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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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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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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41 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 ...
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29 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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121 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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32 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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39 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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41 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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25 views

Are 'if not' and 'except if' equivalent? [on hold]

[ODO:] unless {conjunction} = Except if (used to introduce the case in which a statement being made is not true or valid) Source: p 139, Introduction to Logic (2 ed, 2010) by Harry J. Gensler ...
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142 views

Prove the number is 7? [on hold]

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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37 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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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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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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14 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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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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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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45 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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46 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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34 views

How to intuit 'unless'? [on hold]

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 ...
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4answers
121 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 ...
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79 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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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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52 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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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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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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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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111 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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33 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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24 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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32 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 ...
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41 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 ...
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45 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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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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55 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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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 ...
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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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40 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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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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43 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?
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Suppose the conclusion of an argument is logically equivalent to the conjunction of all the argument’s premises

Suppose the conclusion of an argument is logically equivalent to the conjunction of all the argument’s premises (the conjunction of all the arguments premises is just the statement obtained by taking ...
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1answer
41 views

The law of identity: two interpretations

Some philosophers state the law of identity as "if p, then p" or "p iff p" (i.e. in propositional logic). On the other hand, others state it in a completely different language, for example: "A is A". ...
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26 views

When can we eliminate disjunction within equivalence?

I'm a first year philosophy student and I've got a question about elimination of disjunction. Actually, I'm not sure if this can be called elimination of disjunction, we hadn't covered this yet, but ...
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89 views

The birth of Buddha [closed]

Today my teacher said this during the classroom: Siddhartha Gautam, the earlier form of Buddha, was actually born in Nepal, but since Siddhartha Gautam meditated and found enlightenment to become ...
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Jan Narveson, “Feeding the Hungry.” imply that we do not have a negative and positive duty?

In Jan Narveson, “Feeding the Hungry,” he states that we do not have a moral obligation to help the needy. Does this imply he does not believe we have a positive duty? He also states: "If the fact ...
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soundness and completeness of a proof method

the question : Instead of the standard rule for disjunction (where we process a disjunction A∨B with two branches—one with A and one with B) we use a rule where the result is two branches, one with A ...
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Vacuous Conditionals and How We Feel About Them

Let's take the following propositions : 1 - "If Bill Gates is poor then Bill Gates is rich". 2 - "If Bill Gates is poor then the moon is made of cheese". Both propositions are inevitably true ...
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In Wittgenstein, is all the facts being *all* the facts a fact itself?

Wittgenstein writes in his Tractatus Logico-Philosophicus (p.25 in this version): 1. The world is everything that is the case. 1.1 The world is the totality of facts, not of things. 1.11 The ...
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Is the Tractatus considered to have had any permanent influence on philosophy, given that Wittgenstein himself later repudiated it?

I was reading a text book that stated that Wittgenstein's Tractatus Logico-Philosophicus is rarely criticized in a serious way, since Wittgenstein himself rejected its ideas in his later phase, as ...
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Is the logic precept that for two propositions there are four truth values ever applied to serious matters?

An elementary precept of logic says that where there are two propositions, P and Q, there are four possible "truth values", P&~Q, ~P&Q, P&Q, ~P&~Q, where ~ means "not."   Do people ...