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# Questions tagged [logic]

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

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### Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...
4k views

### Is it a fallacy to say that a sane person cannot apply rational thought to the motivations of the insane?

A common argument in today's news is that: Someone commits a heinous crime by shooting a bunch of people. Anyone who commits a heinous crime must be insane. Sane people cannot apply rational thought ...
2k views

### What fallacy dismisses criticism of a bad law with “just don't break it”?

Let's say someone is criticizing the government for instituting some draconian policy, and/or for persecuting people for doing something minor. And the response is:"Just don't do it and you'll be fine"...
3k views

### How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
2k views

### What's the difference between Aristotle's logic and Frege's logic especially with regard to predicates?

I'm reading a book and the author introduced Aristotelian logic and then he provided an overview of Frege's development of logic, but I don't understand what the difference is between Aristotle's ...
377 views

### Making 'sense' of Wittgenstein's senselessness / nonsense distinction in the Tractatus

For this question I'm just considering Wittgenstein's theory at the time of the Tractatus. As far as I know, for Wittgenstein: Meaning - The object denoted by a word (i.e. referent). Sense - The ...
197 views

### Once it happened, an event was necessary?

What would happen to an event in the past, if time itself ceases to exist? Without time, has what existed (such as the writing of this sentence) never happened? A total disappearance of space-time ...
536 views

### What does it mean that a claim is a claim of nonexistence?

This question has devolved into a discussion. As I understand the discussion, everything is revolving around the veracity of statement Nonexistence can never be proven. and on what exactly ...
8k views

### Invalid arguments with true premises and true conclusion [duplicate]

I'm am study some classical logic and I am having trouble with argument validity. I learned to think of validity as determined by the definition "If the premises are true, then the conclusion must be ...
7k views

### What is the opposite of “x” and why are “opposites” always in the same category?

Since I was a little kid I wondered about what people call opposites. If you ask someone "what is the opposite of white", they usually answer "black", but that's not the opposite, it is just another "...
179 views

### If P is a property, then is (not P) a property?

For a proposition, such as: P: Socrates is a man Then not P is also a proposition: Not P: Socrates is not a man But do the same goes for properties? One can argue in the following way: red ...
1k views

### What is the philosophical study of classification called?

What is the philosophical study of classification called? Taxonomy? Taxology? "Category theory"? "Classificology"? Logic? And which philosopher(s) studied exactly what it means to classify? How we ...
619 views

### What are the differences between hypothesis, supposition, assumption, postulate, and axiom?

What are the differences between hypothesis, supposition, assumption, postulate, and axiom?
4k views

### God's paradoxes and their implications [duplicate]

Possible Duplicate: Is the definition of God consistent? As many of you, I've come across a few paradoxes of all sorts, from logic to math, linguistics and so forth. Some of such involve God or, ...
6k views

Zeno's arrow paradox: Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less)...
155 views

### Material conditional: Why does the absence of the predicate validate the conditional? [closed]

So yeah, basically from what i've read, and i've checked multiple sources on this, is that A -> B = ¬A V B. So to really see where the confusion lies, I'll first state where it doesn't. Where A -> B, ...
6k views

### Does philosophy belong to empirical science or formal science?

According to Wikipedia, science can be divided into empirical science (such as natural science and social science) and formal science (such as mathematics, logic, statistics). I was wondering if ...
570 views

### Shouldn't statements be considered equivalent based on their meaning rather than truth tables?

Consider the following truth table, which serves to define the logical connective ⇔, P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T According to the above truth table, the logical ...
963 views

### Is “Don't blame me; I voted for ___” a bad argument?

Is there a fallacy in the argument, "Don't blame me; I voted for ..."? Or is a voter's entire responsibility for their contribution to whatever current state of political affairs they experience ...
7k views

### Is it possible to be truly unbiased?

I was pondering this question: Inductive Argument Against Believing Anything I his argument, the OP suggests that, in the position of choosing a system of belief where there are multiple, large ...
392 views

### Are truth-claims inappropriate?

Strictly speaking, is it inappropriate to make a truth-claim? I am seeking an answer from Philosophy (Epistemology), and feel free to use logic I am speaking "theoretically", not "practically" I am ...
384 views

### Are Univalent Foundations of mathematics a modern version of logicism?

As I understand it (and mine is just basic understanding) the Univalent Foundations program is an attempt to reduce mathematics to an interpretation of Martin-Löf type theory by using homotopy theory....
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### Aristotle's Syllogistic and Proofs by Contradiction

I'm just reading about Aristole's work on syllogism in Anthony Kenny's A New History of Philosophy book. I'm struggling to understand the tranformations between different forms of syllogisms. So ...
15k views

### In formal logic, how is it possible for an argument with a contradictory conclusion to be valid?

I've recently been trying to introduce myself to formal logic, and I've hit a stumbling point: In the text I'm reading, a valid argument is defined as "an argument in which it is impossible for the ...
4k views

### What logical fallacy is the argument “I have a RACE_NAME friend, so I can't be racist”?

What logical fallacy is the argument "I have a RACE friend, so I can't be racist"? For example, some people will make this point when trying to defend a comment they made: PERSON A: "I think all ...
3k views

