Is a priori knowledge possible?

Discuss any topics related to metaphysics (the philosophical study of the principles of reality) or epistemology (the philosophical study of knowledge) in this forum.
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Hereandnow
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Re: Is a priori knowledge possible?

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All well and good. And you might call the apodicticy of causality, the refutation of Hume's habits of contiguity, to be a real phenomenon since it presses insistently on the intuition. You can't just ignore (which seems to be what you're suggesting) intuitions; after all, they are the very things that structure your thought as you read this. They ARE that which inquiry here is centered on. You can never "get behind" such a thing to observe it.
Surreptitious57
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Re: Is a priori knowledge possible?

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Intuitions cannot be ignored but they cannot always be assumed to be reliable either
They have to be subject to rigorous examination to determine how reliable they are
A MIND IS LIKE A PARACHUTE : IT DOES NOT WORK UNLESS IT IS OPEN
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Hereandnow
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Re: Is a priori knowledge possible?

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And how does one examine this? See Wittgenstein, for one. You would need some third symbolic perspective ( as I recall the way it goes), a metalanguage, to stand apart from the intuition features yo're trying to get at. But this third metalanguage would itself be just as problematic.

I go with Husserl on this, though I can't properly defend his ideas against a century of complaint. Anyway, I think there is a way out of the fly bottle, as Wittgenstein put it, and it is the immediate intuited world. The way is not out, it is all the way in.
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SimpleGuy
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Re: Is a priori knowledge possible?

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Hereandnow wrote: December 18th, 2017, 5:03 pm
Simpleguy:
In fact you don't understand that all these measurements are a part of a stochastic process, and due to a definition of a stochastic process adaptation to a filtration always plays a role of preknowledge. This is the basis of martingale theory in stochastics, that somehow projects radom events ordered into a certain "knowledge" system called sigma-algebras , to which the process is measurable at each time. Wittengstein was neither a mathematician nor a good phyisicist. Pre-knowledge is well defined after the theory of stochastic processes.
For me to give this a nod, you would have to tie in your thoughts about probability theory to the issue of apriority. I have a vague understanding of stochastic processes, but there is nothing here that helps. It seems to me you would have to put out some probabilistic account of the intuitive apprehension of a logical form, such as a conditional or apodictic proposition. But how would this be anything but what Kant calls general logic?; or, an advanced construal of general logic? Apriority is transcendental because it is the form presupposed by statement and judgment as such. Even as you meticulously spell out how necessity and probability can be reduced to something else, your account will possess the very form you are supposed to be examining. This is where Kant has his greatest criticism: In using language and logic to talk about language and logic.

Also, keep in mind that there is yet another form of apriority which is more difficult, impossible, really, and that is causality. Every event has a cause, and this is apodictically true. How does this get explained in term probability theory?

Or am I truly off your mark? Glad to be disabused, but I would ask that you make the effort to address the matter as stated. (I am aware of the temptation present ideas independently.)
Well, the word Filtration is a sequence of \Sigma-algebras, to which the stochastic process is adapted. In the sense of martingale theory , it has the meaning of a preknowlege. A martingale is a so called fair game , it can be under restrictions of L^2 integrability shown, that a representation of a large class of martingale is X_t = E[Z | F_t] where F_t is the filtration to which the process is adapted and Z is for locally L^2 martingales a random L^2 variable. This formula states the following: That projected onto a certain subspace of L^2 given by the filtration , the distribution of the stochastic process is known. Thus the filtration, play's the role of a preknowlege given for a stochastic processes. Under the assumption that the measured process is a semi-martingale , and this is mostly the case for all solutions of stochastic differential equations and with it for many physical processes , the measurability of the semimartingale plays the role of the foreknowlege. For you as an interested person i refer for the standard works of Jacod, Shiryaev, Limit Theorems for Stochastic Processes for a more detailed introduction into this subject. The adaptation can be seen as the knowledge into which a process can be embedded. It is for example an easy task to construct sequences of filtrations , s.th. the same processes can be seen as a fair game or not. That's what i am talking about. It's not about information and entropy in this section but about the adaptation of a stochastic process to a sigma-algebra.
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SimpleGuy
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Re: Is a priori knowledge possible?

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By the way to refer to your, criticism. That you make a statement and this statement is in previous some kind of preknowledge. This statement is exactly contained in the filtration of your stochastic event at time t. All these claims that are made are contained in the sigma-algebra of the current stochastic variable, and with it in the filtration of the process measurable. The event , that you stated is and i emphasize this contained in the filtration and you can calculate with it, so there is no real contradiction of the situation you described, to what i said . If you truly insist , i recommend to you some professors of stochastic calculus, which will affirm my statements. All that you've claimed about a stochastic process is already contained in the sigma algebra and with it in the filtration of the process. Then you have to observe the problem of measurablity if the filtration still satisfies your needs. You can include every event that you want in a sigma-algebra, if you describe the amount of the events properly.
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Re: Is a priori knowledge possible?

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You simply don't understand that you either have to extend the sigma algebra which is the filtration of the process to the claims that you made or if you want to exclude something to restrict the sigma algebra to the claims you want to exclude , you call this preknowledge and look at the consequences of a different filtration for example for the expected values and the variances or the effect of hedging due to this extended filtration of this process as a matter of representing the process as a stochastic integral in a different filtration.
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SimpleGuy
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Re: Is a priori knowledge possible?

