What is Contradiction: Definition and 259 Discussions

In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect."In modern formal logic, the term is mainly used instead for a single proposition, often denoted by the falsum symbol



⊥


{\displaystyle \bot }
; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction.

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  1. pellman

    Fermionic oscillator contradiction

    This is a question with regard to a specific step in a problem. I don't think it is necessary to elaborate the whole problem. Homework Statement Resolve this apparent contradiction. I get two different answers for Na|n\rangle Homework Equations For a fermionic oscillator, we have...
  2. S

    Contradiction between Quantum Mechanics and Special Relativity？

    In quantum mechanics, the phase velocity is f/k=E/p because of E=hf and p=hk where k=1/wavelength. In special relativity, E=mc^2 and p=mV (V<c). So, E/p=cc/V >c. To photons in media, however, the phase velocity is f/k =c/n<c. What’s wrong ?
  3. T

    Relativistic Acceleration Contradiction

    Hello everyone! I apologize if my first post is of a problem that may seem like a really silly one. But it was something we were stuck with today in Modern Physics class. It is NOT a homework assignment! We have proved that relativistic force, F = m*(du/dt)*(gamma)3 where gamma is the Lorentz...
  4. ╔(σ_σ)╝

    What happens in an idealized circuit with a sudden change in impedance?

    I was recently looking at a circuit and I just realized that I didn't understand something. If we have the circuit ( the one attached below:) From what I understand the voltage in a capacitor cannot change instantaneously and the current in an inductor cannot also change instantaneously...
  5. A

    Contradiction on electric field ?

    Hello, I'm have just started on this subject, and I am confused with the following equation: since E(t) = kq(t) => \frac{dE}{dt} = k \frac{dq}{dt} = k*I => E = \int(kIdt) so if there is a constant current, wouldn't my electric field blow up?? Thanks!
  6. G

    Proof By Contradiction Exercises

    Hi guys, I am looking to find some exercises, preferably online to practice Mathematical Proof by Contradiction. I have just finished my A-levels in the UK doing Maths and Further Maths and very little is done in the way of mathematical proof. The is only a single chapter on proof by...
  7. R

    Black hole - contradiction to the Pauli exclusion principle?

    Hello. I was thinking. The collapse of a stellar nucleus into a black hole is an apparent contradiction to the Pauli exclusion principle, right? So which one of those theories fails at that point - quantum mechanics or the theory of relativity? I used to think that it's the theory of...
  8. A

    Hilbert space dimension contradiction

    Hi, I was wondering how the state vector for a particle in a 1-D box can be expanded as a linear combination of the discrete energy eigenkets as well as a linear combination of the continuous position eigenkets. It seems to me that this is a contradiction because one basis is countable whereas...
  9. R

    Proof by Contradiction and Contraposition

    Homework Statement For any integer n, let A(n) be the statement: "If n=4q+1 or n=4q+3 for some q \in Z, then n is odd." (a) Write down the contrapositive of A(n). (b) Is the contrapositive of A(n) true for all n \in N? Give brief reasons. (c) Use proof by contradiction to show that...
  10. E

    Unifying Gravity & GR: A Contradiction in Physics?

    Unification of Gravity versus General Relativity -- The Ubiquity of Contradiction Is it just me or is something smelling rotten about unifying gravity with the fundamental forces? Didn't science unanimously agree that Einstein's "Theory of Relativity" correctly explained gravity as not a force...
  11. A

    Exploring the Contradiction of Vacuum: Empty Spacetime?