### Are we are born with some innate sense of critical thinking or is this simply the product of an education? [closed]

I was listening to some young children in my family the other day talking to each other. The one Nephew told the one Niece. Only boys play with cars to which the she replies well then my sister is a ...
710 views

### In Fitch, how does one prove “(P → Q)” from the premise “(¬P ∨ Q)”?

It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck. I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
213 views

### name this fallacy: A was P in the past -> A must be P now

I've been seeing arguments of this form for awhile: (agreed true premise) Some predicate P was applicable to behavior/event/thing A in the past. Variations: P(A) may have been true at some particular ...
2k views

### What fallacy argues that we should do nothing because we can not do everything?

A says to B "we should recycle because it is better for the environment," and person B says "if we wanted to be better environmentally, there's lots of things we could do that we don't, so we shouldn'...
859 views

### How can a tautology not be necessarily true?

My logic/philosophy exercises include the following statement: "Every tautology is knowable a priori but not every tautology is necessarily true." I'm bamboozled. How can a tautology not be ...
658 views

### What does the truth-value of a material implication represent?

This question comes from my attempts to understand what the truth value for a material implication with a false antecedent represents. I have seen several justifications for this convention, usually ...
395 views

### Can strong omnipotence be decomposed into logically possible and logically impossible aspects?

A lot of debate in the "omnipotent being" or "omnipotent, omniscient, omnipresent, omnibenevolent, etc." being debate revolves around the definition of the terms. I consider the "strong form" of ...
887 views

### Are all sufficient conditions necessary?

If X is the necessary condition of A, then it doesn't follow that X is sufficient. However, if X were a sufficient condition, would it also follow that X is a necessary condition? Put otherwise, is a ...
935 views

### What is 'major' about the major term in logic? [closed]

Source: p 264, A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley Each of the three terms in a categorical syllogism has its own name depending on its position in the argument. ...
236 views

### How do we know that if the statement “A → B” is correct, “¬B → ¬A” is correct?

All examples that I can come up with confirm that If "A → B" is correct, "¬B → ¬A" is correct, but is it possible to rigorously prove that negating a true implication always will result in another ...
696 views

### What is wrong with my intuition of Modus Tollens?

Abbreviate Modus Tollens to MT, Necessary Condition to NC, and Sufficient Condition to SC. I pursue only intuition; please do not answer with formal proofs or Truth Tables. I already know of the ...
113 views

### Wittgenstein's solipsist, from Tractatus?

According to the early Wittgenstein of the Tractatus, the solipsist is one and one and the same with the world. He then makes the claim that solipsism coincides with realism. 5.64, Wittgenstein ...
632 views

### What is the term used for logic statements which are non reversible?

Something along the lines of If A then B, if B then not. A has to be true before B can be true but if B is true first then A isn't true. Is there a term describing this in logic or philosophy?
215 views

### How can you intuit that P → Q ≡ ¬P ∨ Q, and not P ∨ ¬Q?

As I forgot to stipulate the pretermission of the logical equivalence P → Q ≡ ¬P ∨ Q here, some of the answers presume this and resemble petitio principii, and so are really proofs rather than ...
122 views

### How does philosophy advance despite irreconcilable background assumptions (“positions”) on every topic?

In philosophy there are always, and on almost everything, many "positions", many different possibilities to choose from, and there isn't mainly some decisive conclusion between positions as to what's "...
105 views

### 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 ...
284 views

### What is the intension of the concept “intension”? [closed]

I think that it should be possible to assign to all concepts a plausible intension, consisting of just one or two words. However, in textbooks or encyclopedias I never found such focused appointments ...
605 views

### Is the real number line actually real when we construct it?

Intuitionism is akin to constructivism in mathematics but not quite the same from what I can tell. In the usual treatment of the real line, the additional numbers are found between the rationals by ...
151 views

### Is a barber a barber if he doesn't get paid?

For reference: The Barber Paradox. The Barber is he who shaves all those, and only those, who doesn't shave themselves. Now the question is: Who shaves the Barber? The paradox being that if ...
251 views

### What is the fallacy that privileges one person over another?

I see this a lot, someone in a category of people attempts to shut down anyone with an opinion that is not from the same category. For example, people without children weighing in on parenting; the ...
302 views

### Why does Zeno's paradox seem valid but remain obviously wrong?

Look at this argument: The 1st introduction: We may present time on an axis; therefore any time interval is a segment, thus consisted of infinite number of points, on this axis. The 2nd introduction: ...
7k views

### If-then in propositional logic [duplicate]

Possible Duplicate: How can we reason about “if P then Q” or “P only if Q” statements in propositional logic? Here's the table for If-then _____ ___________ | A B | (A ⊃ B) | | 0 0 | 1 ...
314 views

### Is it really problematic for Universal Instantiation to precede Existential Instantiation?

Abbreviate: Existential Statement to ES, Existential Instantiation to EI, Universal Instantiation to UI, and Universal Statement to US. Source: A Concise Introduction to Logic (12 Ed, 2014) by ...