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===Most generally===
==Most generally==


'''A priori''' roughly means something like '''"(from) that which goes before"'''.  
'''A priori''' roughly means something like '''"(from) that which goes before"'''.  
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===A bit more practically===
==A bit more practically==
<!--


: '''In more pragmatic settings'''


A priori tends to translate as 'pre-existing'.
===Statistics===


In probability and statistics, particularly (statistical) [[inference]], a priori is the prior knowledge of a population.


A common statement is that "there is no a priori knowledge of X", meaning there is nothing to go on yet,
Basically, it is anything we consider ''already known'', that we can use to improve our model,
and you need some investigation in the real world.
that is more than just estimations or limited recent measurements. {{verify}}




But this is also where some people weasel in extra meanings.  
A priori probability http://en.wikipedia.org/wiki/A_priori_probability
Some of them quite useful,
some of them less so.


Posterior probability
http://en.wikipedia.org/wiki/Posterior_probability






In a setting like everyday scientific discussion,  
Also in statistics, the [https://en.wikipedia.org/wiki/Prior_probability prior probability]
: a priori knowledge tends to mean "what is given without/before further inquiry"
typically refers to the probability distribution before some evidence is taken into account.
: a posteriori tends to mean "what we can conclude from this experiment"


===Modelling===


This is not as clear-cut as it looks.  
In machine learning and pattern recognition, and the models and math that backs it,
a priori refers to factual/good/positive examples that make for supervised learning.


For example, note that "what we know already" can easily blur the line between logic and evidence.
(and a posteriori often short for 'a posteriori estimation' based on it)




Science is all a posteriori, with science being very much about the best explanations of given evidence.
Without such a priori examples, the patterns would depend on data behaviour, clustering and such. {{verify}}


===Knowledge (philosophically)===


You could say the only things in science that are a priori are called mathematics.
Note that while a priori in the general sense can be translated as 'pre-existing',
: ...but math sorta cheats anyway, by only caring about internal consistency, not the real world.
once you start saying 'a priori '' knowledge' '' you trip yourself into [[epistemology]] (a.k.a. 'what can we know'), and a bit of [[metaphysics]] ('what is there?'), so philosophy's answers try to be a little wider - ''could be known'' answers rather than ''a person  currently knows'' answers.




Rverything ''interesting'' and everyday we are trying to do with science is likely to be based on posteriori.
'''A priori knowledge''': are things that ''can'' be knowable independently of experience/evidence {{comment|(pedantry: ...aside from the experience of the language to communicate it)}}.
: say, anything that follows from logic ''alone''.
::: e.g. regardless of observation, we can say "all bachelors are unmarried", whereas for other things we need observation.




That said, the ''process'' of studying something with a scientific methodology often takes
"well this is relevant" (a priori) and "what is under study" (about to be a posteriori)


'''A posteriori knowledge''' are things that can only be knowable, or verifiable, from empirical evidence.
: that which is (or must necessarily be) deduced from epirical evidence, from experience, observation, or personal decision.




Since you can argue a priori barely exists, it's not a useful term/distinction at all,
The distinction is related to objective versus subjective observation.{{verify}}
and it has been co-opted into softer distinctions.


For example, in everyday science it's easy to say "you know that theory that's looked solid for the last hundred years? Let's treat that as fact, i.e. a priori knowledge, for this particular experiment".


Or even to roughly split into "stuff I've finished checking" and "hypotheses I want to look at."
<!--
A priori knowledge often means you can reason it from principles or definitions.  




That sentence makes it really easy to be weasely about it, through,
because a lot of principles and definitions didn't come from nowhere.






: '''A priori used to mean "previous evidence"'''
More practically:
: You might still want to verify it using emperical evidence
: a priori tends to mean we are taking general princtiples/definitions/agreements {{comment|(in part just because a lot of knowledge exists in the form in generalisations)}} and doing something useful with it, involving more specific consequences/effects








: '''A priori as in "settled in the past"'''
In many cases, a posteriori is almost synonymous with "empirical",
because it often goes from particular observations
to more generalized descriptions or theories.


Note that 'coming before or after' can also involve timing, or cause.
"Bachelors tend to be happy" or "George V reigned from 1910 to 1936" or "It is now raining outside" is something you cannot arrive at from reason, because it came from observation and/or requires emperical verification.


There is a similar co-opting of the terms going on here.
Most of what we consider everyday facts, a priori(-ish), are really neither of these things,
but it's still useful to treat them that way.


-->


Before people considered the idea, "Smoking causes cancer" was an proposition,
===Law===
a posteriori in that it was based on observations that cancer seemed to happen more in smokers.


