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On 2/3/2019 at 2:13 AM, intrinsicist said:

Like begets like. How can a combination of simple elements combine to form something which can't be explained by the nature and actions of its elements? Logically there would have to be some other element that comes into play, hence the conclusion that this idea of "emergence" is magical or superstitious.

Bringing two things together involves applying additional energy or removing energy, and manipulating their entropy.  So emergence is caused by that, it isn't causeless.

The real ontology is that there is mass and energy, and via Einstein mass and energy are equivalent in a deep sense and can be transformed one into the other. But there is at least one other thing which is not mass or energy.  The thing is information in the physical, causal Claude Shannon sense.   Mass/energy cannot exist without embodying information and no information exists without being in the form of some mass/energy.  That's not the same thing as what you want to call a 'mental' aspect of existence but it is in the direction you are seeking.   (A mental aspect of existence is incoherent as Eiuol well described above, you need better framing for that thought.)

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Contrast Wikipedia's neutral presentation of the issue (the problem of universals) with the Introduction to Objectivist Epistemology Forward to the First Edition. Here's the first paragraph from

Is it proper to say that individual trees are not concepts they are just trees but the concept tree objectively refers to the particular trees?  In the same way, a similarity (the common denominator t

This is wrong. Knowledge of a thing does not imply the existence of that thing, since you can have knowledge about things which don't exist (e.g. fictional worlds).

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On 2/3/2019 at 2:21 AM, intrinsicist said:

No I wouldn't say that everything "possesses consciousness". These things all posses a nature or essence, which is part material and part formal (or mental)

The bolded implies consciousness though. There is no "mental" without consciousness.

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On 2/3/2019 at 11:00 AM, Eiuol said:

I'm replying here since I know he won't respond in this way. It does seem like this is his view, but that's because he keeps using the word mental. He doesn't mean that everything has a mental characteristic. He means that everything has a Form of some sort, and this Form exists in a metaphysical sense, not an epistemological sense as we mean by the Objectivist position. It's Platonic realism we're talking about here.

Thanks. I do understand this though. But when I asked where these Platonic Forms metaphysically, first he said something like "why are you asking for the location of an abstraction", and the later said his ideas are Aristotelian instead of Platonic. So he essentially believes in "essences" existing "out there" in metaphysical reality but can't tell me *where* they exist.

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On 1/28/2019 at 6:08 PM, intrinsicist said:

No, for something to have a mental aspect it merely needs to have Form (or "essence", whatever you want to call it), it doesn't need to have any mental capacity for sensation, perception, or concept-formation. You can think about this in the sense of Aristotle's hylomorphic compounds; everything that exists is composed of both Form and matter (the Form being the mental aspect, the matter being the physical aspect).

This doesn't mean everything has a mind, just that an aspect of its nature is mental.

You are clearly contradicting yourself here saying everything that exists has a "mental" aspect, and then saying everything doesn't have a mind. 

I"m done following this discussion because of this. FWIW, I agree the second clause in my above sentence is true, but that the first clause is impossible and you are creating a floating abstraction.

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On 2/3/2019 at 11:00 AM, Eiuol said:

Combining certain neurons doesn't "create" consciousness. It kind of just happens. Really, I think this is another way of thinking about the axiom that you're conscious. You might be able to explain how neurons work when you're conscious, or the neurotransmitters that move around, or the computational processes underlying perception, but you won't be explaining why it has to be this way. You won't be explaining why it emerges, only that it has emerged.

It emerges because a sufficiently complex systems capable of storing past data and processing it all is what causes consciousness. On a different note I think we should eventually stop calling AI "artificial" intelligence artificial. At a certain point when it is both conscious and capable of thinking and reasoning via concepts and abstract thought it is just intelligence with nothing "artificial" about it.

The "big bang" phase transition of our pocket of the larger eternal universe created hydrogen, helium, and a bit of lithium. Some other elements were created by comic rays hitting the protons in those elements and everything else was made in supernovas and neutron star collisions etc. Combinations of these elements can combine in certain ways such that they are complex enough to cause consciousness to arise. And in even more specific situations conceptual minds like are own. But it would be foolish to say the combination that produced our own consciousness is "natural" while other combinations are supposedly "artificial". Consciousness is consciousness regardless of what the elements that were used to produce it. We should call AI alternative intelligence instead if we want to differentiate it from our own.

Sorry, I sidetracked but I'm an INTP and probably have a touch of Asperger's so I tend to think of many different possibilities and concepts at once while trying to connect the concepts in novel ways. So I tend to think in multiple tangents at once. I know it probably makes some of my posts difficult to parse, and I apologize for that. But hey you get a peak inside a slightly autistic INTP's mind for free! lol

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4 hours ago, EC said:

It emerges because a sufficiently complex systems capable of storing past data and processing it all is what causes consciousness.

I get the idea, and I agree with what you said about AI. But I'm wary of saying that "sufficiently complex" has really much meaning except for one necessary condition for consciousness to be present. I definitely don't want to say that it causes consciousness. In some sense it does, as an efficient cause, in the sense that complex parts go together and create a data processor of the sort that consciousness appears. It's more or less an association you make. The way of describing how things happen in your day-to-day.

But it doesn't really get at a formal cause, the theory of why things are occurring. For something fundamental as our own consciousness (consciousness does not exist in pieces), I don't think were going to have a formal cause. It just is. Someone someday will probably be able to produce consciousness definitively in a robot or something. But I don't think that will involve the discovery of why consciousness is happening.

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On 1/26/2019 at 8:50 PM, intrinsicist said:

I don't equate the metaphysical with exclusively the mental or non-mental; rather the root metaphysical substance has both mental and non-mental aspects. So universals exist independently of your own concept-formation process as a person, but they can also exist within your mind (insofar as your mind is capable of grasping a concept, the mental aspect of a universal).

I am trying to understand this.

First, “root metaphysical substance” seems like a concept rather than metaphysical. In other words a “root metaphysical substance” is being labeled as a metaphysical entity, while it looks like an abstraction.

If I were trying to see the tree structure (classification):

  • Root metaphysical substance
    • metaphysical substance
      • where no contradictions exist
    • epistemological substance (mental entity)
      • where contradictions can exist

Keep in mind: The usage (where) is being used as metaphorical although it would support your view as in there is an overall containing space that both exist inside. But then, there can’t be a root metaphysical substance, because contradictions can only exist in the mental realm (not in the same space). Unless you are using it as a metaphor.

Like saying, there is a space where contradictions exist, right next to where contradictions don't exist. That is a contradiction.

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@Easy Truth I'm not following your description... let me try to clarify and tell me if this helps with your question. Let's take a given universal, like say, Man. There is a root metaphysical substance, i.e. manhood, or manness, it is the essence of this universal Man. This metaphysical universal has two aspects: a physical aspect and a mental aspect. Whenever we deal with individual men embodied, each one is an instance of this metaphysical universal, which we are aware of in its physical aspect. Whenever we deal with the concept of "man", this universal concept which we hold in our mind is this same metaphysical universal, which are we aware of in its mental aspect. The universal itself is real and we can be aware of it in both its physical and mental aspects. Neither aspect is more real or more fundamental than the other (that is, it's not the case that the physical is metaphysically real and the mental is epiphenomenal, or vice versa), but rather they are both aspects of the one underlying metaphysically real thing.

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18 hours ago, intrinsicist said:

The universal itself is real and we can be aware of it in both its physical and mental aspects. Neither aspect is more real or more fundamental than the other (that is, it's not the case that the physical is metaphysically real and the mental is epiphenomenal, or vice versa), but rather they are both aspects of the one underlying metaphysically real thing.

1

Doesn't (a universal with) metaphysical substance imply "it has a referent", an instance?

Then do "errors of knowledge" have metaphysical substance?
As in, do contradictions have metaphysical substance?

That which is and is not in the same way and at the same time. Does this have a metaphysical substance?

The logic question that comes up is "how can that which that has no metaphysical substance, be a "root" metaphysical substance?"

"The universal itself is real and we can be aware of it in both its physical and mental aspects". Agreed, but there, you are describing only a universal that has an instance, as in it (the universal) refers to something. When it refers to nothing (metaphical), then there is only a mental aspect.

A contradiction is a universal too. But there is no physical aspect, only mental. It is a real concept in the mind (but not real "out there" (metaphysically)).
 

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Continuing this thread...

Rand believes everything in reality is concrete, that, in reality, there is "no such thing" as the universal "manness" which ties together, and holds true for, all concrete men, at all times and in all places. This "manness" is rather our organization of concrete men. She claims that, by properly organizing concrete men, we can thus arrive at a universal "manness" which does hold true for all concrete men, at all times and in all places.

