Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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39 views

How to prove consistency of theory with metalanguage?

I am familiar with first-order model theory. I also know that Tarski's definition of truth was made precisely in order to avoid paradoxes related to metalanguage such as the Liar. My question is: how ...
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38 views

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 ...
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What does it mean for one geometrical axiom to be considered _equivalent_ to another geometrical axiom?

What does it mean for one geometrical axiom to be considered equivalent to another geometrical axiom? For example consider Playfair`s axiom: In a plane, given a line and a point not on it, at most one ...
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Is it useful to be able to define complex words with many definitions?

Greetings fellow earth dwellers. Definitions...useful, sharp, often-times dust clearing, so to speak. But as one progresses into intellectual conversations, definitions aren't so clear and can be ...
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Does there exist truly objective thoughts?

Today I was arguing with my friend that the colour of sky is subjective. I claimed that the colour of sky is a subjective idea and a person who is colour-blind may perceive it as a different colour. ...
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4answers
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Is identity unique and is it valid for only a given time?

Is identity unique and is it valid for only a given time? A river is not the same and changes constantly. Even the same can be said about a chair, so is identity bound to a time y and bound to a ...
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Solutions to the Exercises in Oesterle's Logic: Art of Defining and Reasoning (1963)

Is anyone aware of where I might find the solutions to the end-of-chapter exercises found in the above mentioned text?
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56 views

Is demanding an ureasonable and unrealistic amount of sources a logical fallacy?

Let's suppose the following: Person 1: All scientists agree that the sun is real. Person 2: Oh yeah, why don't you list every single scientists as proof? Here's another example: Person 1: Humanoid ...
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3answers
89 views

In the context of philosophical logic, what does 'extra-logical' mean?

I am having trouble understanding what 'extra-logical' actually means in the context of philosophical logic. Case in point: Bueno and Colyvan argues in their paper Logical Non-Apriorism and the ‘Law’ ...
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Do different elements of logic have different epistemological strength?

Do different elements of logic have different epistemological strength? By epistemological strength, I mean epistemological certainty or the certainty the concept is true and grounded on truth. For ...
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60 views

Are the premises of deductive arg's. founded upon inductive cases?…help is what I am in need of

Let's take this example of a deductive argument: P1: Monkeys like bananas. P2: Lucy is a monkey. C: Therefore, Lucy likes bananas. Disregarding whether this argument is true or false, how does one ...
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Is identity a construct or something real?

If race is a social construct, then is identity also a construct? Is identity the concept of something being itself something that exist in the world or something abstract that doesn't exist in our ...
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What makes a fallacy… a fallacy?

According to Wikipedia, a fallacy is "the use of invalid or otherwise faulty reasoning, or 'wrong moves' in the construction of an argument". I'm curious, however, about how are some things ...
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44 views

Paraepistemic logic?

Suppose a u-operator for "it is understood that" and a k-operator for "it is known that"; let S stand for various sentences. Here are some possible rules for relating these: uS → ...
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Does it make a difference to logic if the law of identity is never true instead of being sometimes true?

Does it make a difference to logic if the law of identity is never true instead of being sometimes true? It seems like when we don't consider the law of identity is not an axiomatic truth, we assume ...
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What things can't logic see or predict?

For example, logic cannot see or predict the possibilities of 'sensing (and different sensations)', 'ability to move (or mobility)' and 'intelligence', that are properties of human life. But I think, ...
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4answers
145 views

Why is non-binary logic not commonly used?

This question has been modified in response to a comment. While many-valued logic exists, rarely is it used. People primarily just use binary logic. Is there a reason for this? So many-valued logic ...
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What's the difference between allowing terms that do not denote any object and allowing models that have an empty domain in free logic?

A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty ...
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5answers
161 views

Is there any counterexample to the law of identity from the real world or outside of the real world?

These are given not just as nice rules of thumb to follow or ways that one should think. Aristotle identified these as necessary conditions for thought. People sometimes try to produce counter ...
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39 views

How is identity defined in the law of identity A = A?

How is identity defined in the law of identity A = A? Is identity the values and properties we assign to the object, or is it a circular definition where A is itself, or is it like a unique Id ...
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1answer
27 views

What purpose does allowing for terms that do not denote any object serves in free logic?

What purpose does allowing for terms that do not denote any object serves in free logic? Free logics may allow for terms that do not denote any object. What exact purpose does that serve. Does it ...
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4answers
47 views

When we say that the law of identity doesn't exist, does it mean it's always A=A is always false or that A=A is not always true?

When we say that the law of identity doesn't exist, does it mean it's always A=A is always false or that A=A is not always true? It seems that saying the law of identity doesn't exist, doesn't mean we ...
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Understanding, knowledge, and analytic truth

I read through this SEP article and wondered about the possibility of "understanding logic" vs. epistemic logic. One difference I could see would be that uS wouldn't necessarily be factive, ...
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Arguments Against Plural Quantification

What are some good arguments against taking plural logic, a slight extension of first order logic with plural quantification as a foundational logic? Alternatively, what are some resources that ...
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Can there be logic without the law of identity?

