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

Does that mean that riding a bike is synthetic a priori knowledge? I certainly would not have said so.

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 don't see how learning a language can be only analytic a priori knowledge.

I think I see what you're saying, but that seems like an odd use of the term "a priori." — T Clark

Or maybe it's not a great term. I see Kant as very cumbersome here.

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.

So the choice is either to rehash the confusions of Kant endlessly, or move on to the cleaner answer.

I've nothing against Kant as he took the next step in the conversation. But he didn't resolve things in a satisfactory way.

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

My take on knowledge and how we know things is very pragmatic. That's one of the reasons I ended up becoming an engineer.

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? Don't you think Einstein's notion of spacetime is a priori constructed?

That's one of the reasons I ended up becoming an engineer. — T Clark

Doesn't an engineer has synthetic a priori knowledge about the bridge?

Kant was probably influenced by Descartes remarks about analytic vs synthetic thinking. Descartes thought there were different kinds of mental operations. Kant thought the bachelor example was analytic and math synthetic.

If there is a difference between acts that are creatively intelligent and ones that aren't there is difficulty in saying which is which for practical purposes.

This is far truer of humans than other creatures. — apokrisis

Yes. Many animals have very complex behaviors that are transmitted genetically. Humans seem to have just a few instincts - sucking and maybe an attraction to human faces. I'm sure there are more. We also have reflexes. Most of what we have seems to be capacities - language, numbers, some aspects of morality.

I don't know whether the story you've told about how this developed evolutionarily is accurate. It's certainly true that humans are born less developed mentally. Less able to take care of themselves. I don't know if this is the reason for our sociality. There are many non-human social animals. No need to go further on this. I don't know enough to argue effectively.

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

Two points - 1) Even if I'm not familiar with the particular landscape, I am familiar with landscapes in general. I'm also likely to move more carefully in an unfamiliar setting. 2) People from the city are probably more likely to fall off a cliff than someone who grew up in the mountains.

Don't you think Einstein's notion of spacetime is a priori constructed? — Haglund

If you mean constructed purely by deduction rather than by induction, then no.

Doesn't an engineer has synthetic a priori knowledge about the bridge? — Haglund

Yes. I said I had a pragmatic understanding of knowledge. I wouldn't call that a priori at all.

Kant thought the bachelor example was analytic and math synthetic. — Gregory

Whatever Kant thought, I agree the bachelor example is analytic, but I'm not sure about math. Perhaps it's both.

Yes. I said I had a pragmatic understanding of knowledge. I wouldn't call that a priori at all. — T Clark

But if there were no bridges before they we're built, you must have had knowledge to build it. How can't that be a priori?

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. 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.

But if there were no bridges before they we're built, you must have had knowledge to build it. How can't that be a priori? — Haglund

This is an oversimplified story, a cartoon, but I'm sure people saw trees fallen across streams before we were homo sapiens.

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

I remember you and me being on the same side of this argument in previous threads.

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

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. We get most of the knowledge we have by falling out of trees, running through the woods, listening to other people, playing with dogs, swimming, hanging around with other kids...

This is an oversimplified story, a cartoon, but I'm sure people saw trees fallen across streams before we were homo sapiens. — T Clark

But they never saw the first bridge built.

People wave a priori knowledge around like it's a magic wand, but it's just fancy words for regular old stuff. — T Clark

Yep. I guess it was useful in as much as I learned at university many years ago that we discover things a posteriori (by observation) or a priori (by theoretical deduction). The simple and common example of the latter being every mum has (or has had) a child. It's tautological, as you have stated. Some people might view certain arguments for god as a priori.

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?

:up: Some would argue that this type of thinking doesn't belong on a philosophy forum. To the extent that philosophy has become what it has in the modern age, I would consider this criticism justified. But to the extent that the "love of wisdom" has turned into a set of fractal linguistic circus games, criticisms against intuition and common sense begin to look like using quotes from a David Lynch film in a courthouse.

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

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.

I find that intuitions are almost never based on reason, but rather instinct or experience. — noAxioms

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?

This type of knowledge is described many ways, among them a priori, self-evident, intuitive, obvious, and common sense. — 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?

It seems that knowing that 2+2=4 is an experience of visuals or a voice in your head.