    Okay, here’s the concept. Is it just “empty space” or something else? But since relativity; we know that space cannot, and does not exist without time, And it’s a continuum "spacetime" rather than space and time. So does it means that vacuum is just “empty spacetime” There arises a...
  12. S

    Proof by Contradiction: Explanations and Examples in JPG and Doc Formats

    1.the qustion is proof by contradiction is in the jpg file 2. the format of the solution is in the attachement doc.
  13. U

    The set of all sets contradiction

    Homework Statement Let A be the set of all sets. #1.) Show that P(A) is a subset of A. #2.) Find a contradiction. Homework Equations The Attempt at a Solution #1.) We know that P(A) is a set. Therefore it must be in A, since A is the set of ALL sets. #2.) I cannot...
  14. R

    Contradiction in Gauss's Law: Analytical vs Intuitive Evaluation

    I was thinking about gauss's law and ran into this contradiction. Consider this situation in electrostatics. You have an infinite line of charge, uniform charge density [text]\lambda[/tex]. In cgs units, E at a distance r from the line of charge along the +y axis (assuming a left handed...
  15. K

    Can AxB be equal to the empty set if either A or B is empty?

    Homework Statement I just need to decide how to show this by contradiction. If either A or B is the empty set then AxB=\oslash. Homework Equations The Attempt at a Solution Here is how I started: Assume either A or B is the empty set and AxB\neq\oslash
  16. C

    Contradiction in special relativity?

    ok so according to special relativity, light moves at a fixed speed C in every frame of reference. Special relativity also makes clear that any two things moving at a constant velocity along side each other, will perceive each other to be motionless. In other words, in any specific frame of...
  17. C

    Why Does Work Done on an Object Differ Between Inertial Frames?

    I've 2 questions: First, is there any particular reasons why accelerating an object from 1m/s to 2m/s requires less work than accelerating from 2m/s to 3m/s? Second, when I see another inertial frame moving 1m/s w.r.t. me, in which there is an object moving 1m/s in the same direction w.r.t...
  18. F

    Aparent contradiction - pressure and velocity

    So, I have in my mind an apparent contradiction that hopefully can be cleared up. From early lessons we learn that an objects velocity in an x direction has no effect on its velocity in the y direction. So, the y component of a particles velocity is not effected when we change its x...
  19. D

    Attempt at proof by contradiction need verification

    Homework Statement GCSE past paper question. prove algebraically that the sum of the squares of any two consecutive even integers is never a multiple of 8Homework Equations none The Attempt at a Solution n and x are integers 2x and 2x+2 represent two consecutive even integers. see attachment.
  20. H

    Do Black Holes Really Exist or Does General Relativity Contradict Itself?

    Stumped about GR "contradiction"--help please Apparently some crackpot blew some $$ on a full page ad in a science magazine, claiming to show that there black holes don't exist because GR contradicts itself about them. I haven't seen the ad, but there's also a blog about it and a thread about...
  21. C

    How Does Proof by Contradiction Validate a/b + b/a >= 2?

    [SOLVED] basic math proof by contradiction Homework Statement prove: If a and b are positive numbers, a/b +b/a>=2 Homework Equations The Attempt at a Solution by contradiction (a^2+b^2)/ab<2 and got lost
  22. A

    Solving a Basic Math Contradiction

    Could someone please sort out this contradiction which must come from some very basic error - but where and which error? If you raise -3 to the power of 1/2, this gives the square root of -3 which has no real value, but if you raise it to the power of 2/4, you are finding the fourth root of -3...
  23. A

    Can Static Friction Exist on a Moving Bicycle on a Flat Track?

    Homework Statement What is the smallest radius of an unbanked (flat) track around which a bicyclist can travel if her speed is 29 km/h and the coefficient of static friction between tires and track is 0.29? Homework Equations coefficient of static friction = (f of maximum static...
  24. K

    Electric field formula vs coulombs law, contradiction?

    1) between two charged plates, the electric field is given by E=U/d=F/Q->F=QE that means that the force on a particle between these two plates is independant on the position between them. But consider that you have two plates separated by a huge distance, then the force is constant wherever we...
  25. rohanprabhu

    But we assumed p and q are mutually prime, a contradiction.

    I read this on cut-the-knot.org: How is this a contradiction? If p^2 = 2q^2 just says that p^2 is even, it doesn't say that 'p' is even. It is a very obvious mistake. So.. is this a stupidity on their part or something that i may have missed [or a stupidity] on my part.. I generally...
  26. Gokul43201

    News Afghanistan - a state of contradiction?

