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. alexmahone

    MHB Find the error in the following argument

    Find the error in the following argument by providing a counterexample. “The reflexive property is redundant in the axioms for an equivalence relation. If x ∼ y, then y ∼ x by the symmetric property. Using the transitive property, we can deduce that x ∼ x.”
  2. MidgetDwarf

    Cannot follow this argument pertaining to geometric series.

    In order to construct a geometric series we do the following: chose a number a such that a does not equal 0 and a second number r that is between (-1,1). We call r the ration because it is the ratio, the progression of each term to its predecessor. We have An=a+ar+ar^2+ar^3...ar^n We multiply...
  3. L

    Integral of Exponential with Polynomial Argument

    How can I find an Integral of an exponential with Polynomial argument with finite limits: \int_0^\pi \exp^{-a x^2 -b x^4} dx \\ \int_0^\pi \exp^{-a x^2 -b x^4} (x - x^3)dx
  4. Philosophaie

    Argument of the Perihelion Projection

    In Celestial Mechanics the equation: LP = w + N (Longitude of the Perihelion = Argument of the Perihelion + Longitude of the Ascending Node) is confusing. Both "LP" and "N" are on the Ecliptic Plane but "w" is not. "w" is on the Elliptic Plane with a tilt of "i" Inclination from the Ecliptic...
  5. Sai-

    Bounding Argument for Comparison Test

    I have the sum, $$\sum_{n=1}^{\infty} \frac{1}{n^{3}}\sin(n \pi x) \text{, where }0 \leq x \leq 1$$ I have to show that the series converges, so I'm going to use the Comparison Test. $$ \text{If }0 \leq a_n \leq b_n \text{ then}$$$$\text{If }\sum b_n \text{ converges then }\sum a_n \text{ must...
  6. znaya

    How to find the argument of a function?

    Homework Statement For the function ##V(f) = A \tau sinc(f \tau)## in the picture how do you conclude that the argument of ##V(f)## is 0º, +180º or -180º? Homework Equations ##arg = arctan({\frac{Im}{Re}})## The Attempt at a Solution The upper graphic represents the absolute value of the...
  7. K

    MHB Verification of argument for global asymptotic stability of equilibrium point

    I am working on proving that an equilibrium point of a two-dimensional dynamical system is globally asymptotically stable. The background and justifications are below. I have gotten to the final steps (in bold), but cannot justify it. It seems right intuitively. Can someone navigate the argument...
  8. LHCSafetyReview

    A hole in the LHC's vacuum bubble safety argument

    A hole in the LHC's vacuum bubble safety argument One of the four specific risks considered in the most recent official safety review for the Large Hadron Collider (LHC) is the possibility that LHC collisions could trigger a transition to a lower-energy vacuum state. The current review by the...
  9. N

    Complex Analysis: Open Mapping Theorem, Argument Principle

    Homework Statement In each case, state whether the assertion is true or false, and justify your answer with a proof or counterexample. (a) Let ##f## be holomorphic on an open connected set ##O\subseteq \mathcal{C}##. Let ##a\in O##. Let ##\{z_k\}## and ##\{\zeta_k\}## be two sequences...
  10. J

    Light clocks measure conformal time - detailed argument

    Let us assume that an observer is stationary at the origin in expanding space. We assume the FRW metric near the origin is given by: $$ds^2=-dt^2+a(t)^2dr^2$$ Let us assume that the observer measures time by bouncing a light beam at a mirror that is at a constant proper unit distance away from...
  11. S

    An argument for "Brocard's problem has finite solution"

    Brocard's problem is a problem in mathematics that asks to find integer values of n for which $$x^{2}-1=n!$$ http://en.wikipedia.org/wiki/Brocard's_problem. According to Brocard's problem ##x^{2}-1=n!=5!*(5+1)(5+2)...(5+s)## here,##(5+1)(5+2)...(5+s)=\mathcal{O}(5^{r}),5!=k##. So, ##x^{2}-1=k...
  12. David McArthur

    Argument for Grand Design, maybe?