So... would you all argue that the universal does exist *mentally* but not *in reality*... it *holds true* in reality, it just doesn't "exist" in reality? I guess that's the crux of the thing, this odd reluctance to grant the existence of something "in reality". That's why it's so hard to bridge this gap in communication.

Under a dual aspect metaphysics, I am just granting this idea of an "abstract reality". Some abstraction which holds true in reality, therefore is *real*. It's giving a kind of reifying existence and power to the abstraction, the abstraction is what is *making* it hold true, as opposed to *something else* making it hold true and the abstraction merely "recognizing" that the truth is holding, presumably for some other reason.

It's kind of an odd question- what is the real thing which is making this universal hold true? There must be something with the force of reality which is making this truth hold- what is that force? where does that force come from?

The weird thing to me, is this assertion that there are NO abstractions with this power: only concretes are "really real". But even some given concrete has to have some abstract nature. Are we supposed to think the *material* of the concrete is powering the *nature* of the concrete? It doesn't really make any sense if you think about it clearly. Only the dual aspect perspective, a la Aristotle's hylomorphic compounds, actually makes any sense.

I guess the Objectivist perspective is that we can't say why, but things just "happen" to work universally. That's just the way the concretes behave- but they don't behave that way because of some abstract principle of their nature. That form or principle is just a "way we describe" what matter is doing, it only exists in our own minds, not in reality itself.

It's just bizarre to say that, and also hold that induction is possible, like McCaskey's article, where he insists we have 100% certainty about regularities despite there being no principle of uniformity. How can we have 100% certainty that a regularity will hold, if we deny the reality of some principle to it? There is no way to make a valid inference from any number of observations of a behavior to a universal rule of the behavior. What's to say it won't change, if it's not a real aspect of the thing's nature?

Since the denial of metaphysical universals undermines the justification for any sort of induction or universal concept which holds in all places and at all times, this yields a presuppositional argument for metaphysical universals: any argument which purports to deny them, if it's a logical and justifiable argument, must presuppose and use universal concepts and induction (which in turn rely on universals having metaphysical reality) in order to make that argument. Hence the conclusion that metaphysical universals must be axiomatic.

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1 hour ago, intrinsicist said:

So... would you all argue that the universal does exist *mentally* but not *in reality*... it *holds true* in reality, it just doesn't "exist" in reality? I guess that's the crux of the thing, this odd reluctance to grant the existence of something "in reality". That's why it's so hard to bridge this gap in communication.

When we say a concept exists, I would agree it may be confusing as it could imply that it metaphysically exists (outside the mind (metaphorically speaking)).

A concept exists implies that "it corresponds to some concretes".
For it to be valid/true/real, it has to correspond.
The fundamental reason that a concept can't be physical, is that a concept is able to be invalid.
Otherwise,  you would be arguing that a unicorn is real, or that you can have dinner with Harry Potter etc.
Harry Potter would no longer be fiction, he would HAVE TO BE real.
But he does not exist.

So then what does exists mean? What does real mean?

The realness of a concrete and the realness of an abstraction are observed differently.
And abstraction corresponds, but a concrete just "is".

Why does correspondence HAVE TO BE a concrete?

In all this discussion you have the responsibility to explain where does an invalid concept exist in reality? Is there a special place in the universe where all the zeros "exist"? Is there some planet of contradictions? After all, there must be since all universals are "real".

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18 hours ago, intrinsicist said:

My argument doesn't actually depend on such a premise, merely that some are real. There can still be abstractions in the mind which do not correspond to real universals in reality.

So there seems to be three levels of reality.

1. Concrete (real)

2. Universals that exist intrinsically (Concrete Universals)(real)

3. Universals that only exist in the mind (some real some not??)

I assume that intrinsic universals (2) are valid ones, tableness that refers to actual tables. They are valid because tables exist. But that which is and isn't at the same time and the same place and same way is also a universal (by definition).

Are you saying that non existence is intrinsic too? As in "the universal is inside the thing" when there is no-thing at all?

Does the concept "contradiction" exist or not? Does it have referents "out there"? Does it only referents in the mind? The concept contradiction is something we all use. It is real in some sense. But a contradiction is NOT real.

In the mind, yes a contraction exists. Outside it does not. As in, does "nothing" exist or not? 

