What is Interpretation: Definition and 832 Discussions

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation. The general study of interpretations of formal languages is called formal semantics.
The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways of presenting an interpretation. In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.
An interpretation often (but not always) provides a way to determine the truth values of sentences in a language. If a given interpretation assigns the value True to a sentence or theory, the interpretation is called a model of that sentence or theory.

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  1. J

    The Higgs Mass and the Many worlds interpretation

    I have a question about the Many worlds interpretation. Does the observed mass of the Higgs boson suggest that the many worlds interpretation is incorrect, as the mass falls smack in the middle of the predicted values of both supersymmetry and multiverse interpretations of the standard model of...
  2. Sirsh

    Interpretation of Isometric Drawing

    I am trying to create a third angle projection of this isometric drawing and for the most part it is very straight forward. However, I cannot figure out where to position a 'circle' of radius 25 to give me the correct curvature that is required for this drawing. Whenever I locate a circle and...
  3. B

    What Does the Integral of Consumption Profiles Represent in Economics?

    1. Homework Statement Ct= (∫0 1 (Ct(i) ̂(1-1/ε)) di)^ (ε/ε-1) So Ct (i) denotes number of good i consumed by the household. But what is Ct ? What does it mean to take the intgral from zero to 1 for all the Ct (i) ?Homework EquationsThe Attempt at a Solution
  4. Narasoma

    I Hidden Variable Interpretation

    What are advantages and disadvantages of hidden variable interpretation of quantum mechanics?
  5. olgerm

    I Are there any alternative interpretations to GR?

    Are there any interpretation to general relativity that described gravity as field (which do not have to be vectorfield, but may have 10 components) and physical-space as classical euclidean space? Can it be mathematically proven that such interpretation can not exist? I am not talking about...
  6. A. Neumaier

    I Particles from a thermal source

    In the following, I want to consider both photons in a sharply focussed, monochromatic beam of light (''type P'') and electrons in an electron beam (''type E'') on the same footing. In the following, X is either P or E. If we only concentrate on the internal degrees of freedom, both kinds of...
  7. L

    Geometric Interpretation of complex numbesr

    z1,z2,z3 are distinct complex numbers, prove that they are the vertices of an equilateral triangle if and only if the following relation is satisfied: z1^2+z2^2+z3^2=z1.z2+z2.z3+z3.z1 so i shall show that |z1-z2|=|z1-z3|=|z2-z3|but i do not know how to start.
  8. D

    Energy minimisation, confusion in interpretation of question

    Perhaps not an appropriate place to ask this. I've completed a question which is phrased as the following: Explain, on thermodynamical grounds, why the minimisation of the energy E(S, V, N) yields the equilibrium state of a system with fixed entropy S, volume V and number of particles N. I...
  9. phillovix

    I Many Worlds Interpretation and Coffee

    Hey there. Based on the many worlds interpretation, is: Everyone simultaneously having coffee with everyone else? Has everyone already had coffee with everyone else? Are these possibilities occurring 'somewhere' continuously? Do these possibilities only occur one at a time, or does the...
  10. D

    Conservation of energy interpretation of percentage conserved

    Homework Statement I get that less percentage energy is conserved from potential to kinetic energy by measuring h and v with two balls for the heavier ball. I am trying to sort of why actually is like that! Two balls where dropped down from a ramp with different masses and volume. The smaller...
  11. O

    How Does Container Volume Affect Vapor and Liquid Densities in Saturated Fluids?

    Homework Statement Two containers with saturated fluid at T0, while having different total volume V1 and V2 definition of total molar volume: total liquid + vapor volume divided by the total moles Problems: 1. Compare the density of the vapor in both containers 2. Compare the density of the...
  12. A. Neumaier

    A Particles in quantum field theory

    In this thread, I want to discuss the implications of quantum field theory for the interpretation of quantum mechanics. To set the stage I'll import in the next few posts a number of posts from other threads. The latest of these is the following: Only if it is the sole particle in the whole...
  13. H

    Correct interpretation of double slit experiment?

    Hiya, Another me trying to grasp some physical experiment. I'm working myself through a Dutch popular science book "Snaartheorie" (String Theory) by 'our' professor Marcel Vonk: it's meant to give the reader a maths-less impression of the theories behind string theory. Vonk starts with an...
  14. C

    Interpretation: Solution to a set of Linear Equations

    Hi, While solving a system of linear equations, there are three possible cases - unique / infinite / no solutions - to the system. One geometric interpretation is when one looks at a set of planes intersecting at one / many / no points respectively, for each of the above cases. While going...
  15. T

    Help with graph units and interpretation

    Hello, I have been doing research with a certain biological substance and its capacitance and conductivity. The following graphs are from a computer connected to a BDS (broadband dielectric spectrometer): I understand the fundamental units, but Re(C'), Re(C''), Re(σ'), lm(σ'') do not make...
  16. B

    What is the Argument Principle in Complex Analysis?

    Hi! I'd like to know of f'(x)/f(x) has some special interpretation, some physics or math concept related. This ratio appears many times in control theory...
  17. thenewmans

    QM interpretation with something moving backward in time?