    I was watching a discussion on wether the the universe is the way it is through design or by chance. The design theory is basically that the universe is such a complex entity and that for it to have evolved exactly as we see it, then it must have been designed. The counter theory is that we live...
  13. P

    Newton's argument, gravitational force inside a sphere

    This is an excerpt from "Introduction to Mechanics" by Kleppner and Kolenkow: "The reason why gravitational force vanishes inside a spherical shell can be seen by a simple argument due to Newton. Consider the two small mass elements marked out by a conical surface with its apex at ##m##. The...
  14. D

    Combinatorial argument probabilities

    Hello 1. Homework Statement Consider fk N*→N, k≥0 fk(n)=Σ jk n>0 We're looking to establish these identities, using a combinatorial argument fk(n)=n if k=0 fk(n)= 1/(k+1) [ nk+1 + Σ ( i , k+1) (-1)k+1-ifi(n) ] if k>0 the sum is about i from i=0 to i=k-1 and (i, k+1) is the combination...
  15. R

    Argument Essay Topic Ideas: AI Research

    Hello all! My class is doing a an argument essay that requires students to choose a topic that is specific and has two sides. My problem is that I can't seem to find a topic that fits this criteria. I was hoping to find a topic in technology. One topic I really wanted to research was artificial...
  16. Y

    Complex Variables - principal argument

    Homework Statement Find the principle argument Arg z when z = (sqrt(3) - i)^6 Homework EquationsThe Attempt at a Solution I'm sorry to say that I'm not sure how to solve this problem. It's my understanding that what this question is basically asking me to do is find theta such that...
  17. Coffee_

    A question about a certain math argument in Griffiths

    1. In the part of the analytical solution of the harmonic oscillator, p38 in my version of the book a certain mathematical trick is used. The position part of the wave function in function of a dimensionless variable z, is given by ##\frac{d^{2}\Psi(z)}{dz^{2}}=(z^{2}-K) \Psi## In the limit of...
  18. H

    How Can Hybrid Functional Calculations Be Quicker Than Hartree-Fock?

    Hi everyone, How hybrid functional can be quicker than HF ? Because we have to use the HF exchange part, so we have to solve the problem with HF before, am I right ? Thank you
  19. D

    Einstein's argument for a finite universe

    After reading some of Einstein's writings on relativity I am confused as to why he finds it necessary that the universe is finite. In his "Relativity", Einstein explains that the ultimate Newtonian picture of the universe (matter in Euclidean space) would be one in which all mass were...
  20. R

    Understanding Time Dilation: Exploring the Effects of Speed on Time

    A question about time dilation.. I find myself in an argument / discussion about the theory of time dilation, and it seems to me, that the terminology is really the problem. Would it not be more accurate to say that the effects of time slow, as speed increases ? To say that our test of clocks...
  21. G

    Is Enveloping the Worm Gear Necessary for Optimal Tooth Contact with Spur Gears?

    I wanted to exchange some opinions about worm gear enveloping. I am designing a worm gear 3d model and, putting the appropriate amount of thought in it, some interesting points arise. One may either: 1) Envelop (is that right?) the worm gear helix, so that its radius increases from the gear's...
  22. 1

    The Logical Argument for the Picture's Claim

    Do the logicians/mathematicians agree with the picture's claim?
  23. B

    Finding the modulus and argument of a complex number

    Hello, I have the point ##-1 + 2i##, for which I am asked to find the modulus and argument. The modulus was simple enough, but I am having difficulty finding the angle. The point is located in the 4th quadrant, and so I need to make certain that I calculate an angle in the range ##(\frac{3...
  24. S

    Integrating sine where argument goes to infinity.

