Considering that there is no reason to think otherwise (i.e., evidence to the contrary does not exist) the most parsimonious assumption is that we are seeing what is really there, even if what we see is an incomplete or partial picture, limited by our sensory organs and cognitive abilities. And yes, technically it is correct that we are experiencing observable "phenomena" rather than Kant's "thing in itself" (the "noumena"), but what alternative is there? That is the nature of, and the definition of, perception. I would not call that a limitation, I would call that the way things work.
That we experience an external reality called "the world", I think, is indisputable. Rather, I should say, as a Philosophical Realist, if someone is in the mood to dispute it, it will have to be with someone other than me. That particular debate quickly devolves into pointless speculation. It is not that there is any particular evidence against this kind of Subjective Idealism or other form of Anti-Realism, but that no evidence could possibly bear on it at all, since any real-world evidence would immediately beg the question of real-world existence. That makes the topic uninteresting. And it is pointless because both sides reach stalemate after the first move, short-circuiting any hope of making intellectual progress. So there is no reason to even have the discussion. In any case, there are no compelling reasons to disbelieve external reality, and plenty of reasons to believe it (though I will admit that no deductive proof of it is possible - see here for more). No acceptable competing explanation has been proposed for our experiences in the world. This doesn’t constitute irrefutable proof, instead utilizing “inference to the best explanation”, meaning that among the only set of available explanations, Realism is by far the strongest. Further, Realism is also the only theory which aligns with the proposition made by Hilary Putnam - the "No Miracles Argument", which is “The positive argument for realism is that it is the only philosophy that doesn't make the success of science a miracle”. All other explanations are highly ad-hoc and rely on a steady stream of miracles for them to be correct.
Given that we are actually perceiving something outside ourselves, we do our best to describe it and understand what we are seeing, experiencing, and measuring. Our descriptions reflect the models of reality that we currently subscribe to. Science, which originates the more quantitative and formal versions of these descriptions, does not attempt to provide a perfect representation of reality, but one that "works". The models of science describe with some level of approximation what is being studied, and they "adequately" explain what is going on, allowing us to predict what we are likely to see concerning a particular phenomenon in the future.
In our everyday lives, the less formal models we form of the world (e.g., the mental map we make of a route to a destination, the recipe for a meal) are also stylized, abbreviated, and intentionally incomplete. We do not attempt to, nor can we succeed at making a model that fully encapsulates the reality it is describing.
The primitive, pre-scientific, model of a sun and moon that actually rose and set in the sky had some basic predictive power (you could be sure that every 24 hours the sun would come up). As a model of reality, it provided some descriptive and predictive value, but overall was not very powerful. Its chief weakness was that it did not correspond to the actual mechanical motions of the celestial bodies - it didn't mirror or take into account the actual paths of the celestial bodies. It predicted the right outcomes (sunrises) for the wrong reasons. The more sophisticated Ptolemaic solar system also was a model of the sun and its planets that worked reasonably well at predicting planetary motion. But again, it failed even to approximate the motions of the bodies in the solar system. A better system (more accurate and "truer" as per the "Correspondence Theory of Truth") was the heliocentric model introduced by Copernicus. It was truer in that it bore a closer relationship to the actual structure of the solar system than Ptolemy's model - its level of "correspondence" to the physical reality it described was higher. At least it acknowledged the roughly circular motion of the planets, and put the Sun in the right spot. But even Copernicus' heliocentric model had problems resulting from his dogmatic commitment to perfect geometric forms - he was convinced that the orbits had to be perfect circles, which they aren't. Kepler corrected this error by showing that the orbits were actually ellipses. But Kepler had his own ideological biases. He wanted to fit the five Platonic solids inside each other, wrap them in nested spheres, producing six concentric layers corresponding to the orbits of the six known planets — Mercury, Venus, Earth, Mars, Jupiter, and Saturn. This conceptually attractive ideological position was also was incorrect. Eventually, astronomers who came after Kepler refined our understanding of planetary orbits to the highest level of detail we could achieve using classical Newtonian mechanics. However, in the 20th century, we saw that the orbit of Mercury was different than had been predicted by classical mechanics due to relativistic effects ("frame dragging"). The orbits, once again, had to be refined to take relativity into account.
