Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the few fundamental philosophical subdisciplines, along with metaphysics, ontology and aesthetics. Logic has taken on considerable importance in recent mathematical developments, and one of the ...

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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 ...
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2answers
113 views

What are the practical applications of modal logic?

I'm a computer science and philosophy double major. I know logic is paramount in computer science, but what about modal logic? Are there any practical applications in computer science and perhaps even ...
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1answer
51 views

Does the slippery slope fallacy have any usage outside of formal logic?

I already searched for this but it doesn't really contain what I'm about to ask. The slippery slope fallacy, according to Wikipedia's definition, is "a logical device, but it is usually known under ...
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45 views

How do we know something is a “category mistake”?

I believe that Gilbert Ryle introduced the term "category mistake", but I am struggling to apply the term. Could you please give me an obvious and less obvious instance of a category-mistake? And if ...
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0answers
59 views

How to define extent? [closed]

How do I define a term's extent as X? “extension” indicates its range of applicability by naming the particular objects that it denotes How do I say that a term's extent if logically ...
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1answer
38 views

How to work with a premise containing multiple 'if' s?

This was alleged erroneous; so please explain as though I were 10 years old. See the bolded in the following. 3 and 4 confuse me because they are premises, but they themselves are conditional ...
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1answer
80 views

Is cognitivism compatible with moral anti-realism?

According to my professor, Sharon Street is both a cognitivist and a moral anti-realist. I can't seem to reconcile with that. How can you form a propositional statement about something that doesn't ...
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4answers
91 views

How would you translate the sentence “Some philosophers love all philosophers, only if they love themselves”

I have it as: ((x)(Px&Lxx))>(($y)(x)(Py&(Pz>Lyz)) Where P is a philosopher L is loves (Predicate logic)
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1answer
43 views

Why is most modal logic about necessity vs possibility rather than permission or wishes?

It seems to me that the notions of modal logic are all shaped primarily by one modal, 'can/must' (konnen/mussen). Has anyone looked at all deeply at how this convention compares with the other common ...
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40 views

If G is absent whenever F is absent, then F is a sufficient condition for G

True or false and why? I am very confused on this topic: If G is absent whenever F is absent, then F is a sufficient condition for G. I know that if F is a sufficient condition for G then F ...
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3answers
91 views

What is the logical form of a question?

A common thread in Analytic philosophy, starting with Frege, and through Russell, Wittgenstein and the Logical Positivists, is that there is an ideal and purely logical language, with which we can ...
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1answer
44 views

Understanding a paragraph from George Boole's An Investigation of the Laws of Thought

The books is available in public domain here: http://www.gutenberg.org/ebooks/15114 In the introductory chapter Boole explains what the book contains: But although certain parts of the design of ...
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1answer
41 views

Is this an instance of the base-rate fallacy?

Pr(Sx ∣ x∈𝓗) ≫ 0 Pr(Sx ∣ Tx & x∈𝓗) ≫ 0 Pr(Sx ∣ ¬Tx & x∈𝓗) ≪ 1 Therefore: Pr(Tx ∣ Sx & x∈𝓗) ≫ 0 Is this an instance of the base-rate fallacy, or is this line of reasoning valid? ...
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1answer
57 views

Type theory and metaphor

In my experience, textbooks and introductory material on type theory (or constructive logic systems) are remarkably devoid of metaphor. I never found any introductory text in those fields that ...
2
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1answer
35 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 ...
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3answers
177 views

Can anything not be equal to itself?

Consider the statement 1=1 This is the law of identity translated to arithmetic. More generally we could say x=x Whatever x is; it must be equal to itself. Is this always true? Can there ...
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4answers
77 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 it were a sufficient condition, would it also follow that x is a necessary condition? Put otherwise, is a ...
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1answer
43 views

'There aren't any R that aren't B' vs 'There are R and all of them are B'

Source: 14 minutes 40 seconds juncture, Lecture 6-1 (transcription, ... How to Reason and Argue, by Prof Ram Neta PhD in Philosophy So the way we've been using the quantifier all, if you say:   ...
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3answers
44 views

Skeptical hypothesis as undecidable statement

Does anybody support the idea that the skeptical hypothesis (like the possibility that we are brains in a vat) is not assessable? By that I mean that the skeptical hypothesis may resemblance the sort ...
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1answer
162 views

Prove the number is 7? [closed]

Logic professor Ackermann to undergrads Beatrice and Carl, who both earned As in Algebra 2 back in their high-school careers: “In this sealed envelope is a lone piece of paper upon which, in secret ...
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2answers
39 views

How do only counterfactual conditionals need inference? Don't material conditionals?

Source: p 338, A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley Counterfactual conditionals still stupefy me; so please explain as though I were 10 years old. Subjunctive ...
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1answer
21 views

Antecedents of counterfactual conditionals vs those of material conditionals?

Source: p 338, A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley Counterfactual conditionals still daze me; so please explain as though I were 10 years old. Subjunctive ...
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0answers
20 views

How does comparing two sentences imply 'unless' = 'iff not' ?

[Source:] pp 114-115, Symbolic Logic: A First Course (NOT 4 ed, 2011), by Gary Hardegree. For want of brevity, I rewrite 'is on duty' as 'remains'. 1. the pool may NOT be used unless a ...
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2answers
34 views

fallacy of equating terms based on shared properties

I've recently come across a particular errant pattern of argument a couple of times, and I'm wondering if there is a name for this fallacy. The form of the argument is: A has property X B has ...
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0answers
21 views

What does 'material' mean in 'material implication'? [duplicate]

Source: p 339, A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley These observations about conditional statements apply equally to biconditionals. Just as the horseshoe operator ...
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1answer
24 views

Question about information in ampliative reasoning

I'm definitely open to critique here. I see ampliative reasoning (basically, induction or abduction) as different than explicative reasoning (deduction) in that ampliative reasoning adds additional ...
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2answers
52 views

The fallacy of proving correctness by claiming opposing arguments as predictions under one's paradigm?