    It's happening again...will it end the same way this time too? Nearly 2 years ago, Abdul Rahman was sentenced to death for converting from Islam to Christianity. While there was intense international pressure on President Karzai to overturn the verdict, he was in no legal position to do so (and...
  27. B

    Rolling Motion, a Contradiction

    For a wheel in pure roll, or smooth rolling motion, with constant angular velocity, \omega, the velocity of the point on the top of the wheel is 2v_{com}, and the velocity of the point at the bottom of the wheel is 0. (all relative to the ground) However, since centripetal acceleration is...
  28. E

    Apparent contradiction with orbital mechanics

    Consider a two body system for simplicity: M1 << M2. M1 is in a circular orbit about M2. The tangential speed of M1 is inversely proportional to its distance from the center of M2. However, in order to move to a lower orbit, or to de-orbit completely, M1 must lose tangential speed (in the...
  29. quasar987

    A contradiction in Spivak's Calculus on manifold?

    Homework Statement I don't have great expectation that this will get a reply but here goes, because this is bugging me. I will assume that you are familiar with the notation used by Spivak. In the last section of chapter 4, he shows how to integrate a k-form on R^m over a singular k-cube...
  30. daniel_i_l

    Proving or Disproving Continuity and Limits for Functions in R

    Homework Statement You have the function f:R->R and f(x) = f(x+k) where k is in R and k>0. Prove or disprove: 1) If f is continues at x0 then it's also continues at x0 + k 2)If the limit of f at infinity is 0 then f(x)=0 for all x in R. Homework Equations The Attempt at a...
  31. L

    Generalized PDEs with an apparent contradiction

    I have a question which has perplexed me for a time and thought maybe someone here would have some insight that might prove useful. My research involves a generalization of first order partial differential equations. The simplest case can be defined in the following manner: Let V be an arbitrary...
  32. P

    Matrices - An apparent contradiction?

    Homework Statement Consider T:V->V where the basis vectors in V are {v1, v2} So T(v1) = a(v1) + b(v2) T(v2) = c(v1) + d(v2) With T = the square matrix a c b d Now let v1=(1,1) v2=(1,-1) T(1,1)=1(1,1)+1(1,-1)=(2,0) T(1,-1)=2(1,1)+1(1,-1)=(3,1) So T= the squre matrix 1 2 1 1 But...
  33. K

    Contradiction about Electric Potential / Voltage in my Textbook

    Of course it's not a contradiction, it's really just my misunderstanding. But here's what I don't get: (N.B.: I'll be using the terms "electric potential" and "voltage" interchangeably in this post.) Consider a charge moving in the direction of an electric field. If it moves a distance of x...
  34. K

    Does Gauss's Law Allow for Non-Enclosed Point Charges on Gaussian Surfaces?

    Consider a gaussian surface of arbitrary size and a point charge located outside of the gaussian surface at an arbitrary distance. Gauss's law states that the flux through the gaussian surface is zero, since there is no charge enclosed by that surface. From this we can deduce that the...
  35. P

    Is Proof by Contradiction the Most Popular Technique in Mathematics?

    How widely used is this method? Is it the most popular proof technique? All it takes it to find a condradiction or counter example in order to prove something which is often much simpler than listing all the cases (not to mention if there are infinite of them to start with) or directly proving...
  36. W

    Paradox of the Expanding Universe: Debunking the Big Bang Theory

    My dad asked me the other day... if space orginated from a big bang as we think... does that not mean it is expanding outwards? How can it be expanding if it is infinite already. I couldn't answer him there and its a serious paradox in thinking. So where is he wrong and what's the go with that?
  37. A

    Photoelectric Effect contradiction

    Hiya, I'm about to teach the photoelectric effect in class. Everybody knows that observations contradict the classical prediction. Which is: Stopping voltage schould go up with light intensity. OK. But I have a problem: What EXACTLY is the classical prediction? I mean, is there a formula that...
  38. L

