A priori, a posteriori: Difference between revisions

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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.
Basically, it is anything factual that we can use to improve our model.
It is more than just estimations or limited recent measurements. {{verify}}


A common statement is that "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.


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


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




===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.


In a setting like everyday scientific discussion,
(and a posteriori often short for 'a posteriori estimation' based on it)
: 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"




This is not as clear-cut as it looks.  
Without such a priori examples, the patterns would depend on data behaviour, clustering and such. {{verify}}


For example, note that "what we know already" can easily blur the line between logic and evidence.
===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]].


Science is all a posteriori, with science being very much about the best explanations of given evidence.


'''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.


You could say the only things in science that are a priori are called mathematics.
: ...but math sorta cheats anyway, by only caring about internal consistency, not the real world.




Rverything ''interesting'' and everyday we are trying to do with science is likely to be based on 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.




That said, the ''process'' of studying something with a scientific methodology often takes
The distinction is related to objective versus subjective observation.{{verify}}
"well this is relevant" (a priori) and "what is under study" (about to be a posteriori)




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


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


Or even to roughly split into "stuff I've finished checking" and "hypotheses I want to look at."




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 used to mean "previous evidence"'''


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.




: '''A priori as in "settled in the past"'''
-->


Note that 'coming before or after' can also involve timing, or cause.
===Law===


There is a similar co-opting of the terms going on here.
In ''law'', a priori refers to being based on hypothesis or deduction, rather than experimentation.
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,
It can still refer to subjective, semantic details:
a posteriori in that it was based on observations that cancer seemed to happen more in smokers.
testimonials are automatically subject to a priori plausability - personal back knowledge. {{verify}}


Now that evidence has shown this link to be pretty damn convincing,
the ''next'' discussion could choose to consider it a priori knowledge,
in the meaning of "stuff that came before, that we are reasoning from"


===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.


So it depends a bit (too much, arguably) on the question being asked, and on when it is asked.


If a statement is based on evidence, it will be a posteriori even after everyone considers it presumable or obvious.
-->
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,
...'''but this is also where some people weasel in extra meanings'''.
you will have questions that will call on a posteriori information.
Some of them quite useful,
People ''can'' say they have some a priori knowledge about it, meaning you say you know things about how it was collected.
some of them less so.


This fuzzes the difference somewhat, because here, "a priori knowledge" is used in a "what we already know about this empirical information" sense.
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.  


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


However, when your context is


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


===Statistics===
You could say the only things in science that are a priori are called mathematics.
: ...but math cheats anyway, by only caring about internal consistency, not the real world at all.


In probability and statistics, particularly statistical inference, a priori is the prior knowledge of a population.
Basically, it is anything factual that we can use to improve our model.
It is more than just estimations or limited recent measurements. {{verify}}


Everything ''interesting'' and everyday we are trying to do with science is likely to be based on posteriori.


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


Posterior probability
That said, the ''process'' of studying something with a scientific methodology often takes
http://en.wikipedia.org/wiki/Posterior_probability
"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,
Since you can argue a priori barely exists, it's not a useful term/distinction at all,
a priori refers to factual/good/positive examples that make for supervised learning.
and it has been co-opted into softer distinctions.


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


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',
'''Is this mostly just about timing?'''
once you start saying 'a priori '' knowledge' '' you trip yourself into [[epistemology]] (a.k.a. 'what can we know'), and a bit of [[metaphysics]].


That is, a priori often seems use to mean "previous evidence" or "settled in the past".


'''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)}}.
But more importantly, what was a posteriori for us, once accepted widely ''enough'',
: say, anything that follows from logic ''alone''.
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.
Most of what we consider 'everyday facts',  
: that which is (or must necessarily be) deduced from epirical evidence, from experience, observation, or personal decision.
and treat as a priori(-ish),  
are really neither of these things,
but it's still useful to treat them that way.




The distinction is related to objective versus subjective observation.{{verify}}




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


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


That sentence makes it really easy to be weasely about it, through,
If a statement is based on evidence, it would be a posteriori even after everyone considers it presumable or obvious.
because a lot of principles and definitions didn't come from nowhere.


Even though the evidence is pretty damning, 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.


More practically:
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.
: 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




---


It's easy to consider datasets (or just data in general) evidence,


In many cases, a posteriori is almost synonymous with "empirical",
If you have a dataset, there is the assumption that there is  
because it often goes from particular observations
"A dataset" is
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.


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.


===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===
 
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]]

Revision as of 16:34, 23 October 2023

✎ 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 factual that we can use to improve our model. It 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


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.


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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