Questions tagged [deduction]

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Proof truth is absolute and not relative

First of all, I want to point out I am not any expert in philosophy, so this question is not based in no further readings, but only my own knowledge in logic. Imagine I want to proof the truth is ...
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3answers
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Have I totally misunderstood conditionals all along?

I've been talking to a friend of mine about modus ponens (and modus tollens) and I'm wondering if I have totally misunderstood something fundamental about conditionals. Here are the two opposing ...
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Why is “an invalid argument, the conclusion of which is a tautology” not possible? [duplicate]

A similar version of this question was answered before, (An invalid argument, the conclusion of which is a tautology) but I'm still a bit confused about why this is not possible. Like the other asker, ...
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Is it standard to distinguish two versions of the hypothetico-deductivist conception of science : confirmation approach and falsificationism?

In his course on Philosophy Of Science, Pr Folse ( Loyola University New Orleans) distinguishes two trends in the " empricist consensus " ( that emerged in the 19th century) : inductivism ...
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How to deduce V from (U → V ), (¬U→V) using Deduction theorem?

We have these axioms and modus ponens: Axiom 1 is: P→(Q→P) Axiom 2 is: (P→(Q→R))→((P→Q)→(P→R)) Axiom 3 is:(P→Q)→(¬Q→¬P) Modus ponens is: from P and P→Q infer Q Edit: I still couldn't solve it, so I ...
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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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1answer
75 views

Are inferences in everyday life often combinations of inductive, deductive and other possible methods of inference?

Logicians have distilled methods of inference into some fundamental kinds like deduction and induction. In everyday conversation, though, we are constantly making inferences both inductively and ...
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How to prove: 1. (A^B)v(A^C) 2. (AvD) -> E //E

This proof has stumped me. It seems that getting (AvD) alone then using Modens ponens to therefore prove E would be the correct way of going about things but I cannot seem to find a way to get (AvD) ...
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1answer
38 views

Intro Natural Deduction Problem: Given premise (p -> q) -> p show p using deduction

This is from the Daniel Bonevac Deduction text, page 122 #12. Given premise (p -> q) -> p show p using deduction. I can do this using made up rules on steps 4+5, not given in the book. The other ...
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1answer
581 views

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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1answer
65 views

Counterfactuals in Premises for Arguments

Can counterfactuals in premises make an argument sound and valid? I understand that soundness requires both validity and true premises whilst validity requires the premises to follow to the conclusion....
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Deductive reasoning & conditionals

What would be a good example of explicit deductive reasoning that doesn't seem to be possibly interpreted correctly as a conditional (If A, then B)?
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1answer
114 views

Hey all can you help prove the following from Garson's ML for Philosophers: [closed]

Exercise 1.7 (e) Modal Logic For Philosophers 2nd edition: []p v []q/[](p v q) {hint: set-up vout first} I would appreciate it if you can solve it using the methods laid out by Garson (PL+[]in+[]out)...
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2answers
100 views

In a deductive reasoning system, what happens if we have unfounded axioms? [closed]

What if our axioms are false? What happens then?
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1answer
160 views

Classification of deductive reasoning types

Please, could you help me make sense of/classify types of deductive reasoning? When studying mathematical logical, I have noticed there is this Hilbert's axiomatic system (Hilbert calculus) with its ...
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158 views

Are all non-deductive arguments inductive?

I am having troubles with understanding this question. Can someone give me an example/insight about where to go from here?
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2answers
241 views

Logical fallacy: Person argues with wrong probability of event, without considering similar events

I know that this is a common error in argumentation that people make, but I don't know if there is a term for it. It's when people argue from an event being remarkable because of its low probability, ...
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70 views

Is there a semantically complete system of direct-method natural deduction/sequent calculus?

Does anybody know of a system of direct-method natural deduction/sequent calculus, in other words, a system that does not require (or even incorporate) conditional (and indirect) proof method(s) and ...
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2answers
55 views

(p->q) v (q->p) with Natural Deduction

Well, indeed I have the answer to this exercise but I don't understand some steps. From 6 to 17 are OK for me but from 2 to 5 and then when step 5 is again called in step 10 is something I don't get ...
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4answers
605 views

Why is this deductive reasoning incorrect?

All goats have a beard. Karl Marx had a beard. So, Karl Marx is a goat. Here, first premise = "All goats have a beard" second premise = "Karl Marx had a beard" conclusion = "Karl Marx was a goat" ...
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Thoughts on Open Logic Project?

I'm currently thinking about starting to expand my knowledge of logic beyond what I retain from my previous study of logic by making use of the materials available through: OpenLogicProject (https://...
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66 views

Clarifications on 1) Modus Ponens, 2) Modus Tollens, 3) Inductive, 4) Incomplete based on examples

My second lecture on Hypothetico-Deductive methods (based on Popper's falsification theory). In the class, we were given the following examples. We had to classify which examples belong to 1) Modus ...
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1answer
272 views

Does the Law Of Excluded Middle Apply to the Principle Of Identity and Non Contradiction? [closed]

This argument will seem confusing, precisely because it observes the laws of identity being subject to equivocation. If this is kept in mind, the following should make more sense and explain why the ...
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1answer
121 views

Reasoning for Inductive inference?

Just out of curiosity, if I should replace the deductive inference related questions to inductive inference, then which are true? Inductive inferences rearrange current knowledge in such a way that ...
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Reasoning for deductive inference?