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1 hour ago, Easy Truth said:

I assume that intrinsic universals (2) are valid ones, tableness that refers to actual tables. They are valid because tables exist.

I will get into my answer later for intrinsicist, but as a matter of clarification.

Rand would probably claim that all that exists metaphysically speaking (apart from your consciousness)  is 1. The only universals that exist are 3, with the emphasis that they only exist in the mind. 2 would not be anything valid that exists (there are no universals outside of the mind). Objective thinking (rational thinking) is the way we connect 1 and 3 in a valid way. Connecting 1 with 3 would not require some intermediary existent like 2. 

 

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20 hours ago, intrinsicist said:

Rand believes everything in reality is concrete...

It's been awhile. Can you remind me where you're getting this view of Rand's belief? To what specific passage or statement are you referring? You seem to be using some major concepts that Rand did not use to express her view.

In the ITOE workshops ("Concepts as Mental Existents"), Rand makes a distinction between physical entities and mental entities. Both exist metaphysically, but mental entities only exist mentally (in the mind). To me this means that the existence of mental entities depends on the existence of animals capable of producing them. This is imperfectly analogous to physical phenomena, such as the existence of a roar depending on the existence of a lion capable of producing a roar. I say "imperfectly" because we're dealing with fundamentally different kinds of existents. To Rand "mental entity" was a partly metaphorical term, because "entity" implied something physical. She wanted a new word for "mental entity" but was against neologisms. I am not against neologisms and would like to see "mentity" take the place of "mental entity." A mentity is like an entity in that both are things that exist in reality, but it's dislike an entity in that it apparently lacks physical substance and exists only as the product of a brain-possessing organism.

22 hours ago, intrinsicist said:

So... would you all argue that the universal does exist *mentally* but not *in reality*... it *holds true* in reality, it just doesn't "exist" in reality? I guess that's the crux of the thing, this odd reluctance to grant the existence of something "in reality". That's why it's so hard to bridge this gap in communication.

"In reality" can mean "outside the mind" or "in the universe." Universals (concepts) exist in the mind, which exists in the universe.

22 hours ago, intrinsicist said:

It's kind of an odd question- what is the real thing which is making this universal hold true? There must be something with the force of reality which is making this truth hold- what is that force? where does that force come from?

I might be dense but I'm confused by your use of "hold true." A universal is a product of a process of cognition. So the integrity of that process is what determines whether the universal accurately represents reality. I suppose the basic force behind that process is life itself. The life force does not exist in a vacuum though. Living things require a suitable environment--or they die.

22 hours ago, intrinsicist said:

Since the denial of metaphysical universals undermines the justification for any sort of induction or universal concept which holds in all places and at all times, this yields a presuppositional argument for metaphysical universals: any argument which purports to deny them, if it's a logical and justifiable argument, must presuppose and use universal concepts and induction (which in turn rely on universals having metaphysical reality) in order to make that argument. Hence the conclusion that metaphysical universals must be axiomatic.

Are you accounting for the fact that man is not omniscient? By "universal" we cannot mean a concept that "holds true in all places and at all times." Our context of knowledge does not include all places and all times. We might conceive of swans as white, long-necked waterbirds--until we find a black one. The fact that we form erroneous concepts based on limited information suggests that we lack access to "metaphysical universals" even supposing their existence. So why would a rational person base his argument for universals on such a presupposition? I think the basis for universals is the fact that we observe similarities among things. This does not mean, however, that our observation is infallible, because it includes an evaluation which must be constantly checked against new information.

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First, a few points of clarification:

On 11/18/2020 at 1:33 PM, Easy Truth said:

Concrete Universals

"Concrete universals" is a contradiction in terms. You have, on the one hand, concretes, which are specific and particular, and on the hand, universals, which are abstract and general. A concrete would be something like "the man Easy Truth". A universal would be "Man", referring to all men at all times and places.

 

On 11/18/2020 at 4:00 PM, MisterSwig said:

Can you remind me where you're getting this view of Rand's belief? To what specific passage or statement are you referring?

Quote

"I was discussing the issue of concepts with a Jesuit, who philosophically was a Thomist. He was holding to the Aristotelian position that concepts refer to an essence in concretes. And he specifically referred to ‘manness’ in man and ‘roseness’ in roses. I was arguing with him that there is no such thing, and that these names refer merely to an organization of concretes, that this is our way of organizing concretes."

