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. J

    Furnishing a contradiction in my proof involving Lagrange's Theorem

    Homework Statement The Attempt at a Solution I'm trying to show that Case 1 implies that \tau \in H, and since \tau was an arbitrarily chosen 3-cycle, then H must contain all 3-cycles, thus contradicting that H has 6 elements.
  2. R

    Schrödinger's cat contradiction

    Hi, i didn't understand why we can't explain the situation simply as the cat is either dead or alive immediately after the poison was released or not, and not to assume that only when the observer opened the box the state of the cat was determined, what assumption does it contradict?
  3. B

    Prove by Reductio Ad Absurdum (Contradiction)

    Q: S is a subset of the natural numbers (the counting numbers) with the following property n \in S \Rightarrow {1,...,n-1} \subset S. Prove, by Reductio Ad Absurdum, that S is equal to the set of all natural numbers.First of all, I want to make sure I got all the meanings of the symbols right...
  4. S

    Discrete Math: Proof by contradiction

    Homework Statement Using contradiction, prove that for every four positive real numbers c, d, e and f, at least one of c, d, e, f is greater than or equal to the average of c, d, e, f. Homework Equations I don't believe that there are any relevant equations for this problem. I do know that...
  5. D

    Proving the proof by contradiction method

    Proving the "proof by contradiction" method This can get a little bit fundamental or "axiomatic", if you will. Let's say we can describe sets by prescribing a fixed property P on objects of a certain type, and claiming that a set is a collection of objects satisfying P; i.e. A = \{x : P(x)\}...
  6. G

    Proof by contradiction - For any integer n, n^2 - 2 is not divisible by 4.

    Homework Statement Just as the title said, I need to prove: For any integer n, n2 - 2 is not divisible by 4 by the method of proof by contradiction. Homework Equations (Relevant by division into cases) Even numbers = 2k for some integer k Odd numbers = 2m+1 for some integer m...
  7. E

    A contradiction? - Calculus III Question

    yz = ln(x+z) So I'm trying to find the tangent plane to the surface at a particular point (x0,y0,z0). Here's the general formula: Fx(x0,y0,z0)(x-x0) + Fy(x0,y0,z0)(y-y0) + Fz(x0,y0,z0)(z-z0) = 0, where Fx, Fy, and Fz are the partial derivatives of the below F(x,y,z): 1. F(x,y,z) = ln(x+z)...
  8. C

    Phase diagram contradiction: why does vapor exist?

    When you learn about phase diagrams of pure substances, you learn that the liquid and gas phases are in equilibrium only along the line separating the pure liquid and pure gas regions. But if you have a sample of liquid in a closed container with some empty space in it, that empty space...
  9. khurram usman

    Wave function , robability density , probability contradiction?

    i just started studying quantum mechanics in my college...i asked a number of teachers and seniors that why psi(ψ) is maximum at r=0, also (ψ)^2 is maximum at r=0 but probability is maximum at r= a(knot) for 1s orbital this seems a contradiction to me that on one side we are ssaying ψ is...
  10. H

    Contradiction regarding capillarity

    I am currently studying surface tension. I came across a topic named "capillarity" where it is said that mercury falls down in capillary tube. But it rises in a barometer . Why is it so?
  11. H

    Equilibrium constant contradiction

    I recently studied that equilibrium constant is independent of concentration. But if you multiply both sides of equation by any number, equilibrium constant changes. Isn't this contradictory?
  12. B

    Proof by contradiction - polynomials and infinite primes

    Homework Statement Two Questions: 1. Prove, by contradiction, that if a and b are integers and b is odd,, then -1 is not a root of f(x)= ax^2+bx+a. 2. Prove, by contradiction, that there are infinitely many primes as follows. Assume that there only finite primes. Let P be the largest...
  13. E

    Why Does a Charged Particle Inside a Neutral Shell Experience No Force?

    So "A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated at the center of the shell" and also, "If a charged particle is located inside a shell of uniform charge, there is no electrostatic force on the particle...
  14. M

    Contradiction in the laws of thermodynamics?

