Representationalism is about correspondence between the language and the world. — RussellA

I'm on a Brandom kick, so I'll mention his take. Representings are responsible to the represented thing, which functions like a target. Gadamer may come into play here. A kind of unspecified completeness is imagined from the beginning.

As reason and judgement are attributes of the mind, they can only be the responsibility of the individual making that reasoning and judgement. — RussellA

From a certain perspective, reason and judgement and the mind are abstractions or fictions, just like the self, just like responsibility. It looks to me that we have an entire system here of inherited concepts, which only make sense together.

Imagine practical animals who start with a limited cognitive vocabulary, which they use relatively rationally to thrive together in their environment. Now imagine the slow development of a metacognitive vocabulary, with words like 'judgment' and 'epistemology' and 'responsibility. ' As I see it, one accomplishment of philosophy has been to make the sociality of reason explicit to itself.

What is in the mind corresponds to what is in the brain. What is expressed in the mind must be in some way be expressed in the brain, in that the mind doesn't have a soul outside of time and space allowing it to act independently of the brain. The mind cannot change without a corresponding change in the brain. — RussellA

I think this is fairly reasonable but still a little problematic. As long as the mind is (understood as) a factory of stuff that will "forever remain private knowledge," it's hard to see how anything comprehensive can established about it. The lurking assumption is that there is just one 'forever private' experience of red (for instance.) But 'forever private experience' opens up an abyss of possibility. It's outside the space of reasons. At the minimum we need claims, entry into the symbolic realm, such as 'The square looks red to me.' (Or a recorded measurement of a change in heart-rate, etc.)

Hume’s denial that there is an inner perception of the self as the owner of experience is one that is echoed in Kant’s discussion in both the Transcendental Deduction and the Paralogisms, where he writes that there is no intuition of the self “through which it is given as object” — RussellA

The 'self' I'm talking about is the persona or reputation. A rough analog is your LinkedIn profile. The metaphysical subject, on the other hand, is a hot mess. I agree with Kant and Hume that no such subject is available (or not one worth bothering with.)

I like Brandom because to me he's just describing the philosophical situation itself ( the interpersonal structure of rationality. ) For instance, you mention Hume's denial. A 'scorekeeping' conception of rationality will emphasize how we'll contextualize this denial against Hume's other claims. Hume is like an actor on a stage among other actors. His speeches are unified as his speeches..and interpreted as such a unity. As are we. This social situation seems basic to rationality.

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Nice post on Berkeley. I'm glad to hear he's more sensible than the cartoon version of him.

We learn by observing nature. Then we take those observations and extract their essences. — jgill

I'm with you in spirit, but perhaps we dream up those essences and only later learn to check if they or their implications are compatible with observations. — igjugarjuk

In all my years as a mathematician, however, I must confess that I have never worked in applied mathematics. Like most in my profession, I explored an intriguing abstract concept. Still do.

I think all participants here know about the statement of the unreasonable effectiveness of mathematics. Shouldn't we, rather, speak of it's reasonable effectiveness? I can't see nothing unreasonable about it and can't even imagine how else it could be. — Landoma1

If you start with a logical system, it shouldn't be a surprise that you end up with something logical.

Not only do we use logical. I would make the bold declaration that animals use logic, even if they don't understand they are using logic.

In all my years as a mathematician, however, I must confess that I have never worked in applied mathematics. Like most in my profession, I explored an intriguing abstract concept. Still do. — jgill

I guess I was just emphasizing what Popper also emphasized. Theory creation ('projecting' a pattern on reality) can itself be 'irrational' or mysterious without science failing to be science. This is because the science consists in the way we treat such theories, independent of their source. Another common point is that theory guides observation in the first place (tells us what to look for, frames the situation.)

I would make the bold declaration that animals use logic, even if they don't understand they are using logic. — ssu

I think this makes sense, though folks can fuss over the ideal application of 'use.' Along these lines we can picture a distinctly human metacognition laid on top of an inherited and more common animal cognition.

Understood correctly, Berkeley was a defender of common-sense who cannot be interpreted as saying that the world is a 'figment of the imagination — sime

Did Berkeley believe that the world is a "figment of the imagination"

Bertrand Russell The Problems of Philosophy - 1912
He then proceeds to consider common objects, such as a tree, for instance. He shows that all we know immediately when we "perceive" the tree consists of ideas in his sense of the word, and he argues that there is not the slightest ground for supposing that there is anything real about the tree except what is perceived. Its being, he says, consists in being perceived: in the Latin of the schoolmen its "esse" is "percipi." He fully admits that the tree must continue to exist even when we shut our eyes or when no human being is near it. But this continued existence, he says, is due to the fact that God continues to perceive it; the "real" tree, which corresponds to what we called the physical object, consists of ideas in the mind of God, ideas more or less like those we have when we see the tree, but differing in the fact that they are permanent in God's mind so long as the tree continues to exist. All our perceptions, according to him, consist in a partial participation in God's perceptions, and it is because of this participation that different people see more or less the same tree. Thus apart from minds and their ideas there is nothing in the world, nor is it possible that anything else should ever be known, since whatever is known is necessarily an idea.

IEP - George Berkeley
Berkeley’s famous principle is esse is percipi, to be is to be perceived. Berkeley was an idealist. He held that ordinary objects are only collections of ideas, which are mind-dependent. Berkeley was an immaterialist. He held that there are no material substances. There are only finite mental substances and an infinite mental substance, namely, God.

