However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

' A modern respondent might say they are both mammals ( an abstract, or a priori answer, which depends only on the meanings of the words ' dog ' and ' rabbit ' ), whereas someone a century ago might have said that humans catch rabbits with dogs ( a concrete, or a posteriori answer, which depended on what happened to be the case at that time ).

However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori.

Under European patent practice and case law, lack of unity ( of invention ) can appear either " a priori ", before the prior art was examined, or " a posteriori ", after the prior art was examined.

In an inductive analysis of the historical information over Sirras, through an a posteriori argument, Elias Kapetanopoulos, a Greek historian, also says that Sirras must have been a Lyncestian, not an Illyrian, as Eurydice as well .. Ian Worthington makes a convincing case for her Lyncestian ancestry, stating that while some dispute her ethnicity thinking her father Sirrhas may have been an Illyrian, " However, this is unlikely in light of a comment that Attalus made at the wedding of Phillip in 337, intended as a sluron Alexander's legitimacy, for his mother was from Epirus .".

A < em > global </ em > criterion is that the sum of errors on all the intervals should be less than t. This type of error analysis is usually called " a posteriori " since we compute the error after having computed the approximation.

We say that this method is a posteriori because we typically miss the actual instant of collision, and only catch the collision after it has actually happened.

The problem was no longer how we know that our representations correspond with things in themselves but how we know that a priori concepts apply to a posteriori intuitions.

But we do prove it a posteriori, i. e., from the things that have been created, following an argument from the effects to the cause: namely, from things which are moved and cannot be the adequate source of their motion, to a first unmoved mover ; from the production of the things in this world by causes subordinated to one another, to a first uncaused cause ; from corruptible things which equally might be or not be, to an absolutely necessary being ; from things which more or less are, live, and understand, according to degrees of being, living and understanding, to that which is maximally understanding, maximally living and maximally a being ; finally, from the order of all things, to a separated intellect which has ordered and organized things, and directs them to their end .</ li >

Thus, we can understand a claim like " goodness is identical with pleasure " as an a posteriori identity claim similar to " Water is H < sub > 2 </ sub > O ".

We can then conclude that we have learned that " right " refers to " maximizing utility " through a posteriori means.

Another problem with the a posteriori moral search is that we lack an epistemic account of how we access moral facts.

Physicalism is then further divided depending on whether it can be known a priori or a posteriori that: If physicalism is true, S is the statement that describes the entire physical nature of the world collectively, and S * is the statement that describes the entire nature of the world, then S entails S *.

In other words, physical simulators usually function one of two ways, where the collision is detected a posteriori ( after the collision occurs ) or a priori ( before the collision occurs ).

* A posteriori knowledge is knowledge that is known by experience ( that is, it is empirical, or arrived at afterward ).

Synthetic knowledge, such as assertions about the real world, must be verified a posteriori by observation.

One is that a posteriori truth can be reached a priori by contingent a posteriori truths.

Maximum a posteriori ( MAP ) soft-decisions for each bit can be obtained by use of the BCJR algorithm.

By comparison, prediction in frequentist statistics often involves finding an optimum point estimate of the parameter ( s ) — e. g. by maximum likelihood or maximum a posteriori estimation ( MAP ) — and then plugging this estimate into the formula for the distribution of a data point.

Blaise Pascal's Écrits sur la grâce, based on what Michel Serres has called his " anamorphotic method ," attempted to conciliate the contradictory positions of Molinists and Calvinists by stating that both were partially right: Molinists, who claimed God's choice concerning a person's sin and salvation was a posteriori and contingent, while Calvinists claimed that it was a priori and necessary.

Kant's work purported to bridge the two dominant philosophical schools in the 18th century: 1 ) rationalism, which held that knowledge could be attained by reason alone a priori ( prior to experience ), and 2 ) empiricism, which held that knowledge could be arrived at only through the senses a posteriori ( after experience ).

The only two kinds of statements accepted by the Vienna Circle are synthetic statements a posteriori ( i. e. scientific statements ) and analytic statements a priori ( i. e. logical and mathematical statements ).

A popular choice for θ is to provide maximum a posteriori ( MAP ) estimates of it by maximizing the marginal likelihood of the process ; the marginalization being done over the observed process values y.

Schmitt opposed what he called " commissarial dictatorship ", or the declaration of a state of emergency in order to save the legal order ( a temporary suspension of law, defined itself by moral or legal right ): the state of emergency is limited ( even if a posteriori, by law ) to " sovereign dictatorship ", in which law was suspended, as in the classical state of exception, not to " save the Constitution ", but rather to create another Constitution.

Modern Romanian historiography has expressed vexation at the appropriation, undertaken by Albanian historiography ( and by the unscientific Western scholarly works relying on faulty and superficial theories ), of not only the Romanian feminist activist and writer Elena Ghica, but also of the whole Ghica family, at the proliferation of dubious spellings of the family names, false information concerning the birthplaces and other historical facts, and at the family's a posteriori labeling as the " Albanians of Romania ".

The most likely value of a desired parameter ( the mode ) could then simply be selected by choosing the sample value that occurs most commonly ; this is essentially equivalent to maximum a posteriori estimation of a parameter.

Hence he endeavoured to attain to the ultimate grounds of things by induction ; that is to say, by a posteriori conclusions from a number of facts to a universal.

Similarly, many moral naturalists argue that " rightness " can be discovered as an a posteriori truth, by investigating the different claims, like that of pleasure being the good, or of duty being the good.

This is done by invoking rightness and wrongness to explain certain empirical phenomena, and then discovering a posteriori whether maximizing utility occupies the relevant explanatory role.

Additionally, the subordinate Soviet generals ( especially South-Western Front generals ) were just as willing to continue their own winter successes, and much like the German generals, under-appreciated the strength of their enemies, as pointed out a posteriori by the commander of the 38th Army, Kirill Moskalenko.

Also, it seemed that if courts could quash legislation after it had been enacted and taken into account by citizens, it would introduce legal uncertainties: how could a citizen plan his or her actions according to what is legal or not if laws could a posteriori be found not to hold?

In brain damaged patients, this can only be accomplished a posteriori by analyzing the behavior patterns of all the individuals in the group.

The original study was conducted by Gottman and Buehlman ’ s in 1992, in which they interviewed couples with children, and an a posteriori modeling yielded a discriminant function which discriminate who divorces with 94 % accuracy.

Indeed, an a priori algorithm must deal with the time variable, which is absent from the a posteriori problem.

The following offices from the Medieval court are generally considered a posteriori Great Offices, even though the expression, as such, did not exist at the time:

The pure a priori intuition of space and time is the basis of empirical a posteriori intuition.

The subjective a priori pure forms of sensation, namely space and time, are the basis of mathematics and of all of the objective a posteriori phenomena to which mathematics refers.

On the other hand, a posteriori algorithms cause problems in the " fixing " step, where intersections ( which aren't physically correct ) need to be corrected.

An a posteriori lack of unity usually results from a lack of novelty or inventive step of the subject-matter of one independent claim.

Though when viewed externally thus, it followed that Marx could then make claims to the effect of what state or condition the dialectic objectively existed in history, a posteriori of where any individuals opinion was while comporting oneself to the totalized whole of society.

Numerous methods have been proposed to reduce the number of MPTs, including removing characters or taxa with large amounts of missing data before analysis, removing or downweighting highly homoplastic characters ( successive weighting ) or removing wildcard taxa ( the phylogenetic trunk method ) a posteriori and then reanalyzing the data.

The method of maximum a posteriori estimation then estimates as the mode of the posterior distribution of this random variable: