Is a priori knowledge possible?
- Hereandnow
- Posts: 2839
- Joined: July 11th, 2012, 9:16 pm
- Favorite Philosopher: the moon and the stars
Re: Is a priori knowledge possible?
-
- Posts: 94
- Joined: September 28th, 2015, 12:57 am
Re: Is a priori knowledge possible?
They have to be subject to rigorous examination to determine how reliable they are
- Hereandnow
- Posts: 2839
- Joined: July 11th, 2012, 9:16 pm
- Favorite Philosopher: the moon and the stars
Re: Is a priori knowledge possible?
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.
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
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.Hereandnow wrote: ↑December 18th, 2017, 5:03 pmFor 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.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.
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.)
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
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.
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
- Hereandnow
- Posts: 2839
- Joined: July 11th, 2012, 9:16 pm
- Favorite Philosopher: the moon and the stars
Re: Is a priori knowledge possible?
- SimpleGuy
- Posts: 338
- Joined: September 11th, 2017, 12:28 pm
Re: Is a priori knowledge possible?
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.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?
- Hereandnow
- Posts: 2839
- Joined: July 11th, 2012, 9:16 pm
- Favorite Philosopher: the moon and the stars
Re: Is a priori knowledge possible?
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.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 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.
2023/2024 Philosophy Books of the Month
Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul
by Mitzi Perdue
February 2023
Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness
by Chet Shupe
March 2023