# Tag Info

75

I would say it depends on the situation. Specifically, it depends on whether the person asking you the question wants to know whether you have at least \$100, or exactly \$100. The question could literally mean either, and only the context can decide. The former situation is likely much more common, and includes the example you mention, in which the person ...

44

tl;dr- It's a lie if the speaker intends to deceive the listener(s). More specifically, it's a lie-by-omission if the speaker intends to deceive the listener(s) by neglecting to mention something that, absent their intent to deceive, they'd have otherwise said. Lies are communications intended to deceive recipients. It depends on if there's intent to ...

33

Edit in response to your comment: Okay, long answer: What is the meaning of "the"? (A previous version of the question had the statement "The goblins are pink"; this is an elaboration on that formulation.) First of all, as noted in the comments, the "the" makes things a bit problematic; it is not obvious that "the" is ...

24

As Conifold comments, a real-life intuitionist would not shy away from assuming LEM ... when appropriate. Intuitionism merely permits the failure of LEM, it doesn't assert that it always occurs. For example, consider equality: in intuitionistic mathematics, equality is decidable (= subject to LEM) in the context of the natural numbers but usually not in the ...

20

Because there was a calculus for one-place predicates, Aristotle's syllogistic, roughly equivalent to monadic predicate calculus. Aristotle does discuss "relatives" in Categories, which refer to multi-place relations, or rather to objects entering them. What will later be called oblique syllogisms involving relatives is mentioned in passing in ...

17

There are two ways in which these statements can be non-contradictory: Option A: Non-mutually exclusive It is possible for a goblin to be both pink and yellow, therefore it is possible for a goblin to be both pink AND yellow simultaneously. Option B: Vacuous truth (which is what it seems you are angling for) From wikipedia: In mathematics and logic, a ...

15

They're not equivalent, but they do seem very close together in most contexts when you assume a bivalent (two truth valued) logic. But they pull apart when it comes to several controversial decisions we have to make in formal semantics and the philosophy of language. Lets consider two prominent examples. Supervaluationism: This is one solution to the ...

14

Let me give you a historical background first. Until the end of 19th century logic was almost exclusively associated with Aristotelian logic, the syllogistic. This logic did not have quantifiers, or even propositional variables, in other words it was too weak to support even arithmetic, let alone the rest of mathematics (Chrysippus, an ancient Stoic, and ...

14

You can see: Irving Anellis, The Genesis of the Truth-Table Device (2004) as well as: Irving Anellis, Peirce's Truth-functional Analysis and the Origin of the Truth Table (2012). Before Bertrand Russell (Harvard logic course: 1914) and Ludwig Wittgenstein (Russell and Wittgenstein's manuscript dated 1912; see also: Tractatus (1921), 4.31 and 4.442 for ...

14

We do NOT define vacuous statements as true. A vacuously true statement is vacuously true. A "vacuously false" statement is vacuously false; although nobody ever gives this type of statement any thought. Example: Every element of the empty set is a purple flying elephant. We agree that this statement is (i) vacuous; it doesn't really say anything ...

12

Validity in logic is a somewhat tricky notion to understand as it is different – though only subtly – from related, pre-theoretic notions. For instance, not every valid argument is ‘convincing’ or ‘useful’ in a pre-theoretic sense, nor is every ‘convincing’ or ‘useful’ argument valid. (See examples below.) To address your question more directly, suppose ...

12

Colloquial meanings of the two words are pretty close, accidental is "occurring unexpectedly or by chance", contingent is "subject to chance; occurring or existing only if (certain circumstances) are the case; dependent on". If there is a shade of difference, it is that contingent may well be expected as a possibility, albeit along other options, whereas ...

11

Intuitionism is a philosophy of mathematics that was introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966): he developed a very personal philosophy of mathematics that founds mathematics (partially following Kant; see Kant's Philosophy of Mathematics) on a pure intuition of time. You can see his Intuitionism and formalism (1912) : ...

10

To put it in simple words we have to describe in a couple of words the project of Principia Mathematica, which Russell inherited from Frege: reconstructing mathematics from logic alone. For a broader context see What is the philosophical ground for distinguishing logic and mathematics? Frege himself could not complete the project because Russell discovered ...

10

Your question is about lying by omission, and this requires that you define lying. The definition I use is a communication with the intent to deceive. Thus, whether or not you are lying is a function of your intent, more than the actual quantity of cash you have on your person. Let's examine two cases. In the first, you have \$200, and when asked you state ...

