# Questions tagged [deduction]

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### Fallacy by Sherlock Holmes 'Eliminate the impossible, and what remains must be the truth'

In The Sign of Four, Holmes asks Watson: "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" This may be ...
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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 ...
1k views

### What's the relevance of falsifiability in regards to logical arguments?

Is it reasonable to classify logical propositions that rely on deduction and are non-falsifiable as being inherently not worthy pursuing or does this just applies to inductive reasoning?
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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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### 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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### 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 ...
272 views

### 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 ...
133 views

### What is this technique to gain proof called?

I just found out that I always missused the term deduction. I always thought that deduction meant gaining a proof by showing that all the other possible answers are wrong. But deduction is actually ...
617 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), ...
436 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 ...
214 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 ...
975 views

### 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 ...
691 views

### Malthus's argument on population - Test 1, Q14, by Mark Shepherd

I took a practice test for a law exam and am having difficulty with understanding the logic behind a question. Apologies for the length, but I included the whole question and details for completeness. ...
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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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### 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 ...
669 views

### Help with simple deductive proof

I am taking a class on natural deduction for the first time and we are currently on deductive proofs, I am having trouble with this one: Premise: A Premise: [(A&B) or (C&D)] Conclusion: not (...
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### help with deductive proof

∀x (Fx ∨ x=c), ¬Fb ∧ Gb |- ¬Fa → Ga So far I don't understand how to switch variables around to prove the result. I've got a subproof set up assuming "¬Fa" in order to derive "Ga". In that proof I ...
291 views

### Isnt induction just deduction with an implicit premise?

I have a problem with the distinction between induction and deduction. To me it does not make sense to talk about induction at all. People argue that the following is induction: A_1 is x A_2 is x ...
454 views

### 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 ...
220 views

### 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 ...
220 views

### What were Kant's thoughts on ethics and "Transcendental Deduction"?

What is Kant's thoughts on ethics? And what do his "Transcendental Deduction" ideas have to do with his ideas on ethics? Please keep in mind that I'm a a newb to philosophy, so the simper and more ...
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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 ...
505 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 ...
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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 ...
15k views

### 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 ...
1k views

### 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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### 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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### Argument where premises cannot all be true

Is an argument whose premises logically cannot be true at the same time a valid one? It seems it would be "vacuously" valid but I'm not sure about the precise definitions. Ie, is the following a ...
3k 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 ...
257 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, ...
3k views

### 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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### 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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### 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 ...
205 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
621 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" ...
158 views

### 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 ...
322 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 ...
243 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 ...
139 views

### How can syllogisms with contradictory premises be valid?

A syllogism is valid if it is impossible for the premises to be true and at the same time the conclusion to be false. Consider the following syllogism: P1: This apple is red. P2: This apple is not red....
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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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### 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/...