Can there be logic without the law of identity? If a = a doesn't always hold, can there be logic? I heard there are logical laws where the law of non-contradiction doesn't always hold, so I am ...
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112 views

What are the areas of mathematics philosophers deal with primarily?

Is it just discrete mathematics? I keep seeing symbols used in discrete mathematics on this stackexchange site. Is there any other area or is it just discrete mathematics, also what are the subfields ...
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108 views

Is there any exception or rebuttal to the law of noncontradiction?

Is there any exception or rebuttal to the law of noncontradiction? Do we know for certain that this law is universally true, or are there some situations where the law simply doesn't apply or is false?...
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Is the burden of proof a fallacy?

https://en.wikipedia.org/wiki/Burden_of_proof_(philosophy) When two parties are in a discussion and one makes a claim that the other disputes, the one who makes the claim typically has a burden of ...
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Does Quine's Predicate Functorese maintain the existence of relations?

Quine's predicate functorese has been proposed as a "feature-placing" language for ontological nihilism (Strawson, Azzouni, Dasgupta, Diehl). This is often used to eliminate objects and ...
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Does deflationary truth collapse into a correspondence theory?

If you ask what justifies a deflationary account of truth, doesn’t that reveal an implicit isomorphism within the justification thus collapsing the account into a traditional correspondence theory?
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Semantics of brackets

I'm interested in finding a categorematic semantics for brackets as used in formal languages, i.e. for indicating derivation histories of expressions. A categorematic semantics for brackets assigns ...
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4answers
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Deductively valid arguments and situations

In book 'Logic: A Very Short Introduction', Graham Priest has quote about deductively valid arguments. Here is one problem. Assuming that the account is correct, to know that an inference is ...
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Predicate logic - formula to sentence with a given domain

I need to transform the following formula to a sentence, given the domain = {1,2}: ∀x (P(x)-> ∃y Q(x, y)) My solution is: 1. (P(1)-> ∃y Q(1, y)) ^ (P(2)-> ∃y Q(2, y)) - remove universal 2. (...
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What is the difference between the first two sentences and the third sentence that makes the third sentence an argument but the not the first two?

The ones that aren't arguments: "Her favorite color is yellow because it is the color of the sun." (Critical Thinking) "Pooh is my favorite cartoon character because he has lots of ...
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3answers
251 views

Is Adams' argument Sound?

My friend sent me this argument to "prove the existence of god". I am not smart on Logic and I know people here are. The argument is explained in detail on Pruss's blog. Below is the ...
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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 ...
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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: ...
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25 views

What is the distinguishing factor between conviction and threat?

What is the distinguishing factor between conviction and threat? I want my friend to restrain from doing an action. I am showing him the bad consequences of the action thus, I am trying to convince ...
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Is it possible to find a counter model for epistemic closure in Nozick's system?

The epistemic closure is that: If S knows (if p then q) then (If S knows p then S knows q). In Nozick's Truth-Tracking Analysis S knows p if and only if p is true S believes that p If p were false, ...
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What's the difference between the principles of plurality and parsimony in Occam's razor?

Kasser in the Systems Thinker's Toolbox defines them as such: The principle of plurality: plurality should not be posited without necessity, or don’t make things more complex than they need to be. ...
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What type of argument is this?

This example was in Critical Thinking by Moore and Parker: My landowner will increase the rent, so I should not get a dog. As I was reading the text, I wasn't sure what type of argument this would be. ...
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Structure of “affirming the consequent fallacy”

The formal structure of affirming the consequent fallacy is, P1 - If A is true, then B is true P2 - B is true --------------------------------- C - Therefore, A is true Now if I give another similar ...
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Does a proposition have to have a true conclusion?

“...understand that a belief is propositional, which means it can be expressed in a declarative sentence—a sentence that is either true or false...Recall that in logic, a proposition has been ...
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What the Preface paradox tells us about the principle of explosion

The Preface paradox (adopted on a classical logician): Imagine that a classical logician has just written a textbook (on classical logic). He has included many assertions in it and has thoroughly ...
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Can I lie saying an affirmation onto something that doesn't exists

If someone asks me where I live, and I give an addres I know doesn't exists, for example, "Sunset Boulevard 1600", being the address number 1600 inexistent, ¿Am I lying? If I am lying, then ...
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103 views

Let P does not imply Q, and Q does not imply P. Are P and Q independent?

Let P does not imply Q, and Q does not imply P (P → Q and Q → P are both false). Would it correct that P and Q are independent? Is it possible to have R that can imply both P and Q?
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Ontology - How do we describe actions/scenarios in relation to objects?

Does anyone know how actions to do with objects are represented in ontology or first order logic? Example: the cat sits on the mat. I think the cat and mat have properties that relate them to each ...
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Is there a difference between rejection of a belief, and withholding judgement? Does rejection of a belief B, mean ¬B or does it mean a lack of B?

Is there a difference between rejection of a belief, and withholding judgement? Does rejection of a belief B, mean ¬B or does it mean a lack of B?
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136 views

Generating the simplest sort of Cosmological Argument

First, I am not a philosopher, but rather an applied mathematician. However, the Cosmological Argument has always intrigued me. At times I feel that all attempts are necessarily hopeless, at other ...
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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 ...

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