    After some integration, i am getting a form e^{i \alpha\phi+i\beta\phi\sin(\phi-\phi')-i\gamma\sin\phi} , where ##\alpha, \beta, \gamma## are constants. Now i want to apply the limit where ##\phi ## ranges from 0 to ##\infty ## (ya, in the argument of sine we will encounter ##\infty ## which is...
  25. F

    Understanding Velocity vs Time Graphs for Horizontal Motion

    Quick question about translating what's on the Velocity vs Time graph into what is actually happening to the object. A cart is traveling on a straight horizontal track. So I determined that east is positive direction. So, if the velocity vs time graph is showing a negative slope of -0.2 does...
  26. Maxo

    Can different arguments be correct for the same complex number?

    Homework Statement Calculate argument of complex number -1-\sqrt{3}i Homework Equations The Attempt at a Solution The argument of this is -120 degrees but why couldn't we as well say it's 240 degrees? Since going 240 degrees will go to the same point as -120 degrees. Why is this false?
  27. noowutah

    Exploring the Fine-Tuning Argument (FTA)

    I am doing some work on the fine-tuning argument (FTA), basically P(D|F\&B)>P(D|B) where D is the hypothesis that the physical constants were in some way designed (to make life possible, for example), B is shared background information and F is the observation that the physical constants...
  28. S

    Calculating Argument of w: (-4(√3+i))/(-1+i)

    Hi I am kind of lost Deside an argument for w w= (-4(√3+i))/(-1+i) I know that the arg is the angel.. And the equation is in radians.. where to start?? best Regards! Homework Equations The Attempt at a Solution
  29. J

    Quantum Zeno Effect: What is the argument? (Part II)

    Every general explanation of the quantum zeno effect I've found is (from my perspective) so full of gaps that I cannot understand the explanation. My understanding has improved due to responses to a previous post on this topic as well as to a detailed but still gappy paper that was recommended...
  30. kduna

    Does Cantor's Diagonal Argument Apply to the Rationals?

    I had an undergraduate pose an interesting question to me. "Why doesn't Cantor's Diagonal Argument apply to the rationals?" http://www.proofwiki.org/wiki/Real_Numbers_are_Uncountable/Cantor%27s_Diagonal_Argument Now obviously it doesn't since the rationals are countable. But what breaks...
  31. J

    2 definitions for argument, why?

    In the wiki, I found this definition for the argument: http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Exponential_definitions However, in other page of the wiki (http://en.wikipedia.org/wiki/Complex_conjugate#Use_as_a_variable), I found this definition for...
  32. A

    Matlab help fplot() with 3-input argument function?

    matlab halp! fplot() with 3-input argument function?? Homework Statement heres da link: http://postimg.org/image/uqqr3q0k3/ don't really need to look at that though. Its just a function in another file, I have to call it but it takes 3 input variables, problem with fplot is it only uses a...
  33. J

    Quantum Zeno Effect: What is the argument?

    Every general explanation of the quantum zeno effect I've found is (from my perspective) so full of gaps that I cannot understand the explanation. I am wondering if anyone can help me fill in the gaps here? The most detailed explanation I've found runs something like this: Let |ψ0> be the...
  34. B

    Intuition on Successive Approximation as Pseudo-Power-Series Argument

    The explanation below illustrates why I think the method of successive approximations is merely a sneaky way of working with power series when you're not formally allowed to use a Taylor series expansion for a function (i.e. when it doesn't exist, as in proving the existence theorem on ode's for...
  35. mesa

    Need good argument for why vaccinations are a good thing.

    I love my little girl and so does her mom but she needs to understand.
  36. K

    MHB Permutation representation argument validity

    Hello, I would like to check if the work I have done for this problem is valid and accurate. Any input would be appreciated. Thank you. **Problem statement:** Let $G$ be a group of order 150. Let $H$ be a subgroup of $G$ of order 25. Consider the action of $G$ on $G/H$ by left...
  37. C

    Need Backup in an Argument Against Quackery

    First sorry if this is to some extend kind of against the rules, especially considering that technically this thread is debating pseudoscience. I just need someone with "scientific credentials" to backup my argument. The issue is about a certain Royal Raymond Rife's apparatus supposedly able to...
  38. R

    Does geometry have any bearing on the fine tuning argument.

