# Circularity in definition of Real

I'm having a hard time understanding the adjective 'real'.

In some sense, we get that x is real iff x is in reality. So to say that y is a real boy, is to say that y is a boy, and y is in the collection of things that are real.

So, in some sense, there is a larger collection, call it real-unreal-surreal, that has as a subset the real objects.

But this leads to a circularity: we define 'reality' as the collection of real things -- and define what is real to be what is in reality.

The situation is akin to defining A to be the set of x such that P(x), and then claim that P(x) iff x is in A. This turns into defining A as the collection of x such that x is in A. This makes no sense.

More precisely, the definition A = {x: x ∈ A} makes no sense to me. This is just stating the extensionality axiom in some sense. How can we define Reality = {x: x ∈ Reality} and make it be informative?

• Not a good definition. Perhaps you should use the Kantian approach: there's what is empirical/physical (what comes from the senses) and what is rational/metaphysical (what comes from the mind). Of course, there's a lot of metaphysical facts that have a high load of direct influence from experience, for that, check the meaning of synthetic a priori. Reality can be associated with the former, with the facts of the world, with sense experience. Nov 23, 2023 at 21:59
• time past (and time future)...
– user67675
Nov 24, 2023 at 7:01
• We define "reality" as the collection of things out there, but we do not thereby specify what is in that collection. For that, we have to go out and look. There is no circularity, only ambiguous use of words. Nov 24, 2023 at 7:29
• We cannot define everything; good example: A = { x: x ∈ A } is not a definition. A good definition will be: A = { x: Px } where Px is some "property". Thus, what is the "hyper-general" property that applies to everything? Maybe ontology is the discipline trying to address this question... See Logic and Ontology and Object. Nov 24, 2023 at 8:52
• @MauroALLEGRANZA The issue is the confusion that arises when P(x) is the statement that x ∈ A. I will consult the resources.
– Mani
Nov 24, 2023 at 16:40

OP: How can we define `Reality = {x: x ∈ Reality}` and make it be informative?

Short answer: `Actuality = {x: x ∈ Reality && x.exists}`

Kant defines something as 'real' if it is possible, in contrast to being 'actual' if it is brought to existence by cognition. He does not deal with broad scientific realism because his antinomies have demonstrated incoherence with infinity and finitude in time and space; so he proceeds from what he is certain of: his experiential cognition.

As regards the existence of things, Aristotle defines 'a thing' as composed of concept and predicates: e.g. apple + red. Kant revolutionises this by declaring that existence is not a predicate: i.e. from Kant's Critique of Pure Reason A598/B626, original here:

Being is evidently not a real predicate, that is, a conception of something which is added to the conception of some other thing. It is merely the positing of a thing, or of certain determinations in it. Logically, it is merely the copula of a judgement.

The copula constitutes the "is" in the experiential observation that "the apple is red": the cognitive judgement involved in joining concept with predicate makes the existence of the red apple.

Prior to encountering the red apple Kant holds open the real possibility of apples of any possible colour (for an apple). He might really find a green apple. The sum of all these available, real possibilities he calls reality. For example, as Kant sits under a tree in reality he is mindful that an apple might fall on his head. He has to navigate reality on his daily walk looking out for real possible cyclists speeding round the next corner looking for apples.

His world of possibilities is noumenal while the things he encounters in actuality are phenomenal. The foregoing hopefully elucidates the following, from the Critique of Pure Reason:-

Ch. III. Section ii. Of the Transcendental Ideal (Prototypon Trancendentale).

If, therefore, a transcendental substratum lies at the foundation of the complete determination of things—a substratum which is to form the fund from which all possible predicates of things are to be supplied, this substratum cannot be anything else than the idea of a sum-total of reality (omnitudo realitatis). In this view, negations are nothing but limitations—a term which could not, with propriety, be applied to them, if the unlimited (the all) did not form the true basis of our conception.

This conception of a sum-total of reality is the conception of a thing in itself, regarded as completely determined; and the conception of an ens realissimum is the conception of an individual being, inasmuch as it is determined by that predicate of all possible contradictory predicates, which indicates and belongs to being. It is, therefore, a transcendental ideal which forms the basis of the complete determination of everything that exists, and is the highest material condition of its possibility—a condition on which must rest the cogitation of all objects with respect to their content. Nay, more, this ideal is the only proper ideal of which the human mind is capable; because in this case alone a general conception of a thing is completely determined by and through itself, and cognized as the representation of an individuum.

Heidegger also casts some light in The Basic Problems of Phenomenology, Chapter One Kant's Thesis: Being Is Not A Real Predicate, page 34

The concept of reality and the real in Kant does not have the meaning most often intended nowadays when we speak of the reality of the external world or of epistemological realism. Reality is not equivalent to actuality, existence, or extantness. It is not identical with existence, although Kant indeed uses the concept "objective reality" identically with existence.

The Kantian meaning of the term "reality" is the one that is appropriate to the literal sense of the word. In one place Kant translates "reality" very fittingly by "thingness," "thing-determinateness." The real is what pertains to the res. When Kant talks about the omnitudo realitatis, the totality of all realities, he means not the whole of all beings actually extant but, just the reverse, the whole of all possible thing-determinations, the whole of all thing-contents or real-contents, essences, possible things. Accordingly, realitas is synonymous with Leibniz' term possibilitas, possibility. Realities are the what-contents of possible things in general without regard to whether or not they are actual, or "real" in our modern sense. The concept of reality is equivalent to the concept of the Platonic idea as that pertaining to a being which is understood when I ask: Ti esti, what is the being?

Hopefully that gives a definition of 'real' without circularity. Heidegger carries forward Kant's understanding of the existence of things, but mainly turns his attention to the existential nature of the observer/cogito: Dasein, and then the foundation of Dasein. The subjective nature of 'things' is maintained though, including the real as possibility.

OP: So, in some sense, there is a larger collection, call it real-unreal-surreal, that has as a subset the real objects.

Instead: There is a larger collection: real possibilities (reality), that has a subset of actual objects (actuality).

• So if we define Reality to be the sum of all possible things, then I'm confused as to how to delimit possibility. Let Reality = {x: x is possible}. Then I may ask, what does it mean for the predicate is-possible to hold of x? What is the negation? What object occupies said negation? If this is seen as a universal set, how does one contend with the problems tantamount to universal collections?
– Mani
Nov 27, 2023 at 20:01
• @Mani If a purple apple is-possible then it is possible in Reality. Negation to zero would be 'concept of nothing' + no predicates. Alternatively, 'no determination' would be Kant unaware of possible cyclists or apples. I suppose the possibilities available are always the universal collection although it might not have occurred to Kant to look out for rogue AI robots zipping round the next corner. Nov 28, 2023 at 11:25
• I'm not sure if I follow. If possible in Reality is the overarching set, how do we deal with the problems of self-refrence and such that arise from such universal sets? And, furthermore, I'm not sure if I understand your reply about the negation of zero -- what exact;y do you mean by concept of nothing + no predicate?
– Mani
Nov 28, 2023 at 22:57
• @Mani — Re. "how do we deal with the problems of self-reference"? One's self, (or one's Dasein) is primarily subjective and there might be a difficulty in treating it fully objectively as a 'thing' in the 'universal set' of possible things. There might be a problem including nothing too:— is nothing really possible if it disappears as soon as it is actualised, or perhaps that actually satisfies its actuality. Nov 29, 2023 at 9:03

Some concepts are fundamental, in the sense that they cannot be explained in terms of anything simpler. For example, distance, time, mass and charge cannot be broken down into more fundamental ideas. Reality is similar, in the sense that you cannot explain it in terms of more fundamental concepts, so any attempt to define it will necessarily be circular in some way.

... to say that y is a real boy, is to say that y is a boy, and y is in the collection of things that are real.

You might find it useful to reflect on Real Men Don't Eat Quiche, by Bruce Feirstein: specifically, does Feirstein mean the same thing by "real" as your good self? Does a "real" boy grow up to be a "real" man?

I think the problem is not that "real" is circular; rather it is a complicated word with many meanings (7 in my Merriam-Webster). Are the boys in Lord of the Flies real boys?

