Argument Definition and 388 Threads

In logic and philosophy, an argument is a series of statements (in a natural language), called the premises or premisses (both spellings are acceptable), intended to determine the degree of truth of another statement, the conclusion. The logical form of an argument in a natural language can be represented in a symbolic formal language, and independently of natural language formally defined "arguments" can be made in math and computer science.
Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid or sound: in a valid argument, premisses necessitate the conclusion, even if one or more of the premises is false and the conclusion is false; in a sound argument, true premises necessitate a true conclusion. Inductive arguments, by contrast, can have different degrees of logical strength: the stronger or more cogent the argument, the greater the probability that the conclusion is true, the weaker the argument, the lesser that probability. The standards for evaluating non-deductive arguments may rest on different or additional criteria than truth—for example, the persuasiveness of so-called "indispensability claims" in transcendental arguments, the quality of hypotheses in retroduction, or even the disclosure of new possibilities for thinking and acting.

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  1. chwala

    Find the modulus and the argument of ##\dfrac{2}{(4-2i)^2}##

    In my lines i have, ##(4-2i)^2 = (4-2i)(4-2i)## ##r^2 = 4^2 + (-2)^2 = 20## ##r \cos θ = 4## and ##r\sin θ = -2## ##\tan θ =-\dfrac{1}{2}## ##⇒θ = 5.82## radians. Therefore, ##|(4-2i)^2| = \sqrt{20} ×\sqrt{20} = 20## Argument = ##5.82 + 5.82 = 11.64##. also ##|2|## = ##2## and argument =...
  2. F

    I Can the same argument be used for both radians and degrees in the sine function?

    Hello, I understand that the sine function take an argument as an input and produced an output which is a real number between 1 and -1. My question is about the argument. I know it can be in either radians or degrees which are different units to measure angle. An angle is the portion of the...
  3. chwala

    Find the modulus and argument of ##\dfrac{z_1}{z_2}##

    π My take; i multiplied by the conjugate of the denominator... $$\dfrac{z_1}{z_2}=\dfrac{2(\cos\dfrac{π}{3}+i \sin \dfrac{π}{3})}{3(\cos\dfrac{π}{6}+i \sin \dfrac{π}{6})}⋅\dfrac{3(\cos\dfrac{π}{6}-i \sin \dfrac{π}{6})}{3(\cos\dfrac{π}{6}-i \sin \dfrac{π}{6})}=\dfrac{2(\cos\dfrac{π}{3}+i \sin...
  4. O

    Symbolic integration of a Bessel function with a complex argument

    Hello all I am trying to solve the following integral with Mathematica and I'm having some issues with it. where Jo is a Bessel Function of first kind and order 0. Notice that k is a complex number given by Where delta is a coefficient. Due to the complex arguments I'm integrating the...
  5. W

    I Mainstream interpretation of Newton's bucket argument?

    What is the current mainstream interpretation of Newton's bucket argument in regards to "absolute space" or similar concepts? Wikipedia asserts both that Newton's intention may either have been (1) to prove the "metaphysical" existence of something we'd call "absolute space" (i.e. some some...
  6. H

    I Understanding an argument in Intermediate Value Theorem

    We have to prove: If ##f: [a,b] \to \mathcal{R}## is continuous, and there is a ##L## such that ##f(a) \lt L \lt f(b)## (or the other way round), then there exists some ##c \in [a,b]## such that ##f(c) = L##. Proof: Let ##S = \{ x: f(x) \lt L\}##. As ##S## is a set of real numbers and...
  7. nomadreid

    COVID Need to refine an argument against an (almost) anti-vaxxer

    I am trying to build an argument against a friend (F) who is presently not an anti-vaxxer, but is heading in that direction when he told me that a friend (FF) of his told him (F) that his (FF’s) doctor told him that his Covid mRNA vaccine caused his lymphoma. Of course, FF either misinterpreted...
  8. Y

    I How to find RAAN and argument of perigee for a satellite?

    I have some values and by using them I need to find the RAAN and argument of perigee of a satellite. I have the period, inclination, apogee and perigee (as values not vectors), found semi-major axis and the eccentricity, but facing difficulty on how to proceed on calculating RAAN and the...
  9. S

    Simplifying the Argument of a Complex Number

    Let z = x + iy $$\arg \left(\frac{1+z^2}{1 + \bar z^{2}}\right)=\arg (1+z^2) - \arg (1 + \bar z^{2})$$ $$=\arg (1+x^2+i2xy-y^2)-\arg(1+x^2-i2xy+y^2)$$ Then I stuck. I also tried: $$\frac{1+z^2}{1 + \bar z^{2}}=\frac{1+x^2+i2xy-y^2}{1+x^2-i2xy+y^2}$$ But also stuck How to do this question...
  10. nomadreid

    I This is an invalid argument about eigenvalues, but why?