Now that evidence has shown this link to be pretty damn convincing,
In ''law'', a priori refers to being based on hypothesis or deduction, rather than experimentation.
the ''next'' discussion could choose to consider it a priori knowledge,
in the meaning of "stuff that came before, that we are reasoning from"




It can still refer to subjective, semantic details:
testimonials are automatically subject to a priori plausability - personal back knowledge. {{verify}}


So it depends a bit (too much, arguably) on the question being asked, and on when it is asked.
===Linguistics===
<!--
In linguistics, an "a priori [[constructed language]]" is one created from scratch.


If a statement is based on evidence, it will be a posteriori even after everyone considers it presumable or obvious.  
A posteriori constructed languages are those that mix and match from existing ones.
Any useful answer to "does smoking cause cancer?" will be based on evidence,


...while in a hundred years it may be so thoroughly proven that ''pragmatically'' it can be considered a priori assumption (in the non-scientific, everyday meaning of 'fact') to any discussion about smoking.


-->


==Why the terms are fuzzier than we pretend they are==
<!--


More pragmatically, a priori tends to translate as 'pre-existing',
particularly in the statistical, modelling, and experimental-science sense.


You might find statements like "there is no a priori knowledge of X",
meaning there is nothing to go on yet, and you need some investigation in the real world.


On the other hand, if you have a dataset,
you will have questions that will call on a posteriori information.
People ''can'' say they have some a priori knowledge about it, meaning you say you know things about how it was collected.


This fuzzes the difference somewhat, because here, "a priori knowledge" is used in a "what we already know about this empirical information" sense.
...'''but this is also where some people weasel in extra meanings'''.
Some of them quite useful,
some of them less so.


In a setting like everyday scientific discussion,
: a priori knowledge tends to mean "what is given without/before further inquiry"
: a posteriori tends to mean "what we can conclude from this experiment"




The sense of time refers to the point of derivation - at that point in time we can ''already'' derive new things from prior knowledge (e.g. "all bachelors are unmarried" - ), whereas for other things we need observation.


This is not as clear-cut as it looks.


However, when your context is
For example, note that "what we know already" can easily blur the line between logic and evidence.


-->


===Statistics===
Science is ''all'' a posteriori, with science being very much about only being about evidence, and giving the best explanation for it.


In probability and statistics, particularly statistical inference, a priori is the prior knowledge of a population.
You could say the only things in science that are a priori are called mathematics.
Basically, it is anything factual that we can use to improve our model.
: ...but math cheats anyway, by only caring about internal consistency, not the real world at all.
It is more than just estimations or limited recent measurements. {{verify}}




A priori probability http://en.wikipedia.org/wiki/A_priori_probability
Everything ''interesting'' and everyday we are trying to do with science is likely to be based on posteriori.


Posterior probability
http://en.wikipedia.org/wiki/Posterior_probability


That said, the ''process'' of studying something with a scientific methodology often takes
"well this is relevant" (a priori) and "what is under study" (about to be a posteriori)


===Modelling===


In machine learning and pattern recognition, and the models and math that backs it,
a priori refers to factual/good/positive examples that make for supervised learning.


(and a posteriori often short for 'a posteriori estimation' based on it)
Since you can argue a priori barely exists, it's not a useful term/distinction at all,
and it has been co-opted into softer distinctions.


For example, in everyday science it's easy to say "you know that theory that's looked solid for the last hundred years? Let's treat that as fact, i.e. a priori knowledge, for this particular experiment".


Without such a priori examples, the patterns would depend on data behaviour, clustering and such. {{verify}}
Or even to roughly split into "stuff I've finished checking" and "hypotheses I want to look at."


===Knowledge (philosophically)===


Note that while a priori in the general sense can be translated as 'pre-existing',
once you start saying 'a priori '' knowledge' '' you trip yourself into [[epistemology]] (a.k.a. 'what can we know'), and a bit of [[metaphysics]].


'''Is this mostly just about timing?'''


'''A priori knowledge''': are things that can be knowable independently of experience/evidence {{comment|(pedantry: ...aside from the experience of the language to communicate it)}}.
That is, a priori often seems use to mean "previous evidence" or "settled in the past".
: say, anything that follows from logic ''alone''.


But more importantly, what was a posteriori for us, once accepted widely ''enough'',
is just evidence (a priori) for the next.
Cited, sure, particularly if not just factual, sure, but still.


'''A posteriori knowledge''' are things that can only be knowable, or verifiable, from empirical evidence.
: that which is (or must necessarily be) deduced from epirical evidence, from experience, observation, or personal decision.


