# What is Quantification: Definition and 16 Discussions

In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier

{\displaystyle \forall }
in the first order formula

x
P
(
x
)

{\displaystyle \forall xP(x)}
expresses that everything in the domain satisfies the property denoted by

P

{\displaystyle P}
. On the other hand, the existential quantifier

{\displaystyle \exists }
in the formula

x
P
(
x
)

{\displaystyle \exists xP(x)}
expresses that there is something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable.
The mostly commonly used quantifiers are

{\displaystyle \forall }
and

{\displaystyle \exists }
. These quantifiers are standardly defined as duals and are thus interdefinable using negation. They can also be used to define more complex quantifiers, as in the formula

¬

x
P
(
x
)

{\displaystyle \neg \exists xP(x)}
which expresses that nothing has the property

P

{\displaystyle P}
. Other quantifiers are only definable within second order logic or higher order logics. Quantifiers have been generalized beginning with the work of Mostowski and Lindström.
First order quantifiers approximate the meanings of some natural language quantifiers such as "some" and "all". However, many natural language quantifiers can only be analyzed in terms of generalized quantifiers.

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1. ### How does a Gas Chromatograph-Mass Spectrometer detect quantities?

So I am working on theoretical project that challenges my group to detect and quantify a certain molecule in a sample. For the detection and quantification we have chosen to work with a gas chromatography-mass spectroscopy. However I am finding difficulties in how this device is able to detect...
2. ### What is the International Standard for Quantifying Funk?

The only criterion for judgement of funk is whether it makes you wanna dance. To this end I propose an international standard for quantification of funk. Give Up The Funk is hereby considered the benchmark by which all funk is measured. It is assigned the quantity of one Funk. If some other...
3. ### I have a few questions about Formalization & Pseudo-code

Hello, I have a few questions and I'd appreciate if you can please help me. 1. If I want to say "for every ## i \in \Bbb N ## and ## 0 \leq j \leq i ## define ## A_{i,j} := i ## and ## B_{i,j} := i \cdot j ## ", then is the logical formula used for this is as such?: ## \forall i \in \Bbb N...
4. ### Atmospheric CO2 absorption - actual quantification?

I have read oodles of hand wavy qualitative text about 'the greenhouse effect' and it is clearly dominated by the absorption characteristics of H2O vapour. What I struggle to understand is the part of CO2 in radiative absorption, in relative quantified terms. CO2 has absorption peaks at 2.7um...
5. ### Can we derive quantification of energy mathematically?

I'm studying for my introduction to modern physics exam, and reading about the ultraviolet catastrophe and why equipartition theorem stops working to explain blackbody emissions for high frequencies I was thinking if we could use the theorem to arrive at the quantification of energy (probably...
6. ### Quantification of Entropy and the 2nd Law of Thermodynamics

All of my information comes from my current chemistry class, I just want to know where I either may have misread, misinterpreted, or was mistold information. With the 2nd Law of Thermodynamics we can say [1]\space\space \Delta{S}_{universe} = \Delta{S}_{surroundings} + \Delta{S}_{system} >...
7. ### I Could Planck have used different energy-frequency relation?

Hello, as a non-physicist enthusiast, but with decent math background, I tried to learn a bit about origins of quantum theory and very soon raised some questions, which I hope this community will answer. So, Planck tried to model the blackbody radiation on where Raighley and Jeans have failed...
8. ### B Is quantification random or pseudo-random?

Is quantification, such as for instance with the build op of an interference pattern by individual photons, the measuring of quantum spin, or the measuring of polarized photons through a polarisation filter actually, really random, or is it possible that it might be pseudo-random?
9. ### IOR Uncertainty Quantification for PIV/LDV Measurements

Hello All, I am running some experiments using Particle Image Velocimetry and Laser Doppler Velocimetry techniques. There is a slight mismatch in the Refractive Index of the fluid and my model (Approximately 5% difference) which is creating some uncertainty in my measurements. I was wondering...
10. ### Quantification of Levers and Similar Mechanical Devices

Hello everyone. I am fairly familiar with physics. However I have a question regarding the math behind a lever mechanism. Why is it easier to exert force on something the longer the arm of the lever is? What is the math/equations behind this?
11. ### Force on surface with quantification

I would like to calculate the force on the black surface (cut view) where the black volume (undeformable) is put on pressure with a lot of red ball undeformable. The pressure is give for example with a weight. Like in the slope we can put 5 balls and only 1.5 balls in vertical side I think the...
12. ### Quantification logic and equivalence relations

I wasn't sure whether to post this in the algebra forum or here, but it seems that this is more of a logic question so I'm going with here. I am trying to understand whether there is a difference between the following two definitions of an equivalence relation: Definition 1: A binary relation...
13. ### Rotor Dynamics Quantification HELP

Hi, I'm a UT Mech E student about to graduate who's been tooling around with with some helicopter dynamics books for home machined RC contrarotating helicopter fun and I had some questions for any aerospace pros lurking around here. Being ME I know few aerospace guys so I've got some burning...
14. ### Occam's razor - quantification os Entities

hey all, I have a few questions about Occam's razor. First what is considered to be a entity? Is it any basic law of nature? (that is not a result of other laws). A mathematical axiom/set of axioms that is needed for the theory (like Euclidean geometry for classical optics). Basic...
15. ### Proving Vacuous Quantification in First-Order Logic: A Guide

I'm trying to prove a theorem which makes use of the identity \exists x (P) \rightarrow P (where x is not a free variable of P). Intuitively, I want to believe it, but since I'm trying to do things rigorously, I'd like to be able to justify it to myself. Can anyone offer a suggestion as to how...
16. ### Exploring the Quantification of 'All' with Fibonacci Numbers

Yesterday I was enlightening a friend of mine concerning the many wonders of Fibonacci numbers and the golden ratio (let this friend be represented as X). As I was speaking with X, I learned that another friend of mine (let him be represented as V) was listening very attentively. Here is our...