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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An absolute truth

In 1976 Antoine Léonard Thomas wrote paraphrasing to Rene Descartes: "I doubt, therefore I think, therefore I am". My question is, is there anything else, builded on such basic concepts, that has ...
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57 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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What is the source of source? [on hold]

This may be in the wrong site. But since it's about logical reasoning I guess it is a good spot to ask. Preface: You probably are aware of two theories of how the universe came into existance. 1. If ...
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49 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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110 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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Is something “stupid” because it has no intelligence? [on hold]

One often hears that physical things are called "stupid" by other people. For example: "That stupid chair broke yesterday!". In such an occasion I'm always thinking how can something be "stupid" if ...
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49 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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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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55 views

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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43 views

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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57 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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26 views

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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37 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
131 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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5answers
233 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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34 views

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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2answers
98 views

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 ...
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85 views

What is the difference between ∃ (existence) and A (actuality)?

The existential quantification can, it seems, be used with modal logic. Now excuse my naivety, but: if so, what is the difference between being actual and existential quantification? I'm just ...
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64 views

Word for property such that any object which possesses it is the only object which possesses it?

Suppose that I have a property such that any object which possesses it is the only object which possesses it. For example we might suppose that the property of "being Sally's partner" is such a ...
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32 views

Is there a symbolic formulation of modal realism?

Is there a symbolic formulation of modal realism, i.e. the doctrines of modal realism captured in some formal system?
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113 views

How should one properly characterize mathematical conclusions?

I am a mathematics graduate student, not a philosophy student, so please bear with me. However, I am interested in investigating what exactly it is that I spend the majority of my week doing! As ...
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3answers
84 views

No absolutely consistent foundation for math: logically possible?

Is it logically possible that there really is no absolutely consistent formal system, already discovered or yet undiscovered, that can serve as a foundation for mathematics?
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74 views

In defense of consequentalism

Deontologists such as Thomas Nagel say Consequentialism permits actions that aim at evil, which is why it is a false theory. If a (moral) Theory permits actions that aim at evil then it is wrong. ...
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118 views

What is the fallacy where you completely discredit someone because of a single mistake?

Someone recently told me he felt that an entire scientific field's consensus is invalid because some of its scientists had come to what he believes were incorrect conclusions in the past. For ...
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293 views

Why does the Second-Order Axiom schema of Comprehension not lead to Russell's Paradox for ZFC2?

Let ZFC2 be the Second-Order formalisation of ZFC. The Second-Order Axiom schema of Comprehension (part of the deductive system for SOL) says that for every formula (of SOL) there is a relation with ...
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67 views

Can anyone solve (s→p)→r, ~r, (p→q)→(t→r)//~t

I've been at it for hours. The only tools I'm allowed to use are as follows: Indirect derivation Direct derivation Conditional derivation Modus ponens Modus tollens Double negation Repetition ...
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74 views

If metaphysical grounding of beliefs is not necessary what is to logically compel one to believe anything?

'Grounding' is the notion that 'because of X, Y', X being the reason one can accept Y beyond pragmatic considerations. In this way, X and Y are analogous to cause and effect respectively. If it is ...
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79 views

Infinity is a ridiculous concept [closed]

I just watched a Vsauce video How To Count Past Infinity, and it got me thinking so i post my thoughts here, as i don't know what to do with them. First off, the object of the video is that "Some ...
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4answers
280 views

Question of Identity

Conversing with someone trying to convince me that 2 and 1+1 are not the same thing. His argument was that although 1+1 = 2, they are in fact different because the notation is different. We see "1+1" ...
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4answers
80 views

What Justifies Reason (Newby Question) [duplicate]

I guess reason can't be used to justify itself. This is something Presuppositional Apologists love to play mischief with. So how do we justify anything based on reason when reason itself is ...
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131 views

David Lewis, conditionals and restrictive quantification

In a nutshell: When are conditionals containing adverbial quantifiers true according to the David Lewis account? In particular, how are they to be judged if the situation in the antecedent never ...
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152 views

Are there any books which reduce famous Philosophical Arguments to Logical Notation?

I have just started studying logic and wish to find some example arguments by famous philosophers broken down very plainly into their premises and conclusions, along with the logical notation to the ...
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33 views

Why are these formulas not well-formed in syllogistic logic?

