# Questions tagged [deduction]

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### deductive reasoning and first principle

In continuation of Are the concepts of reductionism and first principles the same? my next question is what is the relationship between first principle thinking and deductive reasoning ?
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### Abduction, deduction and induction in medical diagnosis and intervention

(Apologies if my views on logical inference are overly simplistic -- I'm a radiologist by profession, very far from a philosophy major. My goal is to understand what medical decisions are and where ...
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### What does it mean to say that two theorems (provable statements) are 'equivalent'?

sometimes one sees/reads assertions such as "[the bounded inverse theorem] is equivalent to both the open mapping theorem and the closed graph theorem", but taken formally and literally this ...
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### rules of inference, language into metalanguage

There are rules of inference, e.g. in natural deduction they are listed. These rules follow the same rules than the logic language. If we see Modus ponens, a → b, a ⊢ b We can write for the same ...
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### Proof of soundness of the rule of implication introduction in natural deduction calculus

From the definition of a sound calculus we can infer that a sound implication introduction has to have the form: Γ ⊢ A → Γ ⊨ A. The rule for implication introduction goes (Γ ∪ {A} ⊢ B) ⊢ (Γ ⊢ A → B). ...
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### I have taken my midterm exam 1 hour ago, and I am confused about some question meaning

1 what is the defferenece between "the justification of line 6" and "the application of xx on line 6"? For example, we can find that in the line 6, the application is wrong because ...
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### abductive reasoning in many fields of study

In continuation of the discussion What is the relation between abductive reasoning and fallacy? my question is that if medical science judiciary history all uses abductive reasoning (almost all the ...
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### Question about disjunction elimination in Fitch

I was recently using https://proofs.openlogicproject.org/ and realized that their version disjunction elimination is fairly restrictive. I had a proof set up something like this: p∨q (Premise) p∨r (...
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### Is backtesting inductive reasoning?

We do backtesting in finance; that is, we guess hypotheses/premises, and then use previous data to verify it. Wikipedia Investopedia Is backtesting inductive or deductive reasoning? (Here we have ...
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### Internal vs External Statement in Homotopy Type Theory

I would like to clarify the precise difference between the phrases "statement inside/ internal the theory" and "statement about the theory" in context of Homotopy Type Theory. A ...
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### Does the claim of an is/ought gap presuppose relevance logic (at least for morality-talk)?

Imagine Hume's remarks but with reference to the usual disjunction introduction: In every system of conjunction, which I have hitherto met with, I have always remarked, that the author proceeds for ...
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### Parmenides and deductions about existence

I am beginner in philosophy and have some problem following this paragraph: "From the premise that something exists (“It is”), Parmenides deduces that it cannot also not exist (“It is not”), as ...
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### Double-negation deduction rule in https://proofs.openlogicproject.org/

How can we use double-negation deduction rule? For example, ~~p is the same as p. I am not able to find how to eliminate ~~ in https://proofs.openlogicproject.org/
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### Inference as tentative deduction

I've heard people make confident assertions about the categorical distinction between inference and deduction, but I'm not convinced. I'm curious to hear rebuttals to the assertion that "...
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### Modus Ponens false premises

I just started to get into deductive reasoning and was wondering how to prove an argument to be false. In Modus Ponens: If P then Q P thus, Q If I had an argument like this: P1) If you wear a tin ...
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### Possible vs may (or impossible vs cannot) in Aristotle's Prior Analytics

In chapter 13 of the Prior Analytics, it is written that "it is evident if it is possible for A to apply to B, it is also possible for it not to apply". Which naively speaking makes sense, ...
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### speculative deductive reasoning

Is hypothetico-deductive reasoning https://en.wikipedia.org/wiki/Hypothetico-deductive_model and speculative deductive reasoning same ? (speculative deductive reasoning- WE arrive at the explanans ...
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### Defeasible reasoning

a. If x is a weekday, Xena goes to work on day x. b. If Xena is ill, she doesn’t go to work that day. c.2 Jan ‘07 was a weekday. d. Xena was ill on 2 Jan. '07. e. By (a) and (c), Xena went to work on ...
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### Types of reasoning in mathematics

Can we say that analytical approaches is deductive reasoning and numerical approaches(numerical analysis) is inductive reasoning ?
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### If math is so deductive, why is it so hard to discover new math?

Some considerations: The conclusions of much latter/new math may be said to be already existent within the premises of current math The importance of deduction changes depending on if math is said ...
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### Falsification of a statement

Is falsification only applicable to deductive reasoning (as opposed to inductive, abductive and speculative deductive reasoning)?
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### Logic reasoning problems books

Could you, please, recommend any books with a set of logic problems or exercises on deductive and inductive reasoning, syllogism. Something that contains a set of questions, such as It is known that ...
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### Natural Deduction Proof with double quantifier (predicate logic) [closed]

Premise: (∃y)(∀x)(Px v Py) Conclusion: ~(∀y)(~Py) I'm starting out assuming the negation, i.e., (∀y)(~Py). But then I'm unsure how to find a contradiction within that subderivation. Here's what I've ...
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### How do I apply the reduction to absurdity rule in the Open Logic natural deduction tool?

I'm using the open logic natural deduction tool (https://proofs.openlogicproject.org/) as it makes writing proofs very clear and clean but I can't seem to apply the reduction to absurdity rule ...
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### Causation with Inductive/Deductive Logic

I'm sofa-philosopher and I have a case I can't quite dismantle. My friend (let's call him John) just made a statement that I find philosophically weak, and I'd like to run it thru you guys. So, John ...
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### Is mathematical induction deduction, and if so, why is it so named?

By induction, I mean this screenshot from this Youtube video Abduction as an Aspect of Retroduction | Chiasson, Phyllis | Commens Induction: The prefix “in,” also from the Latin has to do with ...
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### Does 1. extra-, 2. intra-polation fall under abduction, induction or deduction?

How does extrapolation relate to abduction, deduction, and/or induction? Scilicet, does abduction, deduction, and/or induction fully encompass Extrapolation? Same question for Interpolation. I ...
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### Can we use an impossible condition as a premise in a sound argument?

This is going to appear a bit of a mess Can we use a syllogism with an impossible condition as a premise in a sound argument? I am trying to reconstruct an argument. My interlocutor assumes you cannot ...
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### What can be known and what can be believed when neither induction nor deduction is justified?

Kant is well known for taking seriously the lack of justification for induction voiced by Hume and finding what is left for us to be able to know and believe. I wonder, with the knowledge that the ...
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### Is there such a thing as inductive reasoning?

When I form hypotheses, don't I actually only use deduction instead of induction? Suppose I observe that the sun rises 5 days in a row, so I hypothesise that the sun rises every day. But for this I am ...
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### Deductively sound argument

Is there a way to prove that a deductively sound argument (where premises are true and arguments are valid) will always have a true conclusion?
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### 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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### Formal deduction of Whitehead's Philosophy of Organism

In Process and Reality Whitehead starts off the investigation by giving his categoreal scheme - different types of categories and their derivatives, as well as some axioms. If I understand correctly, ...
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### 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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### Does all deductive knowledge stem from inductive observation?

Given the premise that deductive reasoning needs a premise statement to get started, ultimately do these premises come from inductive observation? e.g. When the sun is out it’s daytime. The sun is out....
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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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### 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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### 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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### Deductive methodology in philosophy

Introduction Mathematics uses deductive methodology to produce results called theorems that are indisputable truth by logical necessity, with respect to the axioms of the starting axioms and ...
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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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### 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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### 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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### 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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### 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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