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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The difference between argument, inference, deduction and proof?

I am trying to sort out the difference between argument, inference, deduction and proof. First, let's look at the distinction between argument and inference (if there is one). This online source ...
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Is there a content based equivalence of statements, separate from truth tables?

Consider the following truth table for the "equivalence" statement P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T which we define to be true when both the truth values of P and Q are the ...
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How can I be certain I exist? [on hold]

The question is simply: How can I be certain I exist? Or anything in this "world" for that matter?
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Changing inconsistent to valid

I found the following passage in Mark Sainsbury's 'Logical Forms' If a collection of propositions is inconsistent, any argument whose premises consist of all but one of the collection, and whose ...
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Does studying philosophy help finding answers to questions in life?

In an attempt to find answers for almost life-long critical questions specifically concerning epistemology and logic, I'm currently considering getting a degree in philosophy. For y'all who have ...
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How to deal with ¬∃ (negated existential quantifier) in a proof?

I need to prove that the following premises lead to a contradiction. ∀x (P(x) → Q(x)) ∃x ¬Q(x) ¬∃x (¬P(x)) A couple of things are confusing me. Does the first premise say that if x is a P then ...
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90 views

Why is Hesperus necessarily Phosphorus?

"Hesperus (the evening star) is Phosphorus (the morning star)" is one of Kripke's examples of necessary aposteriori, statements that are true necessarily if true at all, even if their truth can only ...
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62 views

name this fallacy: A was P in the past -> A must be P now

I've been seeing arguments of this form for awhile: (agreed true premise) Some predicate P was applicable to behavior/event/thing A in the past. Variations: P(A) may have been true at some ...
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192 views

“I have X in my blood” arguments

Lately, I have been hearing the argument "Oh, well I have Indian(Native American) in my blood, and 'redskin' does not offend me so why change the name?" coming from people who claim their ...
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109 views

Calculus for Higher Order Logic

Famously, there is no complete calculus for higher order logic that is effective. Therefore, given the rules and axioms of a effective calculus for higher order logic, we must find formulas that are ...
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Is “propositions of logic are tautologies” (Wittgenstein) literal or mystical?

At 6.1 in the Tractatus, Wittgenstein says, "The propositions of logic are tautologies." When he says this, is he referring to the fact that the axioms of propositional logic as presented, for ...
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93 views

Proof that using only logical form is valid?

I'm studying logic. One of the fundamental things that I find everywhere is the claim and I'm quoting wikipedia: "The concept of logical form is central to logic, it being held that the validity ...
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Infinitary logic and algebra

After identification of equivalent formulas, is the algebra of formulas of a two-valued propositional calculus with infinitely long expressions a (free) sigma-complete Boolean algebra?
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Logic – Deduction in Tarski's World (Fitch/LPL 13.36)

I am working on proving the following question: | ∀x [Dodec(x) → LeftOf(x, a)] | ∀x [Tet(x) → RightOf(x, a)] |––– | ∀x [SameCol(x, a) → Cube(x)] The question has the following rules: […] give a ...
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Logic – Deductive proof with quantifiers (Fitch/LPL 13.30)

Here is the question from Language, Proof and Logic (LPL). Problem 13.30: 1. | Likes(carl, max) 2. | ∀x [∃y (Likes(y, x) ∨ Likes(x, y)) → Likes(x, x)] |––– ...| ?? | ∃x Likes(x, carl) I haven't ...
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29 views

The meaning of logical terms

I sometimes find the expression "predicate variable" but I don´t know what its meaning is. A definition would be helpfull. Thanks.
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82 views

Why an infinite set of propositional variables?

A formalised language for the propositional calculus consists of: an infinite (countable) set of propositional variables p_0, p_1,...; a set of propositional connectives (conjunction, disjunction, ...
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104 views

First order languages vs languages with infinitely long expressions

What is the difference between first-order languages (where the universal and existential quantifiers are defined as infinite disjunctions and conjunctions, respectively) and languages with infinitely ...
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What is the difference between deductive reasoning and inductive reasoning

I have been scouring over the internet in pursuit of a valid elaboration as to the difference between deductive and inductive reasoning, especially when explained using examples. The content that has ...
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54 views

Boole on language

I am trying to understand the meaning of this quote of Boole 1847: "Language is an instrument of Logic, but not an indispensable instrument." There are something logical outside language? They are ...
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41 views

Any video course on Logic & Logical fallacies?

After discovering this site and spending some time going through questions, I'm amazed by the answers and comments on Is 'guns don't kill people people kill people' a good argument?. Even though I'm ...
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104 views

Are there any strong reasons to still consider logical monism or a “One True Logic” in light of all the non-classical logics that have been developed?

I know there has always been some debate concerning whether or not a certain logical system (like classical logic) is the correct one, especially when it comes to propositional claims about the ...
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96 views

Formalism: philosophy of mathematics

Is it a contradiction, if I am a formalist but I think that mathematical objects are created by human mind ? In other words: Am I allowed to be a formalist and to believe that ...
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70 views

What form of formalist am I? [duplicate]

I am an formalist in the sense that I think that mathematics is just manipulation of symbols. But I think that this manipulation is motivated by the phantasy of humans: mathematical objects are for me ...
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145 views

Law of excluded middle: mathematical philosophy

Is it a contradiction, if mathematical objects are for me "mental constructions" -- like in intuitionism but I accept classical mathematics and the Law oft excluded middle ?
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63 views

The validity of the definition of a valid argument

I have some serious problems understanding what counts as a valid argument and what does not. I have read some different definitions of what a valid argument is: An argument is valid if (1.) The ...
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66 views

Law of excluded middle in intuitionistic formalism

Does intuitionistic formalism accept the law of exluded middle?
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167 views

Should we make ourselves clear in arguments?