9

First, to dispel false conceptions: Informal logic is not the contrary of formal logic, at least for some established meanings of 'informal logic'. 'Formal logic' is usually reserved for the formal study of truth-preserving inference, like deduction. But there's nothing preventing a formal study of not necessarily truth-preserving inference, so-called ...

9

There seem to be several overlapping concerns in your issue with proof by contradiction. You have an objection to the truth table for material implication: I've never been satisfied with the argument that two false propositions create a true implication however. What good justifications are there for agreeing with this? You seem to misunderstand proof ...

9

It is more complicated than a merely instrumental/metaphysical division. The "logics as mere instruments" were not meaningful until well into the 20th century, after the general disillusionment in foundationalist epistemologies, and the subsequent pluralism of formal systems and interpretations. Originally, Logic meant the study of Logos, reason, ...

9

You've stumbled upon an old problem in philosophy, The Paradox of Inquiry, first formulated in Plato's Meno. The problem can be reformulated as follows: Either you know the answer to a question, or you don't. If you do, then there is no point searching for it. If you don't, then you will not know what to search for. The short answer is that you can ...

9

Here's the example from David Lewis's Counterfactuals (1973): If Boris had gone to the party, Olga would have gone. Now suppose that Boris wants to go, but not if Olga goes, because he wants to avoid her. Olga, on the other hand, wants to see Boris, and wants to go if he does. Given this supposition, the contrapositive of the above is false: If Olga ...

9

Propositions in intuitionistic logic are probably best understood as statements about provability. P ʌ Q means that you can prove P and prove Q, ¬P means that from P you can derive a contradiction, ∃x.P(x) means that you can exhibit a particular x and a proof of P(x) for that x, and so on. There is a law of noncontradiction because there can't be a proof of ...

8

I think you are right to be impressed with the Curry-Howard correspondence. It is a detailed and extensive rule-by-rule and feature-by-feature isomorphism. This strongly suggests that proof and computability are closely related. I also agree that it is under-appreciated within the philosophy of logic and that we can and should allow it to inform our ...

8

My reading of Carnap's "The Elimination of Metaphysics Through Logical Analysis of Language" suggests to me that it is possible to form sentences in a language that are grammatically correct but logically meaningless. The consequence of this is that the statement, due to its logical incoherence, cannot be proven to be true or false. And likewise, if a ...

8

Short answer : NO. Arguments are either valid or not. Premises and conclusions are sentences, and thus they are either true or false. See Valid argument : In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. [see also Hurley, page 44] Regarding the ...

8

Logic, paraconsistent or not, does not exactly make something happen, it is applied to reshuffle information already contained in a system. Paraconsistent logic does not even have to be applied to inconsistent systems, and even when it is, derivable contradictions do not have to be interpreted as "true". What we need is not logic but semantics, although ...

8

As well as the counterfactual example given by Eliran, there are an abundance of examples where the conditionals are uncertain. For example, given the poor record of the Norwegian soccer team, I might believe strongly that if Norway reach the final of the next world cup then they won't win. The contrapositive of this is that if Norway win then they won't ...

8

The thought experiment is known as Chrysippus’s Dog and goes back to the named ancient Stoic. It was discussed by many modern philosophers, including Dennett, see Chrysippus’s Dog as a Case Study in Non-Linguistic Cognition by Rescorla for a survey. Here is the description of Chrysippus's dog given by Sextus Empiricus: "[Chrysippus] declares that the ...

7

THe program of Universal Logic is mostly considered a joke by the professional logicians I have talked to. There seem to be two popular conceptions of logic among philosophers who think about logic. But before going into these, you have to understand first that, among present-day logicians, the philosophical concerns are most frequently secondary or ...

7

What is a variable ? A variable is a "syntactical" object: it lives in formalized languages. In the formalized language of logic and mathematics, it "works" like a pronoun. When we have a propositional function like "x is a red" or "x is odd" we have a statement like "it is red" or "it is odd". What is the meaning of the statement "it is red" ? It ...

7

Topics relating to the question are not neatly partitioned due to the involvement of complex fields and perspectives (e.g., contribution from mathematics and computer science to logic). Risking over-generalization, this is how differences among the three fields can be understood. Logic is like the tools in the shed; philosophical logic is using the tools to ...

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