Is knowing 2+2=4 just you saying in your mind, "two plus two equals four"? I don't think so. This is just knowing how to say it - not knowing what it means or refers to. We all know that children can imitate language use without knowing what it means.

Is knowing 2+2=4 knowing how to arrange the symbols, 2, 2, 4, + and = in the right order? I don't think so. Knowing how to arrange symbols in the correct order is not knowing what the symbols are about.

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.

Reasoning is only useful if it is about something, or can be applied to real-world experiences.

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

It seems to me that the invention of mathematics would not have been conceivable if experience itself was not in some way quantifiable.

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? Instincts evolved because there are aspects of the world that stay consistent. It seems like sexual reproduction and consciousness evolved as ways of adapting to changes within those consistencies, as in the way that children question the previous generations' axioms and filtering instinctual behaviors.

The problem is that when people claim that something can be useful but not true, they are confusing our lack of knowledge of truths that are not relevant to what is being used with truths that we do know that are being used. Just because we may not know everything does not mean that we do not know anything, or that what we do know, instinctually or consciously, isn't true enough to be useful for the goal at hand - which typically isn't having a theory of everything.

It seems to me that reasining itself is instinctual and only realized through experience. — Harry Hindu

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.

I actually question everything, even 2+2=4. Is it objectively true, or is it perhaps only a property of the physics or mathematics of say this universe, and doesn't work in another one? I cannot think of a reasonable counterexample, but that very issue seems to be one of the weakest links in my goal of finding a self-consistent view of how things are.

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

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.
At a much deeper level, one's feeling of personal identity is fantastically instinctual, and yet doesn't hold up to true rational analysis. It is probably a complete lie compliments of evolution (over 650 million years ago when it was put there), and it makes us fit as an individual, a pragmatic benefit at best. Assuming being fit equates to a benefit over not being fit, this makes the truth of the matter harmful, and the lie beneficial.

But they never saw the first bridge built. — Haglund

This is getting silly. Are you saying the only way I could have an original idea is a priori? I can't take things I've learned and put them together in a new way?

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

It's instinct, so I guess, yes, that is analytic a priori knowledge. Maybe not the impulse to fly south but at least the knowledge of how to get where their going. Salmon aren't shown the location of their spawning grounds. They just know it. I don't know if there are many, if any, things people know like that.

Some would argue that this type of thinking doesn't belong on a philosophy forum. — Noble Dust

You can't talk epistemology without talking intuition, no matter what anyone says.

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

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. I don't think it matters whether we see it that way or not. It's the whole concept I don't like. It seems like a totally unrealistic description of how we really know things and how we use the things we know.

Are you saying the only way I could have an original idea is a priori — T Clark

No. I'm saying that you gotta have a priori knowledge of something you gonna construct. If not, the plan is doomed to fail. How can you have knowledge of something not existing before you have made it? How does a beaver know how to build them dams?

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

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.

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

Well, this is something like what we are doing in philosophy, rather than what people are doing when they come to know things. It's what some philosophers do when they're trying to work out what knowledge is. But the comment I referred to was this:

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

This suggests that you understand the process to be one that's proposed to be undertaken by people generally, when they come to know things in everyday life, and not particularly as part of philosophical examination.

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

You think the innate concept of quantity, undeniably present in animals, is an innate knowledge of math? Dunno. You can elaborate playing with quantities in space endlessly. Construct zillions of relationships between them. That evolves. Giving a priori knowledge of the world. Einstein never saw curved spacetime. He had a priori knowledge of black holes. A baby has a lot of instinctive knowledge about the world when pooped in it. It has too. Without a priori, tacit, instinctive, intuitive, knowledge, necessarily vague still, it won't be possible to continue living after being pooped.

I think maybe you're overusing the word "instinct." I've been using it in ways that might not be accurate too. I'm going to check. Here are some definitions from the web:

[1] An inborn pattern of behavior that is characteristic of a species and is often a response to specific environmental stimuli.
[2] A powerful motivation or impulse.
[3] An innate capability or aptitude.
[4] The inherent inclination of a living organism towards a particular complex behaviour, containing both innate (inborn) and learned elements.

Looks like the meaning is broad enough to take in all the ways we're using it. I think I was unclear, even to myself, how I was using it.