- ITOE

 

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On 11/18/2020 at 1:33 PM, Easy Truth said:

But that which is and isn't at the same time and the same place and same way is also a universal (by definition).

One can mentally construct propositions, e.g. "All men are mortal", which are universal propositions. That doesn't necessarily mean they correspond to a real, metaphysical universal. Any contradictory proposition or invalid concept does not correspond to a real universal.

On 11/18/2020 at 1:33 PM, Easy Truth said:

Are you saying that non existence is intrinsic too?

Emphatically no. Non-existence is a relational term, the negation of the concept of existence (where the valid concept of "existence" does correspond to a real universal).

On 11/18/2020 at 1:33 PM, Easy Truth said:

Does the concept "contradiction" exist or not?

Well contradictions don't actually exist. Again we can reference the phenomenon of mental constructs where someone is holding two contradictory propositions as true, this is a real phenomenon, it's not like the concept of "contradiction" itself is invalid. It just doesn't reference something that happens in reality among real universals. There are generally of course real universals referencing mental phenomena.

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On 11/18/2020 at 4:00 PM, MisterSwig said:

I'm confused by your use of "hold true."

I simply mean, if we talk about some universal, take for example the proposition "All men are mortal", or "Water is composed of H2O" - is this true, in reality, at all time and all places?

Objectivists will claim that universals hold true, that we can have concepts which refer to all units of the kind at all time and all places, or generalized propositions (that one arrives at say by induction) that we can rely on always being the case.

What Objectivists will deny are that these universal "are real" or "exist", that they have some metaphysical reality to them. They will say that all that exists are concretes, that is the only thing that is metaphysically real. They will deny that universals are metaphysically real (McCaskey's article is a striking instance of that, but it is held by Objectivism generally too).

This is odd to me, for the reasons I outlined above.

On 11/18/2020 at 4:00 PM, MisterSwig said:

By "universal" we cannot mean a concept that "holds true in all places and at all times." Our context of knowledge does not include all places and all times... This does not mean, however, that our observation is infallible, because it includes an evaluation which must be constantly checked against new information.

This would be a slightly more consistent position to hold, although you run into terrible, ultimately self-contradictory consequences of course, since you are denying that induction, or any generalized knowledge, is possible. Any concepts or propositions made that generalize outside of some specific set of concretes you've previously observed would be unjustifiable.

I can go further into these problems, however this is not the position that Objectivism tries to stake out. See for example Chapter 2 of ITOE,
 

Quote

1. A concept is not formed by observing every concrete subsumed under it, and does not specify the number of such concretes. A concept is like an arithmetical sequence of specifically defined units, going off in both directions, open at both ends and including all units of that particular kind. For instance, the concept “man” includes all men who live at present, who have ever lived or will ever live. An arithmetical sequence extends into infinity, without implying that infinity actually exists; such extension means only that whatever number of units does exist, it is to be included in the same sequence. The same principle applies to concepts: the concept “man” does not (and need not) specify what number of men will ultimately have existed—it specifies only the characteristics of man, and means that any number of entities possessing these characteristics is to be identified as “men.”

2. The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.

Objectivism tries to claim the possibility and validity of universal knowledge, while denying the metaphysical reality of universals which make them actually possible.

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3 hours ago, intrinsicist said:

Objectivists will claim that universals hold true, that we can have concepts which refer to all units of the kind at all time and all places, or generalized propositions (that one arrives at say by induction) that we can rely on always being the case.

Before I finish my response to you, I want to understand something. Don't be worried about saying something that I probably already know, let's just make it clear what you are thinking of exactly.

There are particulars. There are groupings of particulars, which are units. I want to know exactly how these particulars are wrapped up into a unit.  Philosophically speaking of course, because that quickly gets into cognitive psychology. 

As another way to approach the question: I want to know if you consider units to be mental groupings with the universal, or are units already wrapped up into a unit, separate from your awareness? A different option?  

Either way, an example would help. 

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38 minutes ago, Eiuol said:

I want to know if you consider units to be mental groupings with the universal, or are units already wrapped up into a unit, separate from your awareness? A different option?

Epistemologically, I don't see any problem with Rand's description of concept formation in Chapters 1 and 2, including as it pertains to units. One proceeds from viewing individual concretes, to generalizing them into a view of units of a kind.

Metaphysically speaking obviously all concretes intrinsically are units of a kind. Concept formation is just the inductive process of recognizing them as such and identifying the kind that they belong to.