Does this constant abandonment and/or refinement of old models mean that we don't know, or can't know reality? Not at all! It only means that our mental and mathematical models of reality improve over time, and come closer and closer to approximating what is really going on. We are living through this today with constantly evolving climate models that try to predict global warming. Descriptions are not the same as the reality they describe, but only "point" to that reality. They are references with built-in limits. Not insignificantly, they also can reflect our human bias and preference for finding a single cause or explanation of a set of phenomena that are, by nature, multifaceted and not reducible to one description. Most importantly, models are abstractions and simplifications, and they necessarily filter out and lose some of the detailed richness which exists only in the reality they refer to.
Not all philosophers have even this level of trust in our ability to model reality. Wittgenstein said that we humans cannot experience "ultimate reality" (whatever that means!), but only can create a language that "points" to reality. He is highly critical of scientific explanations, saying that not only do they fail to approximate "reality", but that they only have value in supporting each other. According to him, our laws of nature cast the form that any description of the world must take. They tell us nothing about the world, itself. We can infer some things about the world from the fact that it is more easily described by one explanatory system than another. But we are forever separate from direct experience of it. Wittgenstein's view, however, is not currently "in vogue" with philosophers of science. But it is one dissenting voice.
Some people dispute the assertion that our perceptions and descriptions mirror reality, that they have a "high correspondence" with reality, high enough to say that we can "see reality as it really is". They say that our view of reality is an illusion, a misleading and false image. If they are invoking solipsism, subjective idealism, monism, or some other view that denies an external reality, then let's stop the discussion here. As I have described here, here, here, and here, these are philosophical dead ends, and I have no interest in pursuing them. However, if the dispute relates to our limited human ability to perceive "things in themselves" correctly, or if the question of the meaning of "things in themselves" is interesting, we can continue. Let's look at this using the example of the ostensibly "solid" kitchen table. What appears to be solid is really an object composed mostly of empty space sparsely populated with atoms. Even the atoms, themselves, are mostly empty - nuclei surrounded by distant electrons. The nuclei of those atoms are made of protons and neutrons, which are, in turn, made of quarks and gluons. Some physicists now think that the subatomic particles (quarks, electrons, neutrinos, etc) are themselves manifestations of interacting fields and are not "solid" in the sense that we typically think of that word. And Sean Carrol has written that at a level "under" that, the universe is nothing but a Hilbert Space with a single wave function describing all of reality, and that it has a Hamiltonian that describes the evolution of that wave function (but of what use is that?).
So is the table solid, or is it made of scattered particles, or is it not really made of anything at all? I think that it is correct to think of matter as solid, and to also think of it as mostly empty space, and to think of it as energy, and to think of it as many (or possibly just one) wave function. It is all these things simultaneously. It all depends on the scale of our observations, and the purpose for which we are keeping track of the experience. If you are looking at the table as particles and their interactions, it is not going to tell you much about how to lay out silverware or who should sit next to Aunt Martha. If you look at it at the level of serving Thanksgiving dinner, it is not going to inform you about how matter interacts and is structured. Massimo Pigliucci stated this well:
"Let’s pursue this illusion thing a bit further. Sometimes people also argue that physics tells us that the way we perceive the world is also an illusion. After all, apparently solid objects like tables are made of quarks and the forces that bind them together, and since that’s the fundamental level of reality (well, unless you accept string theory) then clearly our senses are mistaken.Or as Robert W. Batterman wrote:But our senses are not mistaken at all, they simply function at the (biologically) appropriate level of perception of reality. We are macroscopic objects and need to navigate the world as such. It would be highly inconvenient if we could somehow perceive quantum level phenomena directly, and in a very strong sense the solidity of a table is not an illusion at all. It is rather an emergent property of matter that our evolved senses exploit to allow us to sit down and have a nice meal at that table without worrying about the zillions of subnuclear interactions going on about it all the time."