    A causal system? the biggest contradiction

    a causal system?? the biggest contradiction! Hey guys - can someone tell me why i get two contradicting asnwers... i am asked to determine whether the following system is causal or not: y[k+1] + 0.64y[k-1] = x[k] + 2x[k-1] method 1: put k = k-1 (delay the signal by one unit) therefore...
  39. P

    Biconditional to lead to a contradiction problem

    I have a problem I'm working on that I'm a bit stuck on. In this problem we are allowed to use Taut Con in our Fitch proof. The goal is to prove the following from no premises: ~∃x∀y ( P(x,y) ↔ ~P(y,y)) My initial thought is to begin a subproof with the problem itself, except without the...
  40. M

    Proving a+br is Irrational Using Proof by Contradiction

    Hello everyone! THe directions are the following: Carefully formulate the negations of each of the statements. Then prove each statement by contradiction. Here is the problem: If a and b are rational numbers, b!=0, and r is an irrational number, then a+br is irrational. I made it...
  41. M

    Trying to prove by Contradiction, but need to make sure negation is correct

    Hello everyone. Before I start this proof i have to make sure my negation is right of the statement and also my translation of it into universal statements before I take the negation. The directions says, prove the statements by method of contradition. The method of contradiction states...
  42. A

    A contradiction of Heisenberg uncertainty principle?

    A contradiction of Heisenberg uncertainty principle?? Suppose an atom is cooled to 0 K (Practically impossible). However theoretically, all its motion will cease ; and therefore it will be possible to determine the exact position of the atom and exact velocity (which is zero).Doesn't this...
  43. F

    I think quantum state collapse is in contradiction with the storage of QBits

    This is my analysis:1)quantum can have two states at one time:0 and 1.So n QBits have the volume 2^n. 2)when it's observed,the quantum state will collapse to a certain one. So the comtradiction is evidence:the information of the 2^n Qbits disappear when I only read n Qbits from it. Ok...if...
  44. T

    Contradiction between personal dream and the social resposibility.

    Dear my friends, Everything become so blurred to me, I don't know what I should do for life. I used to be very ambitious and want to be a good physicist, because the beauty of Nature has been fascinating me for a long time, since the first day I read Einstein Relativiy. But, as I grow...
  45. S

    What is the contradiction in integrating around a contour with a branch cut?

    In complex analysis we say that for fn's like lnz we apply a branch cut along positive x-axis to make sure it's single valued. i.e restrict theta s.t 0<=theta<2Pi but we never allow theta to equal 2Pi as this would make lnz take on 2nd value. Let us integrate around a contour which goes from...
  46. A

    Some contradiction I can't explain about e^(ix)

    Let k be a real number (not necessarily an integer). e^{i\cdot2\pi\cdot k}=\cos(2\pi k) + i\sin(2\pi k)= some complex number on the unit circe. BUT e^{i\cdot2\pi\cdot k}=(e^{i2\pi})^k=1^k=1 so if take \tilde{k}=2\pi k then 1=e^{i\tilde{k}}=every other number on the unit circle. How can...
  47. D

    L's Contradiction Method: Proving EM Laws Independently of Frame of Reference

    Whats the simplest proof that the Electromagnetic laws are independent of frame of reference? .What I know is contradiction method which einstein also used to conclude the postulate of SR. BJ
  48. W

    Is this in contradiction with the theorem of conservation of momentum?

    The theorem of conservation of momentum states that the quantity of momentum is always the same. When two objects collide, during the interval of time they touch each other their velocities are the same but are in the same time changing, if they are both changing but remaining equivalent, why is...
  49. N

    Integration by Parts Contradiction

    Ok guys, this is my first post. Please go easy...:redface: This question is from Morris Kline's Calculus: An Intuitive and Physical Approach and unfortunately there aren't solutions for all questions (really annoying). I'm not even sure if this counts as a contradiction but anyway: Let...
  50. N

    Lines, points and contradiction

    this question may sound kind of dumb, so if it is, i apologize, but let say you have a line with a point taken out of it. (<------- -------->) since a point does not have a defined length, how could you prove that the line is now two rays, and not still a line, because it seems a bit...
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