If we had some sort of diaphanous perception (which we don't) and had automatic mental access to the universal, then you would automatically see every concrete as the unit of its kind. But we don't have innate knowledge like that, you do have to put in the epistemological work to unite concretes together as units and form the concept of the kind.

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20 hours ago, intrinsicist said:

...you are denying that induction, or any generalized knowledge, is possible. Any concepts or propositions made that generalize outside of some specific set of concretes you've previously observed would be unjustifiable.

Consider this.

We don't start out with such universals. Rather we begin with classes limited to previously observed things. We then introspect ourselves classifying new things with similar old things. We then identify the fact that we are classifying all these new things with the similar old things, and so we induce the proposition that all similar things will be classified together. Now we have our universal, our concept. And since we are not omniscient, it is subject to human fallibility and dependent on our context of knowledge.

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21 hours ago, MisterSwig said:

Consider this...

What I said still stands: "you are denying that induction, or any generalized knowledge, is possible. Any concepts or propositions made that generalize outside of some specific set of concretes you've previously observed would be unjustifiable."

McCaskey for example claims:

Quote

If you have good guidelines and follow them, you can be certain that someone absolutely cannot contract cholera unless exposed to the bacterium Vibrio cholerae, certain that all men are mortal, certain that the angles of all planar triangles sum to 180°, and certain that 2+3=5.

Well no, under your system, none of these is certain. No conclusion science has ever achieved can be described as true, or knowledge, or certain. They simply happen to be true under the concretes previously observed, and you predict it will continue to be so.

Yes, even with math. What, you're certain that 2+3=5? At all times and in all places, universally? How? That may have held up under your previous observations, and you may predict that it will continue under similar circumstances, but as you said, all of your predictions are "subject to human fallibility and dependent on our context of knowledge", and as you said, "we are not omniscient", we haven't observed every single instance that has ever occurred. 

@MisterSwigyou said explicitly, "By "universal" we cannot mean a concept that "holds true in all places and at all times.""

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On 11/19/2020 at 3:52 PM, intrinsicist said:

"Concrete universals" is a contradiction in terms. You have, on the one hand, concretes, which are specific and particular, and on the hand, universals, which are abstract and general. A concrete would be something like "the man Easy Truth". A universal would be "Man", referring to all men at all times and places.

Agreed.

On 11/19/2020 at 4:04 PM, intrinsicist said:

That doesn't necessarily mean they correspond to a real, metaphysical universal. Any contradictory proposition or invalid concept does not correspond to a real universal.

Here is where I get lost. Especially when you use the phrase "metaphysical universal". As apposed to what? What is the nature of a non-metaphysical universal? A mental entity? So there are some non-metaphysical universals? So bottom line there are two kinds of universals.

It seems you have:

1. Concretes (metaphysical)

Two types of Universals

A. Valid concepts (metaphysical universals)

B. Invalid concepts/contradictions (non-metaphysical universals)

Versus: there are concretes (metaphysical) and concepts (non-metaphysical)?

1. Concretes

Two Types of Concepts

A. Valid ones

B. Invalid ones

The reason this works better is that "contradiction" is in fact a valid concept. It has no metaphysical referent, no metaphysical concrete that it refers to. But in fact it does refer to something real that is not metaphysical, in the mind or of the mind (non-metaphysical concrete  i.e. mental entity(metaphorically speaking)).

Similar to the concept "nothing". A valid concept, yet non-existent (nothing is a non-existent i.e. there is no such thing).

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19 hours ago, intrinsicist said:

Well no, under your system, none of these is certain.

Not true. I am certain of many things under my system, because my system does not depend on infallibility to achieve certainty. Being fallible, having the capacity for being wrong, does not mean I must always recognize a possibility that I am wrong. First there must be some evidence for that possibility in a particular case. I have the capacity to kill an innocent stranger. That doesn't mean there is a possibility that I killed Nicole Simpson. Likewise I have the capacity to make a mathematical mistake. That doesn't mean it's possible that I made a mistake about two plus three equalling five.

Certainty is achieved when the evidence is sufficient to eliminate all reasonable doubt. In some cases this doubt can be eliminated fairly easily. It doesn't take much effort to lay out two stones next to three stones and see with my own eyes that they total five stones. But if I'm trying to solve the problem of universals, I might never achieve certainty due to the enormous amount of abstract knowledge required to eliminate reasonable doubts.

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