I got a quiz today in my classroom. I need to say True or False to the following: Deductive inferences are typically based on unfounded assumptions. For the valid deductive inference, the conclusion ...
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2answers
51 views

What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
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1answer
229 views

Are there rules for the following in the Open Logic Project's proof checker?

I'm using http://proofs.openlogicproject.org/ but can't find out what the translation of the rules are. I'm new at this, so when I try to make proofs, I know what I want the justification to be (which ...
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3answers
231 views

How to solve this natural deduction problem?

This one is driving me crazy. I don't understand most keys for de morgan, modus ponens, etc, so please abbreviate if possible? EX: DM, MP, SIMP, HS, Conj, Imp (material Implication). Thank you anybody ...
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2answers
341 views

Confusion between deductive and inductive reasoning definitions

The following arguments is always given as a classic example to deductive reasoning: All men are mortal. (First premise) Socrates is a man. (Second premise) Therefore, Socrates is mortal. ...
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1answer
65 views

Quick question on discharging assumptions

Could someone explain conceptually what the consequences are of assumptions NOT being discharged in a natural deduction ? Suppose the objective is to establish a claim of the form : 'If A,then B.' ...
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191 views

What is a natural deduction proof from ~(A↔B) to ~(A→B)?

It feels intuitively correct, but I cannot work out how to prove it. I would appreciate any help.
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485 views

What is the difference between the resolution rule and the elimination in natural deduction?

I understand that elimination is: p v q ¬q then p and resolution is: q1 v q2 v q3...qn ¬q1 v q2 v q3...qn then q2 v q3...qn I see no difference, but my teacher is telling us don't use the ...
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229 views

Tacit inferences?

Does anyone give a useful account of tacit inferences? I am interested in the psychological notion of inference here, and do not in the context focus upon the logical notions of validity and soundness....
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1answer
433 views

If turtles see everything, and nothing seen can see, does it follow that non-turtles exist?

Consider the following argument: Turtles see everything. Seeing is asymmetric (for the sake of argument). Therefore, something is not a turtle. I have problems symbolizing these statements. My ...
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Is deduction based on induction?

I'm wondering if deduction is in the end based on induction. The problem of induction discovered by the Scottish philosopher David Hume is quite well known. On the other hand, it's commonly supported ...
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3answers
243 views

Can all inductive arguments be written as deductive arguments?

Whenever I see inductive arguments being used, it seems as though they can be redone by simply making certain assumptions and rephrasing the argument as a deduction from those assumptions. For ...
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~(~P&Q) & ~(P&Q) : Prove ~Q

This must be proved using only negation, double neg.Intro, double negation Elimination, indirect proof, conj.Intro, and conj.Elim.
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2k views

How to get proof using proof editor and checker

How can I use Natural deduction proof editor and checker or The Logic Daemon to derive the given conclusion from the given premise: (∃x) ( Fx ∙ (y) (Fy → y = x) ) / (∃x) (y) (Fy ≡ y = x) It tells me ...
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Does Hume reject the possibility of is-ought syllogisms?

Suppose the following syllogism: It is impossible for anyone to get X without him/her doing Y. It is possible to get X (by doing Y). I want to get X. Therefore I ought to do Y. There is, very likely,...
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704 views

How do I operate with philosophers if I reject deductive reasoning?

Deductive reasoning is the one that takes premises for granted. I never do it. Therefore I never do deductive reasoning. Well, enough jokes. It is safe to assume that deductive reasoning never should ...
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Is there a single definition of truth?

Is there a single definition of truth in philosophy? Seeing multiple definitions has inclined me to believe that there is no proper definition of philosophy that everyone can agree on.
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Inductive and deductive arguments and mathematical induction

I started reading Paul Teller's A Modern Formal Logic Primer. In the first chapter, the book presents the inductive and deductive arguments with the following examples: The inductive argument: Adam ...
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3answers
610 views

Justification of deductive reasoning

Is a justification of deductive reasoning possible? If so, please tell me how because whenever I try to form a justification of deductive reasoning I end up committing the fallacy of circularity.
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How can I prove ⊢(∀x)(Fx V ~Fx) with natural deduction?

⊢(∀x)(Fx V ~Fx) How can I prove this with natural deduction?
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310 views

Natural deduction proof help!

I've gone through about 40 natural deduction proofs in the past couple days, and mostly they are no problem. For some reason, I've been stuck on 1 tedious problem for an entire day. I just can't seem ...
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2answers
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Does an implied premise mean a formal fallacy if used in deduction?

Let's just say we have an implied premise: 2.a Socrates is a philosopher (implied premise), but not explicit Then is the following a formal fallacy? Socrates is a man. All men are mortal. ...
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3answers
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Deriving “(p.q) v (p.r) from ”p.(q v r)"?

I am new to logic. and here are my tryouts for deriving deriving "(p.q) v (p.r) from "p.(q v r)", and further I want to show that ”p.(q V r)” is equivalent to ”(p.q) V (p.r)”, by using natural ...
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What is the nature of “validity” in deduction when dealing with conclusions unrelated to premises?

I studying graduate math (not very far into it), and I realized that some of the higher-level math texts I would like to read are hard to understand without a strong basis in logic. Now I've taken ...
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1k views

Is there a deduction analog to the problem of induction?

Aren't deductive and inductive reasoning equally unjustified? So, inductive reasoning is going from specifics to general, whilst deductive reasoning is going from general to specific. But in deductive ...
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4answers
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In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)

Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R) I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...