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Now for ordinary school mathematics:

What you did is then to include the claim that you made (or the conjecture) as a set into the event-space like all subsets of {1,2,3,4,5,6} into your event-space, it's still possible to calculate then the consequences.
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Re: Is a priori knowledge possible?

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That means, for pre-knowlede you possible restrict the event-set to the conjecture and compare it to the normal distribution. What is decisive is the changing of this set, and to look at the conditional expectation of the real-distribution under this constraint. This is the every-day , explanation of the previously stated sigma-algebra remarks. So the observation is contained in adapted formulation of the filtration.
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SimpleGuy
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Re: Is a priori knowledge possible?

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The event space is in german school mathematics der Ereignisraum. You alter it and this is exactly the fitting of the filtration.
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SimpleGuy
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Re: Is a priori knowledge possible?

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One can always construct out of a single set, then a sigma-algebra. If one has to take an infinite , uncountable union of set's this may seem hazardous , but this is mostly excluded from mathematical observations.
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SimpleGuy
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Re: Is a priori knowledge possible?

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But if one includes infinite amount , it's possible then to go to the power-set (Potenzmenge) as a sigma-algebra which is an extension of the terminology event-space.
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SimpleGuy
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Re: Is a priori knowledge possible?

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But measurablilty is then sometimes in the sense of a borel-measure not given. This is the meaning of hazardous.
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Hereandnow
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Re: Is a priori knowledge possible?

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Let me see: You are saying that apriority, the universality and necessity of certain propositions that is not derived from empirical observations of the world, but rather from sources "unseen" within, can be understood in the language of stochastic calculus. So, the apriority of "in every triangle the longest leg is opposite the largest angle" or "every body has extension" rises to mind through a process which takes what is random, like the world taken up perceptually, and transforms it into meaning and logic. It is intended to be a stochastic calculus of what thinking is really about, or, a reduction of thought to theory about what is involved in giving structure to random systems?
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SimpleGuy
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Re: Is a priori knowledge possible?

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Hereandnow wrote: December 24th, 2017, 3:07 pm Let me see: You are saying that apriority, the universality and necessity of certain propositions that is not derived from empirical observations of the world, but rather from sources "unseen" within, can be understood in the language of stochastic calculus. So, the apriority of "in every triangle the longest leg is opposite the largest angle" or "every body has extension" rises to mind through a process which takes what is random, like the world taken up perceptually, and transforms it into meaning and logic. It is intended to be a stochastic calculus of what thinking is really about, or, a reduction of thought to theory about what is involved in giving structure to random systems?
It's a reduction of thought in a working theory , already applied for financial mathematics (calculation of asset prices like the black scholes ansatz) physics and many other engeneering sciences. Even the a priory knowledge is treated in financial mathematics as insiders knowledge , through additional random variables and help us to calculate estimated prices for stock options. So this is no , theoretical , thinger , thangerer , nonsense but truly applied already for stock prices and pricing of derivatives of shares as well as life insurances and interest rate modelling. A lot of money depends on that discipline.
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Hereandnow
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Re: Is a priori knowledge possible?

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SimpleGuy:
It's a reduction of thought in a working theory , already applied for financial mathematics (calculation of asset prices like the black scholes ansatz) physics and many other engeneering sciences. Even the a priory knowledge is treated in financial mathematics as insiders knowledge , through additional random variables and help us to calculate estimated prices for stock options. So this is no , theoretical , thinger , thangerer , nonsense but truly applied already for stock prices and pricing of derivatives of shares as well as life insurances and interest rate modelling. A lot of money depends on that discipline.
And to understand clearly, in a discussion about what is in a knowledge claim that is not derived from empirical intuitions we acknowledge the so called synthetic feature of every judgment possible. "Pass the potatoes" employs the concept 'potato' and this refers to anything that conforms to a certain schematic that is, if you will, preontological at the moment before judgment. Seeing the potato is an act of synthesis, taking the particular before you and bringing it into a general concept that applies to like cases. This synthetic act is apriori: the knowledge that X is a potato possesses an aspect not empirically derived from sensory givens. Of course, this occurs in time. And this is crucial, for what you have presented is a description of a sequence in time. In time we implicitly deploy theory ( and this is not an objectionable word. All language is theory and this can be discussed if you like) in any propositional act.

And what do you say about apodicticity, or necessity? What do you say about this: Apriority can be examined phenomenologically, that is, as an apparent structure of thought. Kant did this, as did Heidegger, Wittgenstein and others. But they acknowledged that when the matter turns to the form of logic and language, there was nothing you could really say. As I said before, you can't get "behind" a language using some other metalanguage to analyze and describe the features of a language.

So it's like this: The apriority in question is unspeakable, just like for a physicist to speak about what a force is cannot. These are questions that go to a place that is beyond language. Why?: because you use language to conceive of them. Thus, in answer to the Original post: Yes and No: No, if the question refers rendering apriority as such in terms that make sense, as you tried to do, for the reasons mentioned above. Yes, if you're simply asking if one can know something apriori. I know through the apriori function that allows me to structure thought (perhaps stochastically. You might be right, for all I know) as a conditional statement with its inherent logical features that if it rains, I will get wet; it rains; I will get wet.

But in keeping with your thinking, to prove that apriority can be reduced to the concept you present (again, maybe!), you would need to be more focused on the logical functions of logical synthesis, of causality, of the way all propositions as they present themselves as propositional phenomena.
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