    It’s easy enough to find the interpretations that break counterfactual definiteness in order to maintain locality. But I’m not sure how to find the ones with something (perhaps information) moving backwards through time. The reason I ask is I’ve always had trouble with the idea that a...
  18. J

    What exactly is a world in multiple world interpretation?

    I ask this question because I am confused. I have seen two contradictory definitions. In this link: http://science.howstuffworks.com/science-vs-myth/everyday-myths/parallel-universe2.htm The split causes a whole new universe. In this link:http://plato.stanford.edu/entries/qm-manyworlds/#2.1...
  19. C

    I Cartesian Coordinates Interpretation in GR?

    What is the physical interpretation of Cartesian coordinates in GR? Say, e.g., a system centered at the center of a spherical mass. What are x,y, and z physically, i.e., how are they measured?
  20. T S Bailey

    Is the firewall explained by the Penrose interpretation?

    The firewall has been proposed to explain why entanglement monogamy isn't violated in the AMPS thought experiment. The firewall is hypothesized to break the entanglement between the particle pairs of Hawking radiation created near the horizon so that the total sum of radiation emitted by the...
  21. J

    Understanding the many worlds interpretation

    I have a question regarding the quantum event when a wave live photon transforms into a particle like photon. In the many worlds interpretation there is a split into multiple worlds. My question is this: Do all the multiple worlds supposed to see the photon transform into a particle like photon...
  22. D

    Copenhagen interpretation and entropy confusion?

    I don't see how the Copenhagen interpretation and the second law of thermodynamics can be compatible. In the Copenhagen interpretation, upon losing coherence the system chooses a single definite state and all other possible states are eradicated. This seems to be losing entropy to me, as it's...
  23. A

    Can decoherence validate the Copenhagen interpretation?

    Hi, I am an amateur enthusiast and this is a direct question (not a proposal, I'm not nearly qualified to offer a proposal). I would like to throw to experts and people who are more qualified, because it's got me a bit stumped. Could I ask for an answer which is as simple as I am please, lols -...
  24. Anton Alice

    Common interpretation of coherence

    I don't like the common interpretation of coherence of two waves. Please tell me if something is wrong in my argumentation: 1. It is often said, that, if two waves are coherent, then the interference pattern is stationary, which means, that the amplitudes are the same. And often, this...
  25. entropy1

    How to interpret Bell's theorem correctly

    There's something I don't quite get about most illustrations about Bell's inequality theorem. I will explain what: Consider a pair of entangled photons fired at two arbitrarily oriented polarizers. I most explications, it seems the author suggests that the hidden variable represents the binary...
  26. S

    Is Copenhagen interpretation a collapse theory?

    I have been learning about the different interpretations of QM, and I am trying to build a taxonomy of them in my mind (I find that trying to build taxonomies is a good way of learning about things). I have read about collapse theories and non-collapse theories. If I have got this right, the...
  27. T

    Feynamn-Stuckelberg Interpretation of E<0

    Hi, I don't understand the F-S interpretation of the E<0 energys of the Dirac Equation. I´m mainly reading about this in Francis Halzen´s book: Quarks and Leptons sec. 3.5. The book states: And then says: e^{-i(-E)(-t)} = e^{-iEt} Is he referring to the operator that evolves H eigenstates in...
  28. O

    SPIF formula interpretation assistance

    Hello, I'm trying to apply formula 30 as described on page 12 of this paper: https://lirias.kuleuven.be/bitstream/123456789/261102/1/IJAMT_journal_final.pdf However, the results I am getting when testing against the table of results on that same page for Al 2024 (Rm = 435 N/mm2) are off in my...
  29. N

    Depending on interpretation of QM, can Hilbert space be....

    Depending on interpretation of QM, can hilbert space be considered just as real as space time? In MWI the wave function is real, but still lies in hilbert space, so would hilbert space be considered a real space according to this interpretation?
  30. A

    De Broglie Bohm interpretation with virtual particles....

    Hi all, This question is similar to a question asked previously, but slightly different. I understand that there have now been attempts to extend the Broglie-Bohm, or Pilot Wave, interpretation of QM to QFT. I'm a layman, but if I understand correctly, the standard method for computing the...
  31. A

    Physical Interpretation of velocity potential

    What is physical interpretation of velocity potential? Is a conservative quantity, i.e, line integral of velocity potential around a closed loop is zero>
  32. B

    Physical interpretation for system of ODE

    If an ODE of 2nd order like this A y''(x) + B y'(x) + C y(x) = 0 has how physical/electrical interpretation a RLC circuit, so, how is the electrical interpretation of a system of ODE of 1nd and 2nd order? \begin{bmatrix} \frac{d x}{dt}\\ \frac{d y}{dt} \end{bmatrix} = \begin{bmatrix}...
  33. S

    What is the Interpretation of a Tensor?

