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Questions tagged [deduction]

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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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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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How to get proof using proof editor and checker

How can I use http://proofs.openlogicproject.org/ or http://logic.tamu.edu/daemon.html to derive the given conclusion from the given premise: (∃x) ( Fx ∙ (y) (Fy → y = x) ) / (∃x) (y) (Fy ≡ y =...
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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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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: ...
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3answers
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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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2answers
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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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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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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
229 views

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 ...
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2answers
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Predicate logic proofs - how to split a disjunction bound by two quantifiers

I need to complete the following proof using only primitive rules (the introduction and elimination rules for each connective and quantifier). (∃x)(∀y)(Py ∨ Qx) ⊢ (∀y)Py ∨ (∃x)Qx I've only been able ...
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0answers
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Is this a valid argument (using probability and uncertainties)?

If A, then B (probability of 0.6 that this is true) If B, then C (probability of 0.6 that this is true) A, Therefore C. I'm not sure whether C is probably true if A is true, or if the probability ...
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1answer
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Why can't uniformity of nature (in principle) be proven deductively?

I've been reading about the problem of induction and I have trouble understanding the argument for nature's uniformity being impossible to prove deductively. Stanford Encyclopedia of Philosophy on ...
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Are “if smoke then fire” arguments deductive or inductive?

I'm new to philosophy and have a question regarding deductive vs. inductive reasoning: I'm told that "John ate a strange plant in the forest and got sick. Clearly, the plant made John sick." I ...
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3answers
169 views

Logic question regarding a logical truth

Is the following logically true? ∃x[Cube(x) →∀yCube(y)] I think that it is logically true. When translated into truth functional form we have: A→B. A truth table shows that it is not a tautology but ...
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2answers
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Based on evolution, do we arrive at deductive principles inductively?

If our knowledge of deductive principles is a result of evolution... doesn't this mean that we arrive at deductive principles inductively? Assuming deductive principles are beneficial for survival, ...
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1answer
103 views

What are the rules for a zero-premise derivation involving disjunctions?

I'm having trouble with the following zero-premise deduction that involves two disjunctions: The solution seems simple, but I'm unsure of how to proceed with the two disjunctions. If it were just ...
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1answer
358 views

Is this an inductive or a deductive argument?

Two flowers of the same cultivar were planted in adjacent plots . The first was fertilized with Miracle-Gro and it flourished (2); The second was not and it din't(3) . Therefore , Miracle-Gro ...
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1answer
189 views

Quick logic deduction question

I have to provide a natural deduction derivation for: ¬∀xFx ⊢ ∃x¬Fx That´s what I got so far: 1.¬∀xFx 2.‖ ¬∃x¬Fx (Indirect proof hypothesis) 3.‖‖ ¬¬Fy (Indirect proof hypothesis 2) 4.‖‖ Fy (...
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Proof for the Rule of Absorption in Propositional Logic?

I know there is a "formal proof" for the "rule of absorption" that employs the "law of excluded middle". It is presented in Wikipedia (and I think it is Russell's): https://en.wikipedia.org/wiki/...
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185 views

Is this inductive or deductive?

The fact that we know we have a great great grandfather. Is the reasoning we use for this inductive or deductive?
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2answers
354 views

Implication Introduction formulated as a theorem?

While making a list of the rules of inference for my math students, I came across this list on Wikipedia: I noticed a pattern: for every introduction rule, there seems to be an elimination rule, and ...
0
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1answer
129 views

Is logic based on uncertainty the fundamental logic?

Most formal logics are based on certainty, but certainty is only one probability among others, so a logic based on uncertainty and probability should be considered as the fundamental logic from which ...
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4answers
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How can one intuit that P → Q ≡ ¬P ∨ (P ∧ Q)?