    The second law of thermodynamics states that the entropy in a system, such as our universe, always increases. The third law, however, says that entropy reaches zero as a system approaches absolute zero temperature. Our universe has been cooling off since its origin (because of its...
  15. F

    Contradiction of Galios theory

    Hello. Galois theory tell us $x^5-6x+3$ is not solvable by radical but every equation lower than fifth can solve by radical. If $G$ is solvable and $H$ is solvable too $G*H$ are solvable. For $x^5-6x+3$ we can use Newton’s method and find one root of this equation. We obtain $x=1.4$ and...
  16. M

    Velocity Calculation Contradiction

    Homework Statement I have to design an experiment where I am supposed to project an object horizontally from some point above ground level, measure the distances, calculate the average horizontal distance dx, then use that to calculate the initial and final velocities yatta yatta. Anyway I made...
  17. D

    Is there a better way to present proofs by contradiction?

    Sometimes I find that while a proof can be carried out "by contradiction", this is a pretty sloppy way of proving the desired statement. I wonder if the "←" direction of the following proof is sound presentation of proof by contradiction. Statement. An integer is even if and only if its square...
  18. O

    Yo-Yo on a table contradiction

    Homework Statement A Yo-Yo of mass M has an axle of radius b and a spool of radius R. Its moment of inertia can be taken to be MR2/2. The Yo-Yo is placed upright on a table and the string is pulled with a horizontal force F as shown. The coefficient of friction between the Yo-Yo and the...
  19. B

    MCAT contradiction? - Gauge Pressure

    Homework Statement A large cylinder is filled with an equal volume of two immiscible fluids. A balloon is submerged in the first fluid; the gauge pressure in the balloon at the deepest point in the first fluid is found to be 3 atm. Next, the balloon is lowered all the way to the bottom of the...
  20. E

    Contradiction between ΔV in circuits' wires and Kirchoff's voltage law ?

    A simple electric circuit (such as one composed of a battery with Emf V and resistor with resistance R) is in an electrodynamic state since the battery's potential difference creates an electric field in the circuit's wires, which in turn moves charges around. So potential difference in wires is...
  21. S

    Is the universe 13.7 Billion years old? There seems to be a contradiction

    The universe is said to be 13.7 Billion years (http://en.wikipedia.org/wiki/Age_of_the_universe" . So, for the present galaxy UDFj-39546284 and the present Earth to have traveled as far as they are now, and even if we assume that the big bang occurred right between Earth and UDFj-39546284, it...
  22. Z

    Question regarding a contradiction in conservation laws

    We all know that the universe is expanding and for that matter accelerating. Science is now starting to realize that the universe will expand forever and the big crunch will never occur due to recent data of a supernova. My point to all this is, quantum theory states that a vacuum must always...
  23. T

    Using negation of an for all statment in a proof by contradiction.

    So if I want to prove. A=>B for all x. Does the following work? Suppose for contradiction, B is not true for all x, that is, there exists at least one x such that B is not true. In particular, assume that B is true for x=c and B isn't true for all other x. If I arrive at a...
  24. srfriggen

    Proof by Contradiction

    Homework Statement "Prove that when an irrational number is divided by a nonzero rational number, the resulting number is irrational" The Attempt at a Solution By contradiction: Prove that when an irrational number is divided by a nonzero rational number, the resulting number is...
  25. A

    Proofs using contrapositive or contradiction

    Please Help! proofs using contrapositive or contradiction Homework Statement Prove using contrapositive or contradiction: For all r,s∈R,if r and s are positive,then √r+ √s≠ √(r+s)
  26. T

    Limit definition gives a contradiction

    Limit definition gives a contradiction! say we are given sequences a(n), b(n) such that, a(n)->a, b(n)->b that means for epsilon>0, a-epsilon<a(n)<a+epsilon when n>N1 b-epsilon<b(n)<b+epsilon when n>N2 set N=max(N1,N2) when n>N...
  27. L