    Homework Statement M= \begin{pmatrix} 2 & -1 & 0\\ -1 & 2 & -1\\ 0 & -1 & 2\\ \end{pmatrix} Compute \frac{1}{6}\epsilon_{ijk}\epsilon_{lmn} M_{il} M_{jm} M_{kn} . The Attempt at a Solution I computed the result which is 4, by realizing that there are 36 non-zero levi-civita containing...
  34. P

    B Alternative Interpretation of Bell Test: 40 Nanoseconds & Photon Perspective

    When interpreting the results of the two channel Bell test, I believe there were roughly 40 nanoseconds between when the particles were created and when they hit the polarized lens. It is believed that sometime during this time information passes between the entangled photons so that they match...
  35. Anama Skout

    Is Special Relativity Correct for Observer A?

    So let's say you're sitting on the ground (observer A) and there's a car or something that moves at .99c (observer B). (Of course, this is all hypothetical) Now, my interpretation goes that when A is seeing B, the information he gets is distorted, namely due to time dilation, length contraction...
  36. Hamza Abbasi

    Physical Interpretation of Integration

    I always wondered that what is the physical interpretation of integration . How come integrating position gives as velocity? Can some one explain me what is physical insight of integration ? Ignore my poor communication skills.
  37. J

    Collapses, Quantum Jumps, and the Born interpretation

    In my mind they are all the same. But some serious physicists (Schlosshauer, for example) claim there is no evidence for the existence of collapse. What about Lyman alpha emission, where an electron in a hydrogen atom “jumps” from level two to level one and emits a photon? Or the...
  38. Graeme M

    Modern interpretation of Libet data

    Many may be familiar with the Libet experiments that suggested that the brain begins the process of preparing for a motor action before the subject decides to make the action. This has been discussed and argued over a great deal in the past several decades. I came across this in reading about...
  39. G

    What Are the Key Questions Surrounding Quantum Decoherence?

    Hi, I've been reading some (very) basic texts on decoherence and have some questions about it: 1. What is the difference between decoherence and dephasing? 2. Assuming decoherence, can we completely do away with collapse theories (i.e. theories in which wavefunction collapse must be...
  40. L

    How to Understand Scientific Papers/Judge Quality, Laypeople

    I'd like to learn how I can better understand research papers/scientific studies, judge the quality, the methods used, find out who funded it, etc. I'm a layperson. In researching various topics, especially controversial subjects, I try to find the actual scientific papers behind everything...
  41. vjacheslav

    What is double integral by interpretation?

    Very simple question for you, friends. As is well known, usual integral has interpretation as square under function's graphic. Then, what is double (and triple) integral by analogue? Thanks!
  42. N

    Can string theory and Penrose interpretation coexist?

    Can the M theory/ string theory coexist with the penrose interpretation of quantum mechanics?
  43. Feeble Wonk

    What are the 'warts' of interpretations in QT?

    As I (attempt to) follow the discussions on various QT threads here on PF, many of the subjects being discussed are frequently categorized as being an "interpretational" matter. Typically, this assertion is then followed by some statement that the formalism of QM remains the same regardless of...
  44. Derek Potter

    Is there an interpretation independent outcome problem?

    I have it on good authority that decoherence (probably) solves the preferred basis problem and explains the suppression of interference phenomena; however there remains the question: why do we get outcomes at all? Unitary evolution of coupled systems results in entanglement and thus an improper...
  45. edguy99

    What is the best interpretation of this collision graphic?

    A recent article on Proton/Lead collisions (http://physics.aps.org/articles/v8/61) used a graphic seen in earlier articles on Proton/Proton collisions (ie. http://arxiv.org/pdf/1206.0148v1.pdf). I understand the gray disks to represent protons just after the collision (flattened due to...
  46. S

    Weyl tensor for the Godel metric interpretation

    I have recently derived both the purely covariant Riemann tensor as well as the purely covariant Weyl tensor for the Gödel solution to Einstein's field equations. Here is a wiki for the Gödel metric if you need it: http://en.wikipedia.org/wiki/Gödel_metric There you can see the line element I...
  47. A

    ANSYS: How to interpret this remote force on a spiral disk?

    Hi! I am new to ANSYS and I am trying to understand a simulation done by some one else. I have a disk with a spiral in it, and it looks like there is a remote force being applied at the centre of the disk, but spread over the entire face. I don't understand how this force is being spread...
  48. 1977ub

    Copenhagen Interpretation of Sleep / Unseen brain?

    What is the accepted interpretation of these two similar related issues: 1) When I am sleeping do my brain and body revert to un-collapsed wave state until and unless seen by a different observer? 2) I *never* have "seen" my brain - have the wave functions of the atoms and cells collapsed?
  49. B

    Interpretation of augmented Dickey-Fuller results

    Hi, I have no background in statistics/econometrics but some theory I'm applying to geophysics data requires the data to be stationary (or at least trend-stationary) and I don't believe they are. I've found MATLAB code to apply the Augmented Dickey-Fuller test (from here -...
  50. A

    MWI or Bohm interpretation of this....

    And by "this" I mean this article http://arxiv.org/abs/1305.0168
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