply to all sentences or only to facts (understood as ...
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41 views

Dialetheias in the absence of contraction/absorption?

One of the arguments given for dialetheism is that the paradoxes of self-reference, such as the Liar paradox and Russell's paradox, are most naturally regarded as dialetheias (both true and false). ...
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105 views

Why are implications with false antecedents considered true?

I don't understand what conceptual sense this scenario makes, or what the motivation behind the decision to make implications with a false antecedent true was. Can anyone help me understand this? ...
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1answer
33 views

How do I solve this formalized argument by drawing conclusions from inference rules?

I am given a conclusion and three premises, but I have to draw more inference rules from the three premises in order to prove the conclusion is in fact true, how do I draw the conclusion from the ...
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1answer
25 views

What is the logical form of this sentence using a truth table? [on hold]

How do I properly determine the logical form of the sentence (A*B) > (~A > ~B) using a truth table?
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590 views

What is the philosophical ground for distinguishing logic and mathematics?

I was wondering why the field of mathematics and that of logic are perceived as two distinct fields. Although could be pleased with the intuition that logic is rather meta-mathematics, still would ...
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1answer
35 views

Problematic conditional argument: what is the logical form and is it valid?

I'm trying to reconstruct an argument. The argument is not about what should or shouldn't be done. As you can see the antecedent is never being picked up in the next premise. So it's just a sequence ...
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1answer
61 views

An absolute truth

In 1976 Antoine Léonard Thomas wrote paraphrasing Rene Descartes: I doubt, therefore I think, therefore I am. My question is, is there anything else, built on such basic concepts, that has been ...
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96 views

Zeno's arrow paradox

Zeno's arrow paradox: Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one ...
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1answer
60 views

Tarski's original proof of the undefinability of truth

I'm trying to understand Tarski's proof of the undefinability of truth as given in his paper The Concept of Truth in Formalized Languages (English translation in Logic, Semantics, Metamathematics, ...
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1answer
113 views

Wendelin, Marcus Friedrich - Logicae Institutiones tironum adolescentum

where can I find an English translation of this book? Also, in it he talks about 12 pairs of term categories. which are really 21 (9 actual pairs and 3 "double sided" categories): he writes - De ...
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51 views

Exercise 2.2b from A New Introduction to Modal Logic

I am kind of stuck on page 48 on exercise 2.2b in Hughes and Cresswell; In case you don't have the book at hand here's the question: Let K** be K but with N and K replaced by LT: L( p→ p), ...
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1answer
42 views

Suppose A is a set of premises of an argument, and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B

Suppose A is a set of premises of an argument, and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B. (Use Fitch) I have no idea where to start, can someone help?
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Critical Thinking Course - A Good Choice?

I'm about to retire, and I'm going back to school. I have the opportunity to take an introductory Critical Thinking course, and I think that it will be a little dry, but I'm wondering if it could ...
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1answer
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Individual/Universal Concepts: What does Popper mean in section 14 of Logic of Scientific Discovery?

In section 14 of The Logic of Scientific Discovery Popper discusses the use of universal and individual names or concepts in singular and universal statements. He starts with a pretty ...
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75 views

Are all self-evident truths necessarily redundant?

Every justificationist theory of knowledge has axioms and premises that it begins with. This fact has led skeptics to criticize the possibility of knowledge by noting the infinite regress within any ...
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Extensional interpretation of an argument answer check

The question is: Provide an extensional interpretation (finite abstract model) of the following argument that shows it to be invalid. (3) ∃x(Fx∧∀y(Hy→G(xy)). ∀x(Hx∨Ax). ∀x(Fx→∃y(Ay→G(yx)). ∴ ...
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39 views

Does philosophy fall apart without the law of identity?

What would happen to all of philosophical thinking if the law of identity, i.e. 'each thing is the same with itself and different from another', were false?
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4answers
147 views

Does this philosophical argument about accidents and universal origin contain valid logical structure?

I'm not enough of a philosopher to properly analyze this particular argument, but I'm curious about it and I'd like to see it dissected and explained. "If the solar system was brought about by an ...
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245 views

Is religion fundamentally problematic for logical decision making in society?

From my interpretation, religion is a school of thought that encourages or rather demands that we believe in something on faith. Faith is to believe in something because we have been told that it is ...
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Can different varieties of modality be used with existential quantification?

I'm wondering if it makes sense to talk about worlds which aren't this one being real. It seems like you can claim that something possibly exists. Now I'm wondering, because it seems to amount to ...
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Almighty entities cannot be brave nor trust in the power of love

Given that a all powerful/almighty thing exists (example gods from different religions). Something almighty has nothing to fear, because they are almighty. Since it has nothing too fear it cannot be ...