When children learn mathematics they learn a synthetic skill, not an analytic one. Sure they start out counting the numbers but even this is not analytic
for them sincr ultimately they are to develope a synthetic skill (as Kant pointed out). Synthetic ability is dum da dum creative intelligence! — Gregory
This thread is an example of the creative mentality while analytic thought is usually defined as finding meanings to language instead of combining words to form a new synthesis — Gregory
I think I see what you're saying, but that seems like an odd use of the term "a priori." — T Clark
This is what Peirce fixed with his pragmatic theory of truth. He showed how reasoning involved this feedback loop of abduction, deduction and inductive confirmation. — apokrisis
This is far truer of humans than other creatures. — apokrisis
You seem to think there exists no a priori knowĺedge. But correct me if I'm wrong. But if that's the case how can we anticipate unknown territory with which we don't have interacted? — Haglund
Don't you think Einstein's notion of spacetime is a priori constructed? — Haglund
Doesn't an engineer has synthetic a priori knowledge about the bridge? — Haglund
One thing intuition is very good for is setting off alarms when you hear something that doesn't fit. That happens to me all the time. When I go to check, I'm usually right. — T Clark
Same. I've argued (badly) for intuition over the years here, but I eventually realized it's self-evident that the vast majority of people in the world use intuition primarily, and it's only the smaller minority of analytically-minded people who would bother to join a philosophy forum that deride it's primacy. — Noble Dust
Then it becomes a twofold question of 1) are the vast majority of people deluded and only a select few understand how truth is obtained, and 2) alternatively, is this criticism of intuition just a prejudice of the intelligent against the less intelligent? And where does that path logically lead? The ivory tower is tall indeed. — Noble Dust
People wave a priori knowledge around like it's a magic wand, but it's just fancy words for regular old stuff. — T Clark
I find it hard to understand how people can believe they know most of the things they do by justified true belief baloney or some other mechanical process. — T Clark
It seems to me that reasoning itself is instinctual and only realized through experience. How do you know you're being reasonable vs. unreasonable if not by some experience? What are you reasoning about? What form does you're reasoning take if not some experience of reasoning?I find that intuitions are almost never based on reason, but rather instinct or experience. — noAxioms
Let's take 2+2=4. What type of knowledge is knowing 2+2=4? How do you know that 2+2=4?This type of knowledge is described many ways, among them a priori, self-evident, intuitive, obvious, and common sense. — T Clark
It seems to me that the invention of mathematics would not have been conceivable if experience itself was not in some way quantifiable.I find that intuitions are almost never based on reason, but rather instinct or experience. Many of those intuitions are not true, but don't confuse truth with beneficial. — noAxioms
Well yea. You brought up the 2+2=4 thing, but I'm confident that a human would never figure that out in the absence of experience. Humans are exceptionally helpless at birth, but several instincts are there, like the one to draw breath despite never having the experience of needing to do that before.It seems to me that reasining itself is instinctual and only realized through experience. — Harry Hindu
I can think of several exceptions. On the surface, how about "reproduction is beneficial"? It certainly doesn't benefit the individual. There are plenty of humans living more comfortable lives by becoming voluntarily sterile, but for the most part, reproduction is quite instinctual which is why the above goal can rarely be achieved via just abstinence.For something to be beneficial, or useful, there must be some element of truth involved, or else how can there more or less efficient ways of using something - like intuitions? — Harry Hindu
Does a bird which migrates south for the first time in its life use a priori knowledge to get there, or are they just copying the others? — Tom Storm
Some would argue that this type of thinking doesn't belong on a philosophy forum. — Noble Dust
I’ve never seen justified true belief described as a process before. It’s just an observation (in the Theaetetus) of what we often mean when we speak of knowing, viz., something we believe, that is true and justified. — jamalrob
Are you saying the only way I could have an original idea is a priori — T Clark
Let's take 2+2=4. What type of knowledge is knowing 2+2=4? How do you know that 2+2=4? — Harry Hindu
Is knowing that 2+2=4 knowing what 2+2=4 is about, or how to use or apply to real-life experiences, or a representation of real-life experiences of quantifying and counting experienced objects? It seems that knowing that 2+2=4 is experiencing two of something and another two of something becoming four of something. In other words, 2+2=4 is only meaningful if it can be applied to, or representative of, experience of counting real-world things which are not numbers themselves, just as words are not meaningful if not applied to real-world things that are not words themselves. — Harry Hindu
I've always thought of it as a process, like a checklist. It's true - check. It's justified - check. I believe it - check. Ding, ding, ding - It's knowledge. — T Clark
I find it hard to understand how people can believe they know most of the things they do by justified true belief baloney or some other mechanical process. — T Clark
There seems to be disagreement about what kind of knowledge math is. As I noted in a previous post, there are studies that show that very young children, babies, are aware of quantity, so there seems to be some inborn "knowledge" of math. On the other hand, we have to learn how to use it. — T Clark
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