    Contradiction in relative simultaneity

    let's say a train is traveling at relativistic speed along a straight line to right, and a man is standing in the middle of the train. Both end of the train was installed a gun which aims at the man. The right-ward gun aims at the man's leg and the left-ward gun aims at the man's head. In...
  28. H

    Understanding the Contradiction: Point Charge near Grounded Conducting Sphere

    suppose we have a point charge q near the grounded conducting sphere. we know that the work down by electric field of the sphere for taking the point charge from surface of the sphere to infinite is infinit. but the potential energy in the grounded surface and infinite is zero. what is the reson...
  29. H

    Periodic and Nonconstant Integral Curve: A Contradiction

    M is a smooth manifolds, and X is a vector field on M, y is a maximal integral curve of X. Now suppose y is periodic and nonconstant, show that there exists a unique positive number T(called the period of y) such that y(t)=y(t') if and only if t-t'=kT for some integer k.(For this problem, What...
  30. H

    Understanding the Contradiction in Gauss Law for Planar Capacitors

    we know that the electric field between the planes of planar capacitor is σ/ε (according to gauss law) however we have two conducting plate that each plate produe this electric field that are in the same direction therefore we must have E=2σ/ε what is the reason for this contradiction.
  31. B

    Is Total Energy Always Double the Kinetic Energy in Quantum Mechanics?

    Homework Statement Ok so (1) E = hf and (2) lambda = h/p Homework Equations The Attempt at a Solution For a particle mass m, speed v, momentum p Surely if p^2 / 2m = Ek (kinetic energy) then we can write from (2) Ek = h^2/ 2m lambda^2 But from (1) we can write E =...
  32. G

    Contradiction in Taylor-Wheeler's example of spacetime invariance

    In section 1.2 of Taylor and Wheeler's Spacetime Physics, a rocket moves past a laboratory (on Earth). Attached to the rocket is a pin. From that pin a spark is emitted at two locations in the lab, separated by 2 meters. The observer in the rocket measures the elapsed time between the sparks, as...
  33. G

    Contradiction in Relativistic Simultaneity in Taylor-Wheeler Spacetime Physics?

    In figure 3-1 (page 63) of Taylor and Wheeler's Spacetime Physics, the observer on the train determines that the lightning strikes are not simultaneous because the flashes do not reach her simultaneously. I see two problems with this. 1. The narrative in figure 3-1 contradicts the text in...
  34. M

    Proving Infinite Solutions for sin(x)=b in R using Contradiction Method

    Homework Statement I want to practice proofs by contradiction I am trying to prove that sin(x)=b has infinite distinct solutions in R for every b in [-1,1] Homework Equations The Attempt at a Solution assume it has finite amount of solutions called set Z let k be in real number...
  35. J

    Do the answers and diagram in these exam questions contradict each other?

    Do these two answers contradict each other: Q1) Four students are discussing a circuit. The circuit is in series and contains a lamp, an ammeter and a 10V battery. Andy: the current in the lamp consists of negative charges moving from the negative batter terminal towards the positive...
  36. Z

    Does Temperature Affect the Accuracy of a Steel Metre Scale?

    Homework Statement A metre scale made of steel is calibrated at 20 degrees Celsius to give correct reading. Find the distance between 50cm mark and 51cm mark if the scale is used at 10 degrees Celsius. Coefficient of linear expansion of steel is 1.1 x 10-5 C-1 Homework Equations...
  37. J

    Different frames of reference and particle production? a contradiction maybe?

    Hi, Second time I'm writing this question, the first one seems to have been lost in cyberspace but sorry if it somehow comes back and appears twice. Anyway, you know how kinetic energy depends on velocity, so that the energy of a particle collision will be different for two frames of...
  38. M

    Permutations and transpositions contradiction

    Homework Statement (1 2 3 4 5) (2 1 3 5 4) Write the bottom number as a product of transpositions Homework Equations The Attempt at a Solution 41352 41325 41235 42135 42315 24315 24351 21354 (2 4) (2 5) (2 3) (2 1)...
  39. A

    GR/Hawking Radiation Contradiction

    A thought experiment: Say that you and I decide we are going to go into orbit around a black hole. I am brave and you are weak, so I decide I'm going to take the plunge and you just stay in orbit. As I fall toward the black hole, the strength of the gravitational field increases, and time for...
  40. J

    Is P -> ~(Q ^ ~P) a Tautology or Contradiction?