My religion foresees that you will deny the truth at first, but will eventually accept it. Correct me if I'm wrong, but there are two fallacies here: The argument above tries to subsume ...
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4answers
47 views

Modal Logic - Necessity in Conditional Statements

p = Smith is a brother q = Smith has a sibling i) □(p → q) ii) (p → □q) Which in English form would be: i') Necessarily, if Smith is a brother then Smith has a sibling ii') If Smith is a brother ...
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1answer
35 views

How to intuit 'unless'? [closed]

I already know, and so ask NOT about, the proof of: A unless B =  A if not B =  Either A or B. Because I ask only for intuition, please do NOT prove this or use truth tables. My problem: I want to ...
3
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4answers
129 views

Validity stemming from contradictory premisses

I'm a student new to the study of logic, and having had my first tutorial on it yesterday, while I generally understand the characterisation of logical validity, there were a couple of examples my ...
4
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2answers
88 views

Is a top-down set theory possible?

There are two classical paradoxes associated with set theory; and that is the existence of the Universal set and the Russell set. The usual set theory takes the notion of element as basic; these are ...
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6answers
173 views

If you're the smartest person on earth, how do you know if you're making logic errors? [closed]

In any logical argument, there is the practical step of verifying that it is sound. When there are experts in that particular area, they can check the argument for soundness. For two examples: A ...
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1answer
53 views

Fitch style disjunction elimination

I am having difficulty in formally proving a simple argument. Consider P(x) v Q(x) not P(x) ---------- Q(x) It is easy to see that the argument is indeed valid, but I cannot seem to prove it ...
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0answers
39 views

Looking for a treatment of multiple interpretations in Model Theory/Formal Semantics

A sentence, such as a Godel string, can be given any intepretation whatsoever, so in a sense, when communicating, we have to be benevolent about the interpretation function that we infer our ...
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2answers
47 views

Determining the soundness of arguments

I was recently given the following question in an exam. Determine the soundness of the following argument: John lives on the same street as Mary. Mary lives on the same street as Sam. ...
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3answers
98 views

Is there a logical fallacy for “ignoring the specifics, over-applying the general”?

I haven't found a name for this fallacy, and perhaps it isn't one, but I would describe it as over-application of a general rule while disregarding specific information to the contrary. but here are ...
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2answers
117 views

Trick of just adding: if the premises are true then the conclusion is true

Source: 19 mins 50 s juncture, Lecture 3-7 (transcription), ... How to Reason and Argue, by Prof W Sinnott-Armstrong. Sh, here's a trick. ... You could always make any argument valid just ...
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0answers
35 views

What is a predicate?

There is of course predicate as in predicate logic; but I'm asking about the notion in Aristotles Organon. Consider the proposition: Socrates is a man Man is a universal, Socrates is a ...
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1answer
26 views

Is this argument valid without premise 1.1?

Source: 11 mins 49 s juncture, Lecture 3-7 (transcription), ... How to Reason and Argue, by Prof W Sinnott-Armstrong. Caution: My enumeration differs from the Prof's. For brevity, I abbreviate ...
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2answers
39 views

What is a proposition? [closed]

In the propositional calculus it is a bearer of truth-values; the proposition indicated by, say the letter p, is deemed to have no further structure. Is this all, or can more be said? Consider the ...
2
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1answer
42 views

Meaningless counterfactuals

What is the term for believing that counterfactual statements do not have definite truth values? i.e., that the only possible world is the actual world. Also are there any philosophers known for that ...
2
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1answer
48 views

Is presentism self-contradictory?

One might reach the conclusion of presentism by thinking to oneself: "I do not know if the events that occurred in my memories truly happened, therefore, I can not with 100% certainty say they are ...
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1answer
66 views

What is the history of the concepts “sound” and “valid”?

Could someone tell me when the current terminological distinction between "sound" and "valid" was first made in the development of logic? If the distinction was first drawn in writings in ...
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2answers
60 views

Is there a relationship between implication and supersets?

The "hook" symbol for implication (⊃) is the same symbol for superset. Is this just a coincidence, or is there a relationship between these two ideas?
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2answers
21 views

Exclusive disjunction in terms of conditional

I have the following doubt. I would say that: = p implies not q Though that equivalence seems natural to me, it is not true. Can someone please give me an intuitive explanation of mi error. Thank ...
1
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1answer
34 views

How to learn more about statements such as 'not without = only with'? Is this logic? [closed]

(For this ELL question), I only realised my main problem after user 'Araucaria' identified it: If we use not without in a sentence, it has the same meaning as only with or only by. Yet I never ...
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2answers
42 views

What logics modify conditional detachment in this way?

What logical systems modify conditional detachment such that it is not permitted in cases that would be allowed by 'normal' logics — in particular, such that A⇒B is not equivalent to ~AvB?
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What logical systems categorize A->~A as a contradiction.?

In the basic propositional logic I learned in school A->~A is not a contradiction because it is not false when ~A is true. What logical systems would hold this statement to always be false?
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58 views

Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?

Suppose you know the premises of an argument are inconsistent. Do you have to do a truth table to know whether it is valid or invalid?
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1answer
46 views

Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?

Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?