An a priori justified?

  • Thread starter Willowz
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  • #26
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see below :)
Surely, some bachelors are married...
 
  • #27
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The point is that mathematics comes from empirical observations, as willows is trying to convey.
It would be a comforting thought to think so, but the half-*** example I provided in the OP(Infinity as a limiting concept) baffles me. That we can know our own limits without empirical evidence!
How do you explain such a thing??
 
  • #28
disregardthat
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How could I play a game while not playing by the rules?

What does that have to do with what you quoted?

And surely, no bachelors could be married, for that would strip them of their status as bachelors. Don't you see what's going on here?
 
  • #29
yossell
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The definition of a priori is normally in terms of knowledge or justification:

Roughly, an a priori truth is one which *could* be known without recourse to experience, while an a posteriori truth is one which requires some kind of experience for someone to know it.

Caveats are needed because some experience may be required to gain the relevant concepts. For instance, we may need experience of green things to have the concept `green'. But, once we have the concept, we can know that everything is green or not green without having to go out and check or do experiments.

So it may be true that experience is required for us to form the relevant concepts - say the concepts of a number of things, but that doesn't alone imply that mathematical truths are not a priori any more than the fact we need experience of green things means 'everything is green or not green' is not a priori.

Note that an a priori truth could be known a posteriori. Somebody may find out that everything is green or not green by going out and checking; somebody may come to know that 2 and 2 is always 4 by counting a few cases, and then generalising by induction.
 
  • #30
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What does that have to do with what you quoted?
Maybe I should ask you... What does this mean in your previous post?
You are drawing necessary conclusions based on the rules of the game. You don't need the actual game to do this...
 
  • #31
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And surely, no bachelors could be married, for that would strip them of their status as bachelors. Don't you see what's going on here?
What I don't get with the bachelors example is the ideal situation that is presented to us. How can it be that all bachelors are unmarried? SO many things in reality elude our faculties of reasoning but bachelors being unmarried is almost a universal truth to us, how is this so?
 
  • #32
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So, another question. Can the so called "a priori" truths be only made from within a complete system(Godel)? In this case with the bachelors? It seems so. Should I start a new thread regarding this question?
 
  • #33
disregardthat
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What I don't get with the bachelors example is the ideal situation that is presented to us. How can it be that all bachelors are unmarried? SO many things in reality elude our faculties of reasoning but bachelors being unmarried is almost a universal truth to us, how is this so?

A bachelor is defined as being an unmarried male. Therefore, if we are going to call anyone a bachelor, he necessarily have to be unmarried, or else we would have contradicted our own definition.

Suppose for a moment that a person is a bachelor and married. That implies he is married and not married at the same time. Is this still not a convincing argument for that no bachelor can be married?

Maybe I should ask you... What does this mean in your previous post?

You are drawing necessary conclusions based on the rules of the game. You don't need the actual game to do this...

By knowing the rules of a game, you can imagine possible moves. These moves are necessarily possible given the rules. Hence you are drawing necessary conclusions. These a priori conclusions are not subject to empirical testing, they are contained in the premises (rules), i.e. inherent to the rules which you assume; in the same way as being unmarried is contained within being a bachelor.
 
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  • #34
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A bachelor is defined as being an unmarried male. Therefore, if we are going to call anyone a bachelor, he necessarily have to be unmarried, or else we would have contradicted our own definition.
On what basis can we make this definition? How is it, that this definition applies so strictly to the situation given.

By knowing the rules of a game, you can imagine possible moves. These moves are necessarily possible given the rules. Hence you are drawing necessary conclusions. These a priori conclusions are not subject to empirical testing, they are contained in the premises (rules), i.e. inherent to the rules which you assume; in the same way as being unmarried is contained within being a bachelor.
This is all saying that I am all the time playing the game(following the rules). But, what you said earlier gave me the impression that I wasn't playing the game even if I were playing by the rules: "You are drawing necessary conclusions based on the rules of the game. You don't need the actual game to do this..."
 
  • #35
disregardthat
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On what basis can we make this definition? How is it, that this definition applies so strictly to the situation given.

We can define whatever we want, and no situation was given. By the a priori conclusion we are expanding (or exploring) our notion of the term 'bachelor'. It does not have to apply to any situation. No bachelor would be married even if there was not such thing as unmarried males, or males at all. It is purely a semantical argument without reference to reality.

This is all saying that I am all the time playing the game(following the rules). But, what you said earlier gave me the impression that I wasn't playing the game even if I were playing by the rules: "You are drawing necessary conclusions based on the rules of the game. You don't need the actual game to do this..."

You can imagine possible moves in chess without having the physical game in front of you. That ought be obvious from the context.
 
  • #36
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Categorical distinctions are usually made a priori to the categories being operationalized and compared/contrasted. So, for example, sociological research that compares social classes makes an a priori assumption that individuals cannot be identified with more than one social class. As such, the results will reproduce the mutual exclusion of classes, only because the distinction and assumption was brought in at the beginning of research.

A priori assumptions and premises can only be (in)validated on the basis of philosophical reason. You can't say that because certain categories generate good analytical results that the categories are automatically valid, imo. That could be part of your reasoning as to the validity of the categories, but you still have to explore all issues that come into play. Otherwise your a prioris are going to influence your results without any kind of rigorous basis for them, which would undermine the validity of your research generally, I think.
 
  • #37
Pythagorean
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It would be a comforting thought to think so, but the half-*** example I provided in the OP(Infinity as a limiting concept) baffles me. That we can know our own limits without empirical evidence!
How do you explain such a thing??

In terms of observations, I think the general idea is that if it's bigger than you can "perceive" (i.e. significant detection in a system) it's not much different from infinity. For instance, if I have current in a wire, and I place a charge next to it, as the particle gets closer and closer to the wire, it's as if the wire were infinite because, in terms of the field interactions, if you were looking at the wire from the electrons perspective, the wire would seem to go forever in both directions.

If you pull the particle farther and farther away from the wire, the particle can "see" the whole wire at once (just as if you backed away from the broad side of a barn, at a certain point you can get the whole barn in your view).
 

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