1. No. It is a work of fiction.
2. Yes. William Golding "...read what he deemed to be an unrealistic portrayal of stranded children in the youth novel The Coral Island: a Tale of the Pacific Ocean (1857) by R. M. Ballantyne, which includes themes of the civilising effect of Christianity and the importance of hierarchy and leadership." He wondered about writing a novel about "...children who behave in the way children really would behave?" In this sense they are "real children", or, at least, more real than Ballantyne's children. Maybe "real" is a continuous quantity.
3. Yes. I'd expect Ralph, in LOTF, to grow up to be a "real man", in the 1950s sense of the phrase.

You say :

I'm having a hard time understanding the adjective 'real'.

Well, you should, because no-one knows.

For example, if you go to Wikipedia to find out what is "earth" you will end up with "particle" which can be described by several physical or chemical properties. My point is that by trying to describe something you eventually end up describing its behavioural aspects.

We may agree in the behavioural aspects of things, and even formulate theories about them, but what is "real" cannot be defined with a reference to something other than how the thing appears to us.

"Real" in its purest form, is a philosophical concept, and we can talk about it in the context of ontology only.

• This problem of determining one thing by another is why Heidegger says "Being and the structure of Being lie beyond every entity and every possible character which an entity may possess." (Being & Time, H.38). He might as well say "X and the structure of X lie beyond every entity... ", and then try to figure out what X is. Nov 27, 2023 at 19:33
• First move is to posit that X is the foundation/ground of things (including Daseins), so X cannot have what things have otherwise thingness would be in the foundation of what is founded: one thing determining another. Things come from determination so X must be undetermined. Nov 27, 2023 at 19:48

The statement that the set of real things contains real things obviously does not define "real".

I agree with Descartes, the overarching set is our Experience (all the things in our current experience). Reality is then a matter of definitions within this set.

If we are a scientist we would define reality as things that are tested with the scientific method. This is where other people in our Experience repeat a recipe for observing a phenomenon or relation. If we receive reports in our Experience that the phenomenon is observed then we, as scientists, may say it is real. "Scientifically Real" is then the set of all things that could occur in our Experience that have been tested with the scientific method.

The quale "green" is agreed to occur in the Experience of most people in my Experience so I can admit "green" to a new set: "quality reality". If I have a unique occurrence in my Experience it is in "personal reality"

Are things outside of Experience, like electrons, real? They are implied by scientific reality.

Is "real" all physical things? The idea that reality is all physical things is probably equivalent to saying reality is the universe. It does not aid our analysis of particular events or groups of events and is implied from our Experience, not currently within it. It does not even answer the question "which universe?". The one that is entangled with ourselves as observer?

There was an elegant point made in the comments about the actual and the "scientifically real". Swapping our classification scheme from what is evident in our Experience to what we consider to be "actual" usually involves assumptions about who is doing the viewing. If we imagine an external, universal observer who views the universe then the "actual" could be characterised as its Experience and we as within its Experience. If we do not add this imaginary, external, universal observer we must fall back on our equations as models of a possible wider world.

The idea that something in the universe that has never been observed is actual in the absence of any observation (at any time) can never be scientifically tested. It is a belief, it doesn't even have a probability of being true because there are no means to test the truth (where scientific truth is an agreed description between observers). If there is no observer and there has never been an observer then there is no way to create the sets of any "real" things.

Meanwhile, whilst science ploughs on I still have all the other realities. The last fictional work I read created an imaginary world that was real as an imaginary world. I can even imagine a set of actual things that exist without me or any other observer having observed them or their kind but of course that is only "real" as an imagining.

• "Scientifically Real" corresponds to 'Actual' in Kantian terminology. In contrast, the Kantian 'Real' would include the undiscovered subatomic particles etc. Since most scientists would only be concerned about the real particles that become actual I assume the distinction is not very useful for them, hence the interchangeable use of real and actual in ordinary parlance. Nov 27, 2023 at 13:27
• Good point. I have tried to include it in the answer above. Nov 30, 2023 at 21:06