    The fallacy in the summary is not covered in the sites discussing eigenvalues, so there must be something blindingly and embarrassingly obvious that is wrong. I would be grateful if someone would point it out. Thanks.
  11. Shreya

    Maxwell's Capacitor argument for a time independent Current

    Is it because the current applied to a capacitor will never be time independent? Please help me out🙏
  12. S

    Finding argument of complex number

    Let: ##z=x+iy## $$z+\frac 1 z =1+2i$$ $$x+iy +\frac{1}{x+iy}=1+2i$$ $$x+iy+\frac{1}{x+iy} . \frac{x-iy}{x-iy}=1+2i$$ $$x+iy+\frac{x-iy}{x^2+y^2}=1+2i$$ $$\frac{x^3+xy^2+x+i(x^2y+y^3-y)}{x^2+y^2}=1+2i$$ So: $$\frac{x^3+xy^2+x}{x^2+y^2}=1$$ $$x^3+xy^2+x=x^2+y^2$$ and...
  13. E

    I Help with FLP argument of non-uniformly distributed surface charges

    Hello, I'm reading FLP vol II, and I would appreciate some help to understand the argument supporting Figure 6-6. Basically they claim if a sphere has non-uniform charge distribution whose surface density is proportional to the cosine of polar angle, then this surface charge distribution is...
  14. P

    A Simple argument for critical exponent

    Hello. I wanted to construct a simple and clear explanation for the relation between the beta function and the critical exponents (divergence of correlation length) close to a critical point. I wanted to check if this reasoning is valid. This is my own rewording of complicated arguments I see...
  15. M

    I Using a probability argument I got the sum. Can it be done directly?

    ##\sum\limits_{k=0}^{n-m} \frac{\binom{n-m}{k}}{\binom{n}{k}}\frac{m}{n-k}=1##. Can be derived from question. For ##n\ge m##, pick ##m## marbled out of a set size ##n## labeled from ##1## to ##n##, what is probability distribution of minimum of the number labels on the marbles? The terms is...
  16. K

    I Kinetic energy depends on ##\theta## but this argument says otherwise

    A free particle with coordinates as shown has kinetic energy ##T = \frac{1}{2}m\left(\dot r^2 + r^2\dot\theta^2 + r^2\sin^2\theta\dot\phi^2\right)## So we see ##T## depends on ##\theta##. Now suppose we rotate our coordinate system such that only one coordinate ##\theta## changes from...
  17. S

    I Does this defense lawyer's probability argument sound like BS?

    Either that, or the author is a typical "pop scientist" author that doesn't understand probability too well. https://nautil.us/issue/4/the-unlikely/the-odds-of-innocence
  18. E

    I Opaque-wall-with-hole argument from Feynman lectures

    In Feynman lectures vol I, last part of chapter 31, there was this argument about electric field on the other side of the opaque wall with holes. The argument is attached below. I'm having a hard time understanding the claim in the red box. In particular, I failed to see how "fields arrive at...
  19. P

    I Energetic argument for the tension in a current loop

    The energy stored in a current loop equals ##\frac{LI^2}{2}##. From a dimensional argument, it follows that the inductance grows with the size of the loop. This would mean that, if we assume the current stays constant, enlarging the loop would require external positive work, so, the force...
  20. H

    Question about the argument in a Complex Exponential

    I know that e^-ix = cos(-x)-isin(x), but if we have e^-iwx does that equal cos(-wx) - isin(wx)? Thanks
  21. U

    Principal value of an argument

    This is my attempt of the problem Argz = (11π+θ) - 2πn 0 < (11π+θ) - 2πn < π/2 0 < (11π+θ) - 2πn or (11π+θ) - 2πn < π/2 n < (11π+θ)/2π or n > (21π/4 + θ) (21π/4 + θ) < n < (11π+θ)/2π, what i was trying to do was to find the value of n which i thought would help me obtain the value of the...
  22. S

    Understanding Griffith's Velocity Argument for Charge Integration

    In Griffith’s section 10.3.1, when proving why there is an extra factor in integrating over the charge density when it depends on the retarded time, he makes the argument that there can only ever be one point along the trajectory of the particle that “communicates” with the field point. Because...
  23. SSequence

    Non Existence An argument involving well-orders

    Few days ago, I posted an answer for a mathoverflow question. The question was of elementary nature. The question had a lot of views, and my answer didn't get any upvote. Now since I got a downvote, perhaps there was a (major) mistake somewhere in the argument I posted? Tbh I was reasonably...
  24. Killtech

    I Is the premise of the Michelson–Morley argument still valid?