“The idea being that a phenomenon is emergent if its behavior is not reducible to some sort of sum of the behaviors of its parts, if its behavior is not predictable given full knowledge of the behaviors of its parts, and if it is somehow new — most typically this is taken to mean that emergent phenomenon displays causal powers not displayed by any of its parts.”This is not magic, but an expected property of complex systems. Its opposite - the ability to anticipate all higher level behaviors from primitive parts is what would be surprising - to be able to describe a carburetor by examining its springs, screws, and gaskets would be completely unexpected.
No one description will give you all you want or need when you are trying to "explain" the world. Although it may be logically possible to eventually come up with a quantum theory of dinner, we probably aren't going to see any such theory soon. It would not really be useful, in the same way that planning a summer vacation road trip by examining and evaluating every millimeter of highway that you intend to travel would not be useful. The different levels that we model and describe the world assist us to understand it at that level. They are human-created tools that are meant to increase our human understanding. They are not models given to us by the universe we are trying to explain. It is possible to be a materialist, as I am, and believe that the universe is made of "stuff" that obeys the laws of physics, and also understand that this "stuff" interacts and merges in very interesting ways that exhibit increasingly complicated properties and behaviors as its complexity grows. As complex systems and entities come into being through the interactions of their constituent pieces, higher level descriptions and explanations also become more useful. One of the most well known examples is that of statistical mechanics (a mathematical system that applies statistical methods and probability theory to large assemblies of microscopic entities). It is far better at explaining how air moves in a room than any description that involved examining and itemizing each air molecule in the room. This concept applies to most, if not all, complex systems.
So-called "solid" matter is a network of atoms bound together with electromagnetic force. At the atomic level, matter is a sparse field of distant particles. But at a macro level, it is impenetrable to other objects also made out of matter. At the subatomic level inside atoms, the individual elementary particles are not "things" at all, as we think of material objects. They are entities with properties like spin, charge, mass, color, and flavor (to borrow some terminology from quantum physics). It is not clear at all whether these properties that we measure actually correspond to a "thing", or if the properties and their interactions are what constitute reality. This gets into the realist/anti-realist debate. It is not a new concept to think of objects at this level as not objects at all, but "fields" (Michael Faraday first proposed this back in the 1800's). At deeper and deeper levels, we see one layer of "structure" inside another. It may well be that at these quantum levels, reality is nothing but "structured information" all the way down, with nothing resembling what we would call "matter" at the bottom (See James Ladyman: Every Thing Must Go and Max Tegmark Our Mathematical Universe). At this low level, matter itself may dissolve into nothing but information, properties, and relationships of properties. Quantum particles, the ultimate constituents of matter (as far as we know) may be nothing but collections of mathematical properties. For example, the electron has the quantum properties of mass, charge, and spin, and a wave property called its "wave function". That is all - those properties do not decompose into more fundamental measures. In its relation to an atomic nucleus, an electron can occupy an atomic orbital, and when other subatomic particles with their own properties come together, new properties of the components and their relationships emerge. So, in some sense, our intuitive belief that real objects exist "all the way down" may turn out not to be true. But at the higher level of our normal human perception, they certainly do exist.
The idea that underlying reality is pure information, structure, and mathematical properties is part of the philosophic view of "Ontic Structural Realism", which is gaining some support in recent years. This theory states that underlying the most basic of objects - subatomic particles, there exists nothing but mathematical properties and structural relationships between properties that themselves are incapable of further reduction. They are the primitives from which the universe is constructed. They would represent the "foundation" of Foundationalism. According to this view, our best theories in physics do not describe the actual nature of things, but the structure of reality. We should not insist that the nature of the unobservable objects that cause the phenomena we observe is correctly described by our best theories. However, neither should we be anti-realists about science. Rather, we should adopt structural realism and only commit ourselves only to the mathematical or structural content of our theories. This "Epistemic Structural Realism" focuses on what we can know, rather than what actually is underlying what we know.
