What's the difference between axiom and corollary?

Axiom


Definition:

  • (a.) A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, "The whole is greater than a part;" "A thing can not, at the same time, be and not be."
  • (a.) An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.

Example Sentences:

  • (1) Pair comparisons enable a (partial) test of the axioms of additive conjoint measurement.
  • (2) The clinician has to deal with scientific and ethical issues and keep in mind the axiom 'Primum no nocere--Above all, do no harm.'
  • (3) Proponents of two axioms of biological evolutionary theory have attempted to find justification by reference to nonequilibrium thermodynamics.
  • (4) Fundamental animal studies by pioneers, such as Chang, Thibault and Edwards, taught us nature's axioms for gametogenesis, fertilization, development and differentiation.
  • (5) Emerson approvingly quoted Swedenborg's, "The visible world and the relation of its parts, is the dial plate of the invisible", and asserted, "The axioms of physics translate the laws of ethics."
  • (6) One of the essential axioms of modern politics has always been that voters dislike divided parties and will punish them at the polls.
  • (7) Stereology is the application of mathematical axioms and allows one to quantitate three-dimensional structures from the measurement of two-dimensional cross sections thereof.
  • (8) Synthesis of information in the brain is determined by the same principles, but extremums of the thermo-dynamic potential (their analogues in logic) are based on an arbitrary system of axioms.
  • (9) The axioms of treatment are to remove all pressure, debride necrotic tissue, keep the ulcer clean, and prevent further injury.
  • (10) USCI, DLP, or Axiom cannulas can be inserted femorally.
  • (11) Flash fire victims are exceptions to the axiom that elevation of blood carboxyhemoglobin is a sine qua non for concluding that a decedent recovered from the scene of a conflagration was alive in the fire.
  • (12) Examples are the systematic studies by Denis Burkitt, who through perseverance unraveled the lymphoma that now bears his name, and the thought-provoking description of the immunoproliferative small intestinal disease carried out by the Cape Town group, with both illustrating the axiom that "the study of man is man."
  • (13) It is thus denied axiomatic status, and the effects of natural selection are subsumed as an additional level of constraint in an evolutionary theory derived from the Axiom of Historically Determined Inherent Directionality.
  • (14) The first, the Axiom of Improbability, is shown to be nonhistorical and thus, for a theory of change through time, acausal.
  • (15) Nursing research, as every other research studying human beings, must be guided, attuned and illuminated by ethical principles and axioms.
  • (16) In this review, a few well-established axioms have been challenged while others were viewed from a new perspective.
  • (17) An axiom of Thomas Hobbes states that "people are never more helpless than when the force meant to protect their rights turns against them."
  • (18) The basis for the development for a dynamic compression implant (DCI) is the axiome of the mechanically induced bone reaction.
  • (19) This article reexamines the Sidman stimulus equivalence analogy in the context of a broader consideration of the mathematical axiom than was included in the original presentation of the analogy and some of the data that have accumulated in the interim.
  • (20) This is in contradistinction to earlier work on decision making for patients with laryngeal cancer, and most of the work in medical decision making in general, in which underlying axioms have almost never been tested.

Corollary


Definition:

  • (n.) That which is given beyond what is actually due, as a garland of flowers in addition to wages; surplus; something added or superfluous.
  • (n.) Something which follows from the demonstration of a proposition; an additional inference or deduction from a demonstrated proposition; a consequence.

Example Sentences:

  • (1) This response was compound and was not due to the activity of the identified corollary discharge interneurons, CDI-2 and CDI-3, that are fired by the SGs.
  • (2) An interesting corollary of the present studies is the disappearance of metastability at chain lengths of about 20-22 carbon atoms.
  • (3) Market rules will be important – a cap on individual donations at a low level is a necessary corollary of structural change.
  • (4) A corollary to this suggestion is the fact that, in the giraffe, as in most other Artiodactyls, the vertebral blood does not participate in the supply of cephalic structures because it is confined to the cervical region by the pressure barrier in the carotid-vertebral anastomosis.
  • (5) A corollary is that daily cholate secretion is likely to be normal in these conditions and that therefore the propensity of bile to form cholesterol gall stones is not likely to be directly related to bile salt pool size.
  • (6) The inhibition is mediated by a bilaterally symmetrical pair of reidentifiable feeding neurons that are members of the "corollary discharge" population in the buccal ganglion.
  • (7) The postulate of the non-neurotic nature of alexithymia, along with its many psychopathological and technical corollaries, is completely contradicted by the present findings.
  • (8) A corollary to this view is that protective additives such as glycerol protect cells by acting colligatively to reduce the electrolyte concentration at any subzero temperature.
  • (9) A corollary purpose was to determine the need for inactive technologists, the hiring practices employed, the existence of institutionally sponsored retraining programs, and the institutional views toward providing such programs.
  • (10) Thus, we did not identify a reliable corollary test to the histologic diagnosis of mucosal dysplasia in ulcerative colitis.
  • (11) As a corollary, hyperexposure to corticosteroids induces widespread changes of neuronal cell biology which are of clinical significance for depression research (e.g.
  • (12) It is suggested that the failure of the neonate to sustain adoptive immune responses is explicable on the basis of an active suppression and, as a corollary, unresponsiveness resulting either from macrophage immaturity or the transfer of maternal antibody is discountered as a likely explanation for the immunological behavior of the newborn rat towards the antigens examined.
  • (13) The corollaries to these changes are more restrictive admission criteria, increased severity of patient illness, and changes in patient care.
  • (14) I1 and I2 cells showed consistent corollary discharge bursts with little or no additional activity beyond the duration of the burst.
  • (15) Overall equations of the model and graphical corollaries are presented.
  • (16) These reasons include the following: the simplicity of the electrical signals which are the normal input and output; the availability of a variety of stereotyped behaviors to characterize the system as a whole; the case with which individual receptors or primary afferents can be activated; the demonstrated presence of corollary discharge and reafference mechanisms for motor control over sensory input; the presence of highly specialized CNS structures which have evolved to meet the unusual demands of the electrosensory system.
  • (17) To explore these theories in males, we tested a corollary of these hypotheses: are male rats of the same weight all at the same level of sexual maturation irrespective of prior growth rate?
  • (18) The diversity of beta gene products may be an important corollary to the functional diversity of G proteins.
  • (19) The corollary is that induction of the mono-oxygenases by environmental agents, both recognised and unidentified, is a primary event in pancreatic disease.
  • (20) As a corollary, these tumors had worse prognosis than the others.

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