    I've been thinking about the Michelson–Morley experiment lately and how it would play out with acoustic waves clearly showing the presence of a sonic-ether (well, at least in the case it's not enclosed - the air through which the sound travels has to be exposed to the outside wind ofc). And...
  25. chwala

    Find the greatest value of argument- complex numbers

    since ##|z|≤3## →##z=0+0i##, therefore we shall have centre##(0,0)## and radius ##3##, find my sketch below,
  26. MichPod

    I An argument against super-determinism

    I think I have something which can make an argument against superdeterministic interpretation of QM. Not that I am keen of disproving it, but I think that arguments even against some fringe ideas may have non-zero value and are anyway entertaining. I'll be glad to see feedbacks/review for...
  27. mhsjx

    I What'wrong in this argument? (Atom/Photon interferometry)

    First, we can think a MZ interferometer as a combination of two beamspliter and a phase shifter(from MIT course "Atomic and Optical Physics II", the paper is "Quantum-mechanical noise in an interferometer"), which evolution matrix is B = {{1,-i},{-i,1}},B dagger and P ={{1,0},{{0,exp{i\phi}}}...
  28. F

    Conjugacy and Stabilizers in Group Actions

    Attempt at solution: Proof of i): Let ##x \in X##. Its clear ##G \supseteq HG_x##. Let ##g \in G##.Then there is ##y \in X## such that ##g \cdot x = y##. Since ##H## acts transitively on ##X##, there is ##h \in H## such that ##h \cdot x = y##. So, ##g \cdot x = h \cdot x##. This gives...
  29. W

    B Another consequence of Cantor's diagonal argument

    Thinking about Cantor's diagonal argument, I realized that there's another thing that it proves besides the set of all infinite strings being uncountable. Namely: That it's not possible to list all rational numbers in an order such that the diagonal of their decimal representation has an...
  30. W

    B One thing I don't understand about Cantor's diagonal argument

    Cantor's diagonal argument, essentially, proves (or demonstrates, as I'm not exactly sure if it's considered a mathematically rigorous proof) that the set of all real numbers is uncountable, ie. essentially larger than the set of natural numbers. It does this by, essentially, proof by...
  31. G

    The Vertical Force of a Spring: A Logical Argument

    Because this problem is easier to understand with a picture, I'll just copy paste the original problem. There is no question about the validity of the solution. My question is about the statement in the solution "Consider the instant when the mass is moving vertically upward. In this instant the...
  32. JackHolmes

    A Help with the Derrick scaling argument and topological solitons

    I have been reading Manton & Sutcliffe for some time now and can't quite wrap my head around something. If you take the Hopf invariant N of a topological soliton ϕ then its Skyrme-Faddeev energy (which I hope I've gotten right up to some constants) E=∫∂iϕ⋅∂iϕ+(∂iϕ×∂jϕ)⋅(∂iϕ×∂jϕ) d3x satisfies...
  33. tomdodd4598

    I Argument for Existence of Normal Coordinates at a Point

    Hey there, I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here (26:33 - 35:40). In short, the argument goes as follows (I think): we have some generic metric ##{ g...
  34. D

    B My argument why Hilbert's Hotel is not a veridical Paradox

    Hello there, I had another similar post, where asking for proof for Hilbert’s Hotel. After rethinking this topic, I want to show you a new example. It tries to show why that the sentence, every guest moves into the next room, hides the fact, that we don’t understand what will happen in this...
  35. pellman

    Maxwell-Boltzmann distribution -- Maxwell's argument

    The attached image shows the text I am following. I get that the 3-D pdf F can only depend on the speed v. I also understand that if f_x , f_y, f_z are the pdfs of the individual components of velocity, then rotational invariance requires them to all be the same function f_x = f_y = f_z = ϕ...
  36. H

    Engineering Finding the argument of a Transfer Function

  37. J

    I Fulvio Melia's new argument for a linear cosmology

    I would be interested in what people think of Fulvio Melia's new cosmological paper in which he argues that the comoving frame is locally inertial only if we have a linearly expanding Universe (or Minkowski spacetime)...
  38. B

    What are the rules for argument division in complex numbers?

    above video states that arg(z1/z2) = arg(z1) - arg(z2) this is seems very similar to Log rules but these are inverse function for angles right? And log rules only apply to logarithms, not sure where he got this from? What am i missing?
  39. P

    B Correct way to write multiple argument functions

    Hi, This is on the wikipedia entry for the Euler Lagrange equation. Here is a link. https://en.wikipedia.org/wiki/Calculus_of_variations#Euler%E2%80%93Lagrange_equation The notation I am confused about is this: Aren't the y(x) and the y'(x) unnecessary to list as arguments when x is...
  40. E

    Shift in wavelength of photons from the Sun using energy argument

    I came across a question recently which involved calculating the change in wavelength of a photon between being emitted from the surface of the sun and arriving at the Earth. The method that was implied involved calculating the GPE's of the photon (assuming the photon to have a mass h/[c...
  41. sponteous

    Carnot's Argument (Cryptic passage in Feynman Lectures v. 1)

    In chapter 44 of Feynman Lectures on Physics, Volume I, which covers thermodynamics, we find this passage: Does anyone know what this argument of Carnot's is? I'm not sure exactly what it is that he is supposed to have derived without using the first law. The efficiency of a reversible...
  42. D

    I Changing the argument of a function

    Hi. If I have a function f(x) = √(x+1) and I define u=x+1 is it correct to state f(u) = √u ?
  43. R

    Argument of a complex expression

    Problem Statement: What is the correct way of computing the argument of the following equation? Relevant Equations: I am trying to compute the argument ##\Phi## of the equation $$\frac{r-\tau\exp\left(i\varphi\right)}{1-\tau r\exp\left(i\varphi\right)} \tag{1}$$ which using Euler's equation...
  44. M

    What are the units of the argument "x" for this cos(x) function integral?

    Show that the value of ##\int_0^1\sqrt(1-cosx)dx## is less than or equal to ##\sqrt2## ##1\ge cos x\ge-1## The problem is a worked one but I am just confused by a simple thing. We integrate the function f ##\int_0^1\sqrt(1-cosx)dx in the interval [0,1] but I don't understand that what stands...
  45. P

    A Why the fine-tuning argument for improbable existence is a fallacy

    "In 1961, physicist Robert H. Dicke claimed that certain forces in physics, such as gravity and electromagnetism, must be perfectly fine-tuned for life to exist anywhere in the universe. Fred Hoyle also argued for a fine-tuned universe in his 1984 book Intelligent Universe. Much as been written...
  46. JD_PM

    Understanding the argument of the surface area integral

    Homework Statement Find ##\iint_S ydS##, where ##s## is the part of the cone ##z = \sqrt{2(x^2 + y^2)}## that lies below the plane ##z = 1 + y## Homework EquationsThe Attempt at a Solution [/B] I have already posted this question on MSE...
  47. D

    B Are f(x) and f(-x) Equivalent Functions?

    Hi. If I have a function for example f( x ) = x2 + x then to obtain f( -x) I just put (-x) in place of the x in f(x) so I get f( -x) = x2 - x Am I right so far ? So f(x) and f(-x) look like different functions but if you put a negative number in f(-x) it flips the -x back to +x so are f(x) and...
  48. Michael Santos

    The indefinite integral and its "argument"

    Homework Statement The indefinite integral $$\int \, $$ and it's argument. The indefinite integral has a function of e.g ## \cos (x^2) \ ## or ## \ e^{tan (x)} \ ## If the argument of ## \cos (x^2) \ ## is ## \ x^2 \ ## then the argument of ## \ e^{tan(x)} \ ## is ## \ x \ ## or ## \ tan (x) \...
  49. fluidistic

    I Understanding L&L's argument, constant current in a crystal

    I'm trying to go through chapter III of the vol.8 of Landau and Lifshitz series. (Fortunately the book is uploaded to the archive.org, I guess it is in the public domain.) At page 87 ( << Archive.org link deleted by the Mentors because of copyright violation >> ), they speak about the Joule...
  50. S

    A Small & large argument expansion of plasma dispersion function

    In plasma physics we have what is known as plasma dispersion function. There are two approximation under which this function can be expanded: when the argument is less than 1, we can use power series expansion and when the argument is greater than 1 we can have asymptotic expression. My...
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