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5

These rules are intuitionistically valid, but... Intuitionists accept modus tollens in the form given (2), but not {¬q→¬p, p} ⊢ q, see Can one prove by contraposition in intuitionistic logic? A contradiction out of ¬q only gives us ¬¬q, and removing the double negation is something they reject. This is because p → q is interpreted as "given a proof of p a ...


4

This would be a straight-forward case of "absence of evidence is not evidence of absence" or what is called argument from ignorance. As the article states: This represents a type of false dichotomy in that it excludes the possibility that there may have been an insufficient investigation to prove that the proposition is either true or false. Hence it is ...


4

The purpose of Russell’s Theory of Descriptions is precisely to give meaning (i.e. truth value) to a statement concerning a non-existent entity. The basic assumtpion is that names of individuals must refer to existing objects (individuals). Thus, what does it mean to assert something about a non-existing objects referring to it with a sort of "name" ? The ...


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Many predicate language sentences come in one of two forms: "All A's are B's" and "Some A's are B's". There's also "No A's are B's", but that's just a negation of "Some A's are B's". They are translated as: All A's are B's: ∀x(Ax -> Bx) and Some A's are B's: ∃x(Ax & Bx) All of your sentences in one way or another have one of those two basic forms....


3

The good news is that your intuition is correct, and you got steps 1-3 correct. But, from the OP, you struggled with what action to take in step 4. Honestly, it comes from what you're trying to prove. As a general rule: If the conclusion you are trying to prove is a material conditional then start by either 1) make a sub-proof starting with the ...


3

The issue you are not considering is that the act of 'observation' carries two distinct modes in language: description and ascription. Description is a passive mode that merely notes and relates a characteristic of the observed: e.g., "John has hands and feet". Ascription is an active mode that imports causal relationships into a characteristic of the ...


3

What might seem odd to you is that Russell treats the description operator in a syncategorematic way. That is, the operator itself is not associated with an explicitly defined operation, but formulas containing the operator are associated with satisfaction conditions. The problem with syncategorematic treatments is that the syntax of the formula interpreting ...


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First, let's review some ideas of argumentation. With deduction, we can talk about arguments about being sound and valid. Valid means the structure of the argument leads to the correct conclusion independent of the premises, whereas soundness implies the argument is not only valid, but has true premises. For instance, "If Socrates is in the kitchen, he is ...


1

What the purpose of a speech is? Ideally, no one likes to trick another! Thus, people should ideally try to convey their ideas. This transfer of reasoning is logos: to persuade by logic. Here is my (rhetorical) question: what else is logical? Is "persuading" by touching emotions something really (logically) valid? Of course the fact that an advertisement has ...


1

Ethos, pathos, and logos are a typology of modes of persuasion. They are not mutually exclusive, and in the general case one must invoke all three to be truly persuasive. It's a question of balance and proper usage. Pathos builds an emotional connection with the listener, but an excess of pathos alienates others. Pathos without ethos is manipulative; pathos ...


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Think of variables as names, and a variable assignment as something that tells us what a variable names. If you have an open formula, say Px, then Px will come out true when x names an entity which falls within the extension of P. If you consider the formula ∃xPx, x is bound by the existential quantifier. Since x is bound, what x happens to name under a ...


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Welcome, Tom You deliver a large and complex topic ! The following extract from an article by Matti Eklund (2011) could scarcely be fully satisfying but it does (a) relate sorites and supervaluationism and (b) start a discussion of difficulties: Vagueness, as discussed in the philosophical literature, is the phenomenon that paradigmatically rears its ...


1

A distinction between a statement which describes the essential properties of an object and one which describes only contingent properties is the key point. For instance, 'A triangle is a a plane figure with three straight sides and three angles', states all the definitional properties of a triangle - hence in this specific sense it captures everything (...


1

My understanding of the use-mention distinction is that the former refers to a disposition (behavior) or proposition (meaning bearer) while the latter is merely a reference (syntactical expression such as a string). In this way, dispositions correspond to correspondent truths (combining two individual cookies in results in a state of affairs that a box has a ...


1

1+1=2 is a formula (an expression of mathematical language that express a statement) and "1+1=2" is the way to refer to the expression: correct. 1+1 is a term, i.e. an expression that denotes a number. Thus, it is not a formula. The principle of the Indiscernibility of Identicals (the converse of the Identity of Indiscernibles) in its predicate logic ...


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Generally speaking, a classification system is an inclusion system. The ideal is that if we have a stream of objects in front of us, we can sort those objects into appropriate buckets based on the characteristics of the objects themselves. There may, of course, be buckets within buckets, but the buckets are meant to be mutually exclusive. With that in mind, ...


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You've hit on an important philosophical issue. If we define every-thing as a set then 'everything' cannot be a set. Hence fundamental theories must transcend sets and the categories of thought in the manner of Kant or the Perennial philosophy. If we do not do this we cannot have a fundamental theory. The mystics call this place the 'world of opposites' ...


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Beware of conflating individual attributes themselves with objects that can have those attributes. For instance, "happy" and "angry" are two different emotions. Their individual definitions might be mutually exclusive, but that doesn't mean that their existence is mutually exclusive. It is possible for someone to experience both emotions at the same time. ...


1

It follows from how the formal semantics of the quantifiers and the connectives used with these quantifiers is defined. An existential statement There is a P which is Q is formalized as ∃x(P(x) ∧ Q(x)) A universal statement All P are Q is formalized as ∀x(P(x) → Q(x)) The semantics of the quantifiers themselves and the logical constants ∧ ...


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You might enjoy F.H.Bradley's Appearance and Reality, in which he analyses and sublates a list of everyday categories and distinctions. There is also G. S. Brown's Laws of Form, in which he presents a formal 'calculus of indications' where an 'indication' is a distinction or category-of-thought. There is also C.S Peirce, who did a great deal of work on ...


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I'm getting a PhD in philosophy, and I'm friends/acquaintances with many professional philosophers (i.e. philosophy professors), and I guess I'll weigh in here. The answer depends on what you think a philosophical question looks like and what would count as an answer to one. Most philosopher think philosophical questions have answers (assuming the questions ...


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Fundamental reference : Chance , Love and Logic by C.S. Peirce ( at archive.org). See: Part I, chapter 6 " Deduction, induction and hypothesis"). Peirce is the one who coined this term " abduction". See also : article " reasoning" ( by Peirce) in Baldwin's dictionary of philosophy and psychology. Short answer Both are "ampliative"; but while induction ...


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Consider this material implication statement : If The Eiffel Tower is in Paris then The Eiffel Tower is in the capital-city of France. If the antecedent and the consequent are given the truth value they have in the actual world, then the whole material conditional is true. But that does not mean that the consequent " The Eiffel Tower is in the capital-...


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