I'm studying formal logic, and I get stuck in the beginning. I'm trying to do easier translations in syllogistic logic. I'm using Gensler book "Introduction to Logic". They say that this examples ...
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78 views

In modern logic, why does “All S is P” contradict “Some S is not P”?

In modern logic, the existential import is removed from universal statements. So All S is P may still be true if there is no S at all. Contradictory statements must have opposite truth values. Why ...
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95 views

Is this a valid solution to the liar paradox?

Example: Is the statement "These letters are black." true or false? If the letters are black, then the statement is true. If the letters are not black, then the statement is false. In this example ...
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1answer
33 views

Prove by induction that no terms in FOL of arithmetic begins or ends with 2 plus signs (++)

Prove by induction that no terms in FOL of arithmetic begins or ends with 2 plus signs (++) I have no idea how to start this proof, can someone help me?
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67 views

If “All S is P” is true, does it contradict “No non-S is non-P”?

I have a problem I encountered in a logic textbook that I cannot figure out after multiple tries. Say we assume that "All S is P" is true. Does this allow us to conclude the truth value of "No Non-S ...
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589 views

Logical fallacy classification: comparing the best from one group with the worst in another

I am looking for the name for the logical fallacy that compares the best samples from one group with the worst samples from the second group and concludes that the first group is better than the ...
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5 views

Identifying a statement which weakens the conviction of tribes from the passage

This question is of critical thinking. I opted for option c.) as option a.) and option e.) seem to be irrelevant and option d.) looked too far direct in sense comparison to the passage , meanwhile ...
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58 views

Could there be such a thing as a universal logical language?

That is, are there certain conceptual primitives, such as object, action, structure, property, logic, event, quantity, partial, paradox, system, concept, etc, or connectives/judgements, such as for ...
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92 views

Why do we confine ourselves to static ‘thing’ logic when we are dealing formally with time, which is dynamic?

All ‘temporal’ logic statements are expressed in solely static terms that can be compared to static reference phrases or related to the number line and evaluated with arithmetic. For example, ...
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What philosophical reasoning do proponents of copyright infringement use in support of their position?

Obviously copyright infringement, under every main stream school of thought is wrong. You put work into creating something, such as a video file that is a movie that you spent millions of dollars to ...
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which problem Russell is focusing on while providing a solution, in his introduction to the Tractatus?

In the final part of his introduction to the Tractatus Logico-philosophicus, Russell provides a possible solution to the problem of the impossibility of self-reference of logic: There is one ...
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51 views

Why may I considere Wittgenstein a Kantian thinker with regard to metaphysics?

Wittgenstein is a Kantian philosopher as far as the structure of the Tractatus, as far as the last part (section 6 and comments) are concerned with: that I cannot speak about the subject in the ...
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24 views

Are propositions of sciences to be considered propositions of natural language, in the Tractatus?

Given the following assumptions: 1) When Wittgenstein speaks about meaningful propositions he does refer to propositions of natural sciences. 2) About the problem of the perfection of language, he ...
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68 views

can a vague sentence be considered meaningful in the Tractatus?

In the Tractatus, Wittgenstein draws a demarcation among meaningful sentences (1), the meaningless propositions of logic (2: sinnlos sätze) and nonsensical propositions (3: unsinnig sätze). 1) ...
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60 views

How Can the Unobservable be Verified?

Empirical evaluations and judgments concerning the observable world (e.g. whether or not I'm eating a watermelon right now) are evidently verifiable; you can confirm that I am indeed eating a ...
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65 views

Why should my solution of this logical problem be false?

Consider the three statements A,B and C to be true even if they are different from the commonly known facts I drew two euler diagrams for this and concluded that conlusion II and IV follows and ...
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70 views

Is Logic Pre-Human?

It was German philosopher Martin Heidegger (1889-1976) who famously said, "animals are poor in world." Although this may be true, I do not see them as being poor in logic. Paleontologists have ...
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The reducibility of propositions and the link between them

Is it possible to reduce, or determine the reducibility of a proposition into simpler combinations of state of affairs? For example: "Eating small animals is wrong." in a given context (vegetarian ...