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Questions tagged [quantification]

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What is a physical quantity in science?

The Wikipedia article on Physical Quantities, says that: The meaning of the term physical quantity is generally well understood (everyone understands what is meant by the frequency of a periodic phenomenon, or the resistance of an electric wire).…
Harshit Rajput
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In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?

I am having a discussion whether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation. Discussion follows on the following statements: 1. All…
6thsense
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Can/Do there exist any quantifiers other than "there exists" and "for all"?

I'm curious about why there are only the two logical quantifiers there exists and for all. Intuition and human language support the idea that these quantifiers make sense, but otherwise it seems arbitrary (at least from a symbolic, formal logic…
WillG
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Square of Opposition with percentages?

What happens if you replace the statements of the Traditional Square of Opposition with "percentages of the subject term"? Do all the relationships from the Traditional Square of Opposition still apply? A: 100% of x have y. -- ("All dogs have…
Mike
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General vs Universal

Source: p. 44 Bottom. Ethics ; A Beginner's Guide (2015) by Peter Cave.   The universal and the general are distinct; the general is a matter of degree. Kant sought laws that are universal, applying to everybody everywhere, impartially,…
user8572
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What does the term "mathematical logic" mean?

What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical? Also, is "quantificational logic" a particular type of "mathematical logic"? (cf. "What is the philosophical ground…
Geremia
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Is there a quantitative model of Bentham's Hedonic Calculus?

Jeremy Bentham, in Chapter 4 of his 1781 An Introduction to the Principles of Morals and Legislation, defines what has become known as the Hedonic Calculus. He states, Pleasures then, and the avoidance of pains, are the ends that the legislator has…
Robert Columbia
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Prove ∀w(∀v((v=w∧φ(v))⇔φ(w)))

In this math question of mine, an answer pointed me to this theorem: ∀w(∀v((v=w∧φ(v))⇔φ(w))) which in turn, the answerer stated, implies another theorem: ∃v(v=t∧φ(v))⇔φ(t) which was the fact I needed for my proof. However, how would one prove…
EthanAlvaree
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Multiple universal quantifiers in an argument

Consider the argument ∀x∀y((S(x,a)∧ S(a,y))→S(x,y)), ∀x¬S(x,x) ├ ∀x(S(x,a)→¬S(a,x)) My approach to formally proving this was to first eliminate ∀x and use x0 as the free variable. Then afterwards eliminate ∀y and use x0 as the free variable…
DrDeanification
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Proving the negation of universal quantification

Consider the following argument ∀x(R(x) ∨ S(x)), ∃x(¬R(x)) ⊦ ¬∀x(¬S(x)) My strategy is to try to prove that ∀x(¬S(x)) is a contradiction, and therefore ¬∀x(¬S(x)) must be true. My solution so far ∀x(R(x) ∨ S(x)) Premise ∃x(¬R(x)) Premise ¬∀x(¬S(x))…
DrDeanification
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Do some things not exist?

Quod sic: The Statue of Zeus no longer exists (it was destroyed by fire in the 5th century A.D.) Therefore, there is something (the Statue of Zeus) that does not exist. Contra: How can there be anything which does not exist? [edit] This question…
quis est ille
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Is the multiverse standpoint in set theory "ideologically committed" to plural quantification over universes/axioms?

One of the ways in which Hamkins expresses the multiverse standpoint is as the assertion that there is no "absolute background concept of sets or even ordinals." He spells out examples of ill-founded and nonlinear metatheories of axioms in service…
Kristian Berry
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"Should" there be multiple types of universal quantifiers?

Assumptions/presuppositions. I am trying to set up a logic where every connective/operator comes in at least two flavors. For example, with respect to disjunction, rather than hold the LEM rigidly over every disjunction, we confine its primary…
Kristian Berry
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Devising mathematical or quantitative theories of meaning

Around 1948, the mathematician and electrical engineer Claude E. Shannon presented work that would eventually lead to information theory. A mathematical theory based on uncertainty and probability, which allowed to quantify the "amount of…
Davius
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How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

How would a formal Fitch proof look like. I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic. I am confused on how to proceed with the proof. Please advice me on how to go about with this. Thanks in advance
Moey mnm
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