    Homework Statement Wrie out the truth table for the statement form P -> ~(Q ^ ~P). Is it a tautology or a contradiction? Homework Equations The Attempt at a Solution First off is it true to say that P -> ~(Q ^ ~P) and P -> (~Q v P) are equal. P | Q | ~P | ~Q | P -> (~Q v P)...
  41. B

    Limits of Inequality: Proving by Contradiction

    Homework Statement If f(x) <= g(x) then lim[x->a] f(x) <= lim[x->a] g(x) provided that both of these limits exist. 2. The attempt at a solution I've been able to prove it by contradiction. So I assumed that l = lim[x->a] f(x) > lim[x->a] g(x) = m. Therefore, l - m > 0 and I could...
  42. K

    Meaning of the square root and its contradiction

    Is square root a function in this way? f:\mathbb C\rightarrow\mathbb R^+ However contradiction can be drawn:\sqrt{x^2}=|x|\text{ and } i^2=-1 \sqrt{-1}=\sqrt{i^2}=|i|=1 \sqrt{-1}=1 ??What is the problem in the...
  43. B

    Proving 13 + 2√6 is an Irrational Number with Proof by Contradiction

    Homework Statement Prove or disprove the statement: 13 + 2√6 is an irrational number Given that √6 is irrational Homework Equations Rational number = p/q where p and q are integers The Attempt at a Solution Assume that 13 + 2√6 is a rational number Rational number =...
  44. N

    Is There a Contradiction in Calculating Magnetic Fields in Infinite Planes?

    Okay, the title is promising something big. I'm sorry, it's probably not big, but it does seem important, although for some it will be unsignificant, I suppose it depends on your interests in physics: So if you have an infinite plane with current density J (current per meter width) (say...
  45. N

    Exploring the Contradiction of Non-Interacting Fermions in Superconductors

    Hi In superconductors, the fermions are interacting. In order to diagonalize our Hamiltonian (which contains the product of four fermion operators), we use Wick's theorem to approximate the product of four fermion operators by the product of two fermion operators. Now, a Hamiltonian...
  46. B

    Apparent Contradiction: Every Map from a Contractible Space to any X is trivi

    Hi, everyone: I am confused about the result that every map from a contractible space X into any topological space Y is contractible. I think the caveat here is that the homotopy between any f:X-->Y and c:X-->Y with c(X)={pt.} is that the homotopy is free, i.e., the...
  47. M

    Solving the Rope Falling off a Table Problem: A Contradiction?

    I am studying differential equations from this book by Edwards and Penney, and I seem to have stumbled on this rather bizarre contradiction which I can't seem to get myself out of. The problem, which is a variation on the classic rope falling off a table, goes as follows: "Suppose that a...
  48. e2m2a

    A Contradiction in Moment of Inertia Formulae by reductio ad absurdum?

    In physics the moment of inertia of a thin rod which rotates around an axis through its center of mass is : I cen = 1/12 m L sq (1) Where: m is the mass of the rod, L is the length of the rod. The moment of inertia of a thin rod which...
  49. N

    Contradiction on kvl kcl laws question

    http://i49.tinypic.com/1yu634.jpg this is a part of the solution " the is a voltage drop on capacitor C1 which makes current shock on C1 and a current shock on R2 and R3 and it makes a KVL contradiction on the right branch and the outer branch. and that's why the continuety laws...
  50. M

    Contradiction in the equations of motion ?

    Contradiction in the equations of motion...??! I' ve found a strange contradiction between the fist and second equations of motion. First we start with the second equation: s = ut + 1/2at2 We factor 't' out, whoch gives us: s = t(u + 1/2at) We divide both sides by 't', and on...
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