Let's say there's the claim: There is a place that men are forbidden to enter. I think we are allowed to say that ginger-haired men mustn't enter there. But are we allowed to say that there is ...
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77 views

Mathematical philosophy: intuitionistic formalism

What is intuitionistic formalism? Tarski called himself an intuitionistic formalist.
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637 views

What practical methods can be used to prove a negative claim?

I realize that the burden of proof falls squarely on the shoulders of the person making the claim, but they often seem unwilling to do the footwork. It is difficult to prove a negative case except by ...
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67 views

Mathematical logic question from Rosen book

I am working through the Rosen Discrete Mathematics book. The question is; M(x,y) = x has sent y an email message Use quantifiers to express; There are 2 students in your class who have sent each ...
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FOL – Quantifiers and prenex form (from LPL 11.37)

Prenex form – when all the quantifiers are at the front I am struggling to figure out a couple questions from my book: #7 – ∃x [Cube(x) → ∀x Small(x)] #8 – ∃x [Cube(x) → ∀x Cube(x)] I never came ...
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49 views

What's the difference (if any) between demonstration and description?

How do philosophers of various schools* explain the difference (if any) between demonstration and mere description? Are they synonymous, or are they different? How so? My first impressions: To ...
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What's the name for this kind of argument: This book or this person says P is true, therefore P must be true

People often claim P is true because a single book or person says P is true. This is most often the case when the book or the person is said to be divine. So is it a fallacy when people theorise the ...
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1. “X is a subset or part of y. x is true. so, y is true.” 2. “x came from y. y is true. so x is true”. Which fallacy are they?

example of the second argument. 'ad-duniya' (an arabic word) means 'nearer'. the word is denoted 115 times in Quran. In some cases the word 'ad-duniya' has been used for the meaning 'this world'. So ...
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48 views

“Change” last forever? If not what fallacy breaks the chain of reasoning shown here?

In movies, a frequently mentioned idea is that "Nothing lasts forever" .There's also a Chinese saying 變幻是永恆 Having thought too much into treating concepts as something similar to "building blocks", I ...
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46 views

Does this sacrifice dilemma has a name and has been studied by anyone?

The dilemma is the following. There's a button, if you press it, the world will get fixed by curing aids, cancer, fixing world hunger, homelessness, etc. HOWEVER You will die in 6 hours and receive no ...
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If V, then W. If W and X, then Y or Z. Not Y. Not Z. How to deduce the conclusion?

Prescript: I quoted the standard form of argument because its use of colours improves readability. Source: 6 minutes 01 seconds juncture; Lecture 13, Video 5 (transcription inexistent); MITx: 24.00x ...
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138 views

Would two identical people ever be able to communicate successfully?

Let's say you know some guy. And you told him that he was going to be copied and both him and the clone moved to an area where there are no external factors. After telling the man this, the man is ...
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220 views

Do humans make decisions based on logic or emotions?

I often hear that we are emotional beings, that we make decisions based on our feelings, mood and emotions. These decisions may not be logical and serve us best. On the other hand some argue that we ...
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LPL 10.26 - Fitch - How to use ∀ Intro and ∃ Elim?

I am using LPL (Language, Proof, and Logic, commonly known as LPL) and the bundled Fitch program. I am trying to solve problem 10.26: 10.26: ∀x Tet(b) ↔ ∃w Tet(b) Looks simple enough, as the ...
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66 views

Looking for references for some remark of Quine's

I'm looking for a comment I think I remember Quine having made. He's talking about our understanding of proofs. I think he says something along the following lines... If you understand many different ...
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90 views

Can the “accident” fallacy be applied to religious laws?

I need help understanding a discussion of the accident fallacy from the following site: http://www.logicallyfallacious.com/index.php/logical-fallacies/2-accident-fallacy It describes the following as ...
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Why is Tarski's notion of logical validity preferred to deductive one?

Its flaws are well-known and serious. To recall, an inference from A to B is valid iff all interpretations of "non-logical constants" that make A true also make B true. What are interpretations, ...
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An invalid argument, the conclusion of which is a tautology

Why it is not possible to have such argument? I found some textbook Introduction to Formal Logic and this is from one of the first excercises. This is marked as impossible, but I do not understand ...
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What is the relation between a conditional sentence and the corresponding universal statement?

I had a technical question about conditionals. To use an example, consider the following conditional statement, (1) If X is a man, then X is a father I consider (1) to be false because I consider ...
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When an individual makes a discovery

When an individual, or society as a whole, makes a discovery, different outcomes can occur e.g., they can enrich the individual or, they can debilitate the individual or, they can confront the ...
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When a fallacy actually occurs

Assume a debate has occurred and a result ended the debate, but in this result a slippery slope is coming true - more specifically the contrapositive used as a basis for argument that relied on a ...
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Argument against democracy/socialism as an ethical system [closed]

If n=4 people showed up and told you, "we're going to take our combined wages and vote about what to do with half of it", most people would consider it theft at best. Even in theory, I can't imagine ...
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Handling “paradoxes” in logic: The sentence after this is true. The sentence before this is false

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false When contradictions appear in proofs, ...