 
Most of what we consider 'everyday facts',
The distinction is related to objective versus subjective observation.{{verify}}
and treat as a priori(-ish),
are really neither of these things,
but it's still useful to treat them that way.




<!--
A priori knowledge often means you can reason it from principles or definitions.




That sentence makes it really easy to be weasely about it, through,
----
because a lot of principles and definitions didn't come from nowhere.


'''An a posteriori conclusion that is certain enough can be taken as a priori assumptions.'''


If a statement is based on evidence, it would be a posteriori even after everyone considers it presumable or obvious.


More practically:
Even though the evidence is pretty damning, any useful answer to "does smoking cause cancer?" will be based on evidence.
: You might still want to verify it using emperical evidence
: a priori tends to mean we are taking general princtiples/definitions/agreements {{comment|(in part just because a lot of knowledge exists in the form in generalisations)}} and doing something useful with it, involving more specific consequences/effects


...while in a hundred years it may be so thoroughly proven that ''pragmatically'' it can be considered a priori assumption (in the non-scientific, everyday meaning of 'fact') to any discussion about smoking.


Before people considered the idea, "Smoking causes cancer" was neither of these things - it was a possibility, then a proposition. The observation that cancer seemed to happen more in smokers isn't enough to call it a priori facto or a posteriori conclusion.




In many cases, a posteriori is almost synonymous with "empirical",
---
because it often goes from particular observations
to more generalized descriptions or theories.


"Bachelors tend to be happy" or "George V reigned from 1910 to 1936" or "It is now raining outside" is something you cannot arrive at from reason, because it came from observation and/or requires emperical verification.
It's easy to consider datasets (or just data in general) evidence,


If you have a dataset, there is the assumption that there is
"A dataset" is


-->


===Law===
On the other hand, if you have a dataset,
you will have questions that will call on a posteriori information.
People ''can'' say they have some a priori knowledge about it, meaning you say you know things about how it was collected.


In ''law'', a priori refers to being based on hypothesis or deduction, rather than experimentation.
This fuzzes the difference somewhat, because here, "a priori knowledge" is used in a "what we already know about this empirical information" sense.


---


It can still refer to subjective, semantic details:
-->
testimonials are automatically subject to a priori plausability - personal back knowledge. {{verify}}
 
===Linguistics===


In linguistics, a priori [[constructed language]]s are those that are created from scratch.


A posteriori constructed languages are those that mix and match from existing ones.
-->


[[Category:Clarification]]
[[Category:Clarification]]

Latest revision as of 13:50, 4 March 2024

✎ This article/section is a stub — some half-sorted notes, not necessarily checked, not necessarily correct. Feel free to ignore, or tell me about it.


Most generally

A priori roughly means something like "(from) that which goes before".

Often used in a "prior to experience/measurement".


A posteriori roughly means "(from) that which comes after".

Often meaning after experience, often using said experience


A bit more practically

Statistics

In probability and statistics, particularly (statistical) inference, a priori is the prior knowledge of a population.

Basically, it is anything we consider already known, that we can use to improve our model, that is more than just estimations or limited recent measurements. (verify)


A priori probability http://en.wikipedia.org/wiki/A_priori_probability

Posterior probability http://en.wikipedia.org/wiki/Posterior_probability


Also in statistics, the prior probability typically refers to the probability distribution before some evidence is taken into account.

Modelling

In machine learning and pattern recognition, and the models and math that backs it, a priori refers to factual/good/positive examples that make for supervised learning.

(and a posteriori often short for 'a posteriori estimation' based on it)


Without such a priori examples, the patterns would depend on data behaviour, clustering and such. (verify)

Knowledge (philosophically)

Note that while a priori in the general sense can be translated as 'pre-existing', once you start saying 'a priori knowledge' you trip yourself into epistemology (a.k.a. 'what can we know'), and a bit of metaphysics ('what is there?'), so philosophy's answers try to be a little wider - could be known answers rather than a person currently knows answers.


A priori knowledge: are things that can be knowable independently of experience/evidence (pedantry: ...aside from the experience of the language to communicate it).

say, anything that follows from logic alone.
e.g. regardless of observation, we can say "all bachelors are unmarried", whereas for other things we need observation.


A posteriori knowledge are things that can only be knowable, or verifiable, from empirical evidence.

that which is (or must necessarily be) deduced from epirical evidence, from experience, observation, or personal decision.


The distinction is related to objective versus subjective observation.(verify)


Law

In law, a priori refers to being based on hypothesis or deduction, rather than experimentation.


It can still refer to subjective, semantic details: testimonials are automatically subject to a priori plausability - personal back knowledge. (verify)

Linguistics

Why the terms are fuzzier than we pretend they are

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