    Now I think there are arguments for the Fine Tuning of the universe. I like Martin Rees' book but I know there are others who disagree with what he said in his book (Just Six Numbers) On another forum I've got involved in a discussion on this topic and I've seen an argument that I think has no...
  39. F

    MHB Do you need absolute value around argument for log and ln?

    When I learned about derivatives I was taught to put the absolute value sign around the argument for ln and log. For example \log{|x|} and \ln{|x|} instead of log(x)ln(x). Does this make a difference? Should both brackets and the straight lines be used? When taking the derivative what is the...
  40. M

    Equivalence of Log and Argument for Complex Functions?

    Hello! So I have questions on this equivalence: Imlog[(1+x)/(1-x)] = arg [(1+x)/(1-x)] where x: complex number How is this true? Is it always applicable no matter what form of complex function is under calculation? Thank you.
  41. P

    MATLAB Solving an Argument in MATLAB with Linprog

    Dear All Firstly, thank you for looking at my post. I am so close to a solution to a problem that has been given me a massive headache. I am also very stupid and was wondring if one of smart guys could take a look at my problem and see if you might be able to help. I am trying to...
  42. A

    Cantors diagonalization argument

    I am sure you are all familiar with this. The number generated by picking different integers along the diagonal is different from all other numbers previously on the list. But you could just put this number as next element on the list. Of course that just creates a new number which is missed...
  43. T

    Application of the Argument Principle

    I've been studying for a test and have stumbled upon another type of problem I'm not comfortable with yet. I need help applying the argument principle - the practice problems in my textbook all consider only polynomials in the first quadrant. In solving this type of problem I consider...
  44. IridescentRain

    On nonnegative-order first-kind Bessel functions with large argument

    Hello. I'm not terribly proficient with Bessel functions, but I know that those of the first kind are given by \begin{eqnarray} J_n(x) & = & \left(\frac{x}{2}\right)^n\,\sum_{\ell=0}^\infty\frac{(-1)^\ell}{\ell!\,\Gamma(n+\ell+1)}\,\left(\frac{x}{2}\right)^{2\ell}, \end{eqnarray} where...
  45. Alpharup

    Argument on centrifugal force

    My grade 11 textbook never mentioned about inertial frame, non- inertial frame, rotating frame of reference and so son.The derivation of centripetal acceleration was very intuitive.This derivation was given after Laws of Inertia and other Newton's laws of motion.Ideas like cross product and dot...
  46. H

    Argument principle for a rectangle

    Homework Statement . I want to prove that there is one solution for e^z-z in every shifted copy of the fundamental strip by applying the argument principle to the boundary of a rectangle −M≤Rez≤M , 2kπi≤Imz≤2(k+1)πi for large M and integer k . I need help in using the...
  47. U

    Argand Diagram: Difference in argument = pi/4

    Homework Statement Sketch the locus of points in the argand diagram defined by z: arg (z-1) - arg(z+1) = ∏/4 Homework Equations The Attempt at a Solution By simple geometry i worked out that at a point in the x-y plane, the angle subtended from that point to -1 and 1 must...
  48. T

    Limits at Infinity for the Argument Function in Complex Variables

    ℂI am working on an assignment and have come across a question that I'm not quite sure how to approach. Here it is, with my "solution" and reasoning: "[F]ind the limit at ∞ of the given function, or explain why it does not exist. 24. h(z) = Arg z , z \neq 0" (Complex Variables Second...
  49. T

    Topology of the Set {1/n} for Positive Integers Z

    Determine the interior, boujdary, and closure for the set: { 1/n : n is in the positive integers Z}. Attempt: two things bothering me. 1) if i am in the set of positive integers, how does 1/n even exist? 2) now let's say it does exist, then the inteior would be empty because every...
  50. alpha358

    Argument for quantum indeterminism

    If any application of probability and statistics dosen't imply that particular proces dosen't have deterministic laws, then how quantum physicists come up with an idea that determinism is false ? P.S. I am second year bachelor student of applied physics and I will have quantum physics course...
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