AC Grayling - Berkeley's Argument for Immaterialism
Berkeley's philosophical view is often described as an argument for "immaterialism", by which is meant a denial of the existence of matter (or more precisely, material substance.) But he also, famously, argued in support of three further theses. He argued for idealism, the thesis that mind constitutes the ultimate reality. He argued that the existence of things consists in their being perceived. And he argued that the mind which is the substance of the world is a single infinite mind – in short, God.

Blake Winter - Berkeley's Arguments on Realism and Idealism
Bertrand Russell credited Berkeley with being the first philosopher to show that the position of idealism may be held without contradiction (Russell, 1997). However, in addition to this, Berkeley also attempted to show that realism was absurd, because it required concepts which could not in fact be conceptualized (1977). From this, Berkeley concluded that idealism was not merely possible but necessary, or at least necessarily the only theory we could understand. That is, he concluded that we are epistemologically forced to renounce realism in favour of idealism.
We will take realism to mean the ontological position that there are things which exist that are neither minds nor ideas in minds. We will take idealism to mean the ontological position that everything that exists is either a mind or an idea in a mind.

If Realism is the belief in a mind-independent world, and Idealism is also a belief in a mind-independent world, then how do Realism and Idealism differ ?

Realism may be defined as the ontological position that there are things which exist that are neither minds nor ideas in minds. Idealism may be defined as the ontological position that everything that exists is either a mind or an idea in a mind.

From the above texts, Berkeley's position was that of Idealism, believing Realism to be absurd. Berkeley was also an Immaterialist, in that there are no material substances but only ideas in the mind and ideas in the mind of God. Berkeley may admit that the tree continues to exist when we shut our eyes, but this continued existence is due to the fact that it remains as an idea in the mind of God.

Imagination is defined as the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses.

IE, as Berkeley's position is that all that exists in either in our minds or the mind of God, and as something that exists as an idea is part of an imaginative rather than real world, I stick by my statement that "some Idealists think the world is a figment of the imagination", including Berkeley.

A kind of unspecified completeness is imagined from the beginning. — igjugarjuk

Yes, as with Kant's a priori pure and empirical intuitions, people have a historically-effected consciousness and they are embedded in the particular history and culture that shaped them. Given this, our interpretation of the world is a matter of "the give-and-take of question and answer, and our understanding of the world changes with the questions we ask of the world and the answers we get back.

It looks to me that we have an entire system here of inherited concepts, which only make sense together. — igjugarjuk

Yes, as with Kant's a priori pure and empirical intuitions, which provides the framework of the mind, as you say: "we have an entire system here of inherited concepts". Through millions of years of evolution we have an inherited framework of the brain, and consequently the mind and self, which of necessity sets limits to what we are able to reason and judge.

But 'forever private experience' opens up an abyss of possibility. It's outside the space of reasons — igjugarjuk

However, even if I may never know your particular subjective experience when observing a wavelength of 700nm, through reason, judgment and imagination, I am able to gain an extensive understanding about it.

The tool we use is language, allowing private sensations to be publicly discussed.

For example, the start of the Universe may forever remain private to us, yet through reason scientists have developed a cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. They have understood how the universe expanded from an initial state of high density and temperature, and have offered a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure.

IE, even private experiences are not outside the space of reason, if the tool we use to understand them is language.

Hume is like an actor on a stage among other actors. His speeches are unified as his speeches..and interpreted as such a unity. — igjugarjuk

Yes, in the world is the mind and the mind-independent. Yet the mind is part of the world, so the mind must share characteristics with what is mind-independent, giving us a link between the mind and what is mind-independent.

In a sense, the mind and the mind-independent make up one unity, giving the mind the possibility of being able to understand the mind-independent, because the mind has evolved in synergy over millions of years within the world. The mind is a product of the world, as is that which is mind-independent.

IE, the mind and mind-independent are part of one greater unity, the world.

Math may be factual and absolute but our senses and understandings are not.

That is to say, take the matryoshka doll for example. You have two in front of you. Any able-visioned person not familiar with the item would conclude you have two dolls. However, if you know more than what can be currently seen (modern science) you would there is in fact much more than two. Same can be implied with half-life and various chemical reactions not yet understood.

Say you know every chemical reaction with 99.99% of possible elements except for one unknown combination never tried before. Due to not properly understanding the nature of it's reactivity you may reach an unexpected result. This is how medicine and chemistry works. The math is not wrong, per se (that is to say, yes, 1 understood value and 1 understood value will equal 2 or it's expected value), simply that there are additional variables that are unknown.

Another common point is that theory guides observation in the first place (tells us what to look for, frames the situation.) — igjugarjuk

I speculate my specialty (infinite compositions of complex functions) is a solution awaiting a problem. :cool:

I speculate my specialty (infinite compositions of complex functions) is a solution awaiting a problem. :cool: — jgill

I hope something comes along and make your work suddenly practical. That'd be exciting. I know it's happened for some mathematicians. (I'm a lesser angel in the field myself, working more in programming languages these days, though, for better or worse.)

Pseudomathematics, or mathematical crankery, is a mathematics-like activity that does not adhere to the framework of rigor of formal mathematical practice. Common areas of pseudomathematics are solutions of problems proved to be unsolvable or recognized as extremely hard by experts, as well as attempts to apply mathematics to non-quantifiable areas. — Wikipedia