I have not succeeded in intuiting P → Q ≡ ¬P ∨ Q in the sense of imagining how one would conjecture or divine the equivalence without any "foreknowledge" of ¬P ∨ Q to invoke formal proofs or truth ...
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3answers
287 views

Logical analysis of “Free will and god(s)” argument

Please evaluate the following argument strictly for formal logical validity. I am NOT interested in debating the content or in philosophical perspectives on the content. However, I AM interested in ...
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1answer
660 views

⊢ ((AvB) -> C) -> (A -> C) using simple derivation rules

My thought process: - This derivation has no premises. - The desired conclusion is a conditional, therefore assume the antecedent and derive the conditional. What I have so far: 1 1) (AvB) -&...
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2answers
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How to prove 1. ~(KvF) 2. ~F=>(KvC) 3. (GVC)=>~H / ~(KvH) using natural deduction

I need help with this question using the first 13 rules of inference. Here is what I have so far: ~(KvF) ~F=>(KvC) (GVC)=>~H / ~(KvH) ~Kv~F DM 1 ~Fv~K Com 5
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3answers
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Question regarding logical fallacies

So I'm not sure whether the following statement is a logical fallacy but it seems to me like it is. If statement A is true then statement B must be true as well. Not sure if I properly constructed ...
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1answer
92 views

How to infer ¬Q when there seems to be no way to

Rule #1: No man shall hit another man. Rule #2: If someone breaks Rule #1, then Rule #1 does not apply to such a one. My specific question is: How can someone infer that Rule #1 does apply to him? ...
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7answers
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Is the logic of this argument valid?

If God exists, it is rational for people to believe he exists without relying on facts: If God exists and he wanted to be known by people he would provide a means of knowing him. If God wanted as ...
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How do you prove that this is a tautology?

((p->q) and (r->s) and (p or r)) -> (q or s) How would you prove that this is a tautology? Using natural deduction? My attempt on this question is the following. Since a tautology means W entails ...
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1answer
898 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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1answer
155 views

Does a logical answer equal a simple answer in deductive reasoning?

I am aware that deduction is used to get a logical answer. Consider a historical theory being the result of deductive reasoning. Would deductive reasoning be used to get a simple answer? After all, it ...
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4answers
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How does it make sense to infer the existence of a group from a sequence of events?

Just read an interesting section in The Drunkard's Walk - L. Mlodinow and this section made me think: [people]... confuse[ing] the probability that a series of events would happen if it were the ...
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Are “If P then Q” and “Q only if P” equivalent?

My textbook says "If P then Q" and "Q only if P" are logically equivalent, but consider this: "If it's green, it's poisonous." "It's poisonous only if it's green." Now say there's a purple ...
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1answer
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The difference between argument, inference, deduction and proof?

I am trying to distinguish argument, inference, deduction and proof. First, let's look at the distinction between argument and inference (if there is one). This online source states: An argument ...
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5answers
190 views

Proof that deduction is valid in all possible realities?

I was wondering, how can we know that deduction is a valid way to argue for something in all possible realities? How do we know that, in some alternative universe, something is not both ~P and P? How ...
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7answers
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What is the difference between deductive 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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4answers
3k views

Propositions that are always true, but aren't tautologies?

Consider the following statements: "Snow melts during the day in the Sahara" "A human will die without oxygen" "Photons have no rest mass" These are statements that are always true, not because ...
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1answer
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Challenges to the principle of deductive closure

Consider the principle of deductive closure: PDC. K(p) ∧ K(p → q) ⊢ K(q) Informally (and roughly) this means that we know the logical consequences of the things we know. Despite ...
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279 views

Introductory Natural Deduction Question

So I'm new to logic and taking an introductory logic course, and I'm really having trouble with these 2 questions: Using the system of Natural Deduction in the textbook, provide a derivation to ...
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1answer
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If deduction does not exist in regards to the free will, is omniscience possible with omnipotence?

As the argument goes: If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means he can't change his mind about ...
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Anyone can help me with proving ~(AvB) |- ~(BvA) via natural deduction?

~(AvB) ㅡㅡㅡㅡ ~(BvA) I have to provide a derivation to establish validation of this argument. First of all, can I first change ~(AvB) into ~A&~B by using the De Morgan rules? And the second is:...
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4answers
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What is the logical form of the definition of validity?

My text book gives the definition of validity as "An argument is valid IFF if the premises are true, then the conclusion must be true". Using a conditional elimination on the RHS of the IFF yields "An ...
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1answer
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Does the alleged answer overinfer? - Test 2, Q21, p 113, by Mark Shepherd [closed]

The passage is exactly this. 21 It is implied that public opinion has changed most on which issue in recent years? (a) Unmarried heterosexual couples (b) Gay couples (c) Neither (d) Both (e) There is ...