This allows retention of our structural understanding even as our theories change, augment each other, and even sometimes replace each other. So, Einstein's theory of gravity does not "cancel out" Newton's theory, but alters the understanding of the underlying structure referred to by both theories, which doesn't change. The same would be true of any future Quantum theory of gravity to General Relativity theory. The underlying structural reality of a phenomenon called "gravity" still exists. Our theories and models change and are refined or even revolutionized, but the structural aspects of the reality they describe remains intact. The same could be said of many theories that, over time, have required significant revision or replacement. For example the Thermodynamic/Kinetic theory of heat exchange replaced the Caloric theory, or Lavosier's oxygen theory of combustion replaced the phlogiston theory, and there have been numerous models of the atom over time. Despite the changes to, or even replacement of, those models and theories, the underlying structure representing "heat" and "atoms" persisted. A simple statement of Epistemic Structural Realism is that all we "know" of reality is the structure of the relations between things and not the things themselves. A correspondingly rough statement of Ontic Structural Realism is that there are no "things" at all (at least at the lowest levels) and that structure and relationships between structures is all there is. This is very non-intuitive for a macro-level being. However, that should not be a problem for someone wanting to use the table simply to serve breakfast on, which is how most of us use tables.
It was very likely surprising for our ancestors to discover that supposedly solid matter was a thin collection of atoms interacting with each other from a distance. So what? Whether we like it or not, that is just how matter works, regardless of any pre-scientific opinions we may have harbored (or still harbor) about it before the discovery of atomic and chemical interactions. No doubt it went against conventional "common sense" for this to be the case. Much of what we have learned in science disturbs our complacency - that is the nature of scientific discovery. It certainly went against what seemed to be the case to learn that white light was actually composed of a rainbow of colors, that continents floated on Earth's mantle like bars of ivory soap in a bath tub, that the Earth was not the center of the universe, that space was curved, that simultaneous events were not simultaneous at all, that there were living organisms too small for the eye to see, and so on. Just because new knowledge is intuitively disturbing or (seemingly) illogical, we must defer to what the universe is actually doing rather than what we would prefer it to do. And if it seems to offend our sense of what is and is not possible, so much the worse for our preconceptions. It is wise, humble, and properly respectful to allow Nature and Reality to instruct us, rather than to arrogantly impose our ill-informed, human-centric biases on it.
The view we have of reality (of real objects) depends on our perspective. We know that at a quantum level, objects have one set of characteristics, at an atomic and molecular level a different set, and at a visible macro level, yet another set. The salient characteristics that you focus on at any particular time depend on what use you are making of that object. Our view of reality is not purely objective - we are motivated to describe it in terms that will help us interact with it or understand it in some self-interested way. We describe reality with our models, but our models are not exact mirrors of that reality - they are "approximate" mirrors that only are "provisionally" true (true until proven otherwise), and valuable only to the extent that they help us achieve our goals. If you need a place to set your coffee cup, a wooden table can be regarded as a solid, flat piece of material. If you are a woodworker, suddenly the grain of the wood becomes interesting. If you are a botanist, the individual plant cells in the wood take focus. A structural engineer would see it as the solution to a load-bearing problem, a chemist might be interested in the structure of its cellulose, and a physicist could lecture us on what is going on inside the atoms, etc. The table is all these things. These different perspectives don't contradict each other - they enhance each other. They just describe the same object in different, complementary ways. Each new description deepens and enriches our understanding of the table, rather than muddying it. Choosing among them allows us to focus on the aspects of reality that matter to us at the present moment.
James Ladyman, in his 2013 book Every Thing Must Go (mentioned above), discussed this issue. He proposed that at the level of experience which human beings usually operate, the patterns we perceive really are those of a table. It makes sense to call the pattern we experience in daily living a table because it stable enough in space and time at that level that, for our purposes, it is a table. At the atomic level, you can't say that the table is "really" made of protons, neutrons, etc, because those things are patterns that instantiate yet a more fundamental understanding of reality, which is that they are not made of "things" at all, but interactions of different types of quantum fields. What it means to say, "there really is a table", is that we can be descriptively, predicatively, and explanatorily successful in our dealings with the world by taking there to be an enduring physical object with a certain mass and certain dimensions. Conceiving of that pattern as a conventional table will enable us to keep track of the phenomena and to make predictions, serve dinner on it, and so on. That is the scale of description that we are mostly interested in. At the more fundamental scale of description, not only is it that the alleged particles themselves are made of something else, but rather at this level the table doesn't really exist. Its boundaries give out. At a low enough level, it's not "useful" to track the phenomenon as a table at all.