I think you're adding a bit to the confusion. Relativist and myself are confused with your philosophy regarding what is natural and an illusion.

You are contradicting yourself when you say Pierce recognizes the laws of nature but when we talk about physics you are denying such phenomena.

You also seem to be denying the paradox between what's reality and illusion

If something is an abstract illusion, then by definition it is not a reality. — aletheist

That's correct. The reality of time is just an illusion. And therein lies your paradox.

@Relativist and myself are confused with your philosophy regarding what is natural and an illusion. — 3017amen

Where have I ever said anything about "what is natural and an illusion"? I have consistently been discussing the distinction between existence and reality.

You are contradicting yourself when you say Pierce recognizes the laws of nature but when we talk about physics you are denying such phenomena. — 3017amen

Where have I ever denied laws of nature? On the contrary, I have explicitly affirmed them, but suggested that they are not strictly exceptionless due to the reality of absolute chance.

You also seem to be denying the paradox between what's reality and illusion — 3017amen

I keep asking you to provide a succinct summary of the specific paradox that you have in mind, and you keep failing to do so.

The reality of time is just an illusion. And therein lies your paradox. — 3017amen

No, either time is a reality or time is an illusion. I hold that time is a reality, and you apparently hold that time is an illusion; so there is no paradox, we simply disagree.

If you care to continue the discussion, let's start with this basic understanding regarding time as an illusion, and you tell me what is wrong with this paradox(s):

Sorry, I hate watching videos and strongly prefer reading, so I will ask one more time: Please provide a succinct summary of the specific paradox that you have in mind.

If you care to continue the discussion, let's start with this basic understanding regarding time as an illusion, and you tell me what is wrong with this paradox(s): — 3017amen

Since I do value the conversation, I went ahead and watched the video more carefully, this time typing up a transcription so that I could study what was said and provide my own summary.

The first alleged paradox (attributed to Aristotle) is that the past does not exist (although it did exist), the future does not exist (although it will exist), and the present is just a limit between them; "so time seems to be a nothing dividing something nonexistent from something nonexistent." As I have already explained, my view (and Peirce's) is that the past does exist, and the present--as the determination of time at which the nonexistent (possible/necessary) future becomes the existent (actual) past--is an indefinite lapse, rather than a durationless instant.

The second alleged paradox (attributed to McTaggart) is not as clearly identified. One candidate is that "every event must be one or the other [of past/present/future], but no event can be more than one." My view (and Peirce's) is that every event is realized at a lapse of time such that it is future before the commencement of the lapse, when the initial state of things is realized; present during the lapse itself, when a gradual state of change is realized; and past after the completion of the lapse, when the new state of things is realized.

The other candidate is that "this moment is the only present moment; on the other hand, every moment is present." This is straightforwardly false, or at best equivocal. Every moment is present when it is present, but no longer present when it is past and not yet present when it is future. Moreover, the continuity of time is such that being present rather than past or future is a matter of degree, not a sharp distinction. In Peirce's words, "The events of a day are less mediately present to the mind than the events of a year; the events of a second less mediately present than the events of a day."

Hence I continue to disagree with you (and McTaggart) that time is an unreal illusion.

Abstractions do not exist (not in the real world), they are mental devices that we create via The Way of Abstraction. They reflect types of objects that share some common properties. For example, the abstract object triangle does not actually exist (not in the real world) but triangular objects exist - they are instantiations of the abstraction.

Yes.

Numbers are abstractions, some of which are instantiated in the real world.

As far as we can see integer numbers are instantiated or mapped to the real world, how do you find it reasonable to assume this relation abruptly stops above some very large number or below number one?

As far as we can see integer numbers are instantiated or mapped to the real world, how do you find it reasonable to assume this relation abruptly stops above some very large number or below number one? — Zelebg

I was referring to that fact that infinity is not a number that is mapped to. That fact doesn't entail an upper bound.

And yet, if space is finite, it's contents are finite - which would entail some upper bound. Current physics indicates that space, and its contents, extends in space through a temporal process (described here). This means the extent can only be unbounded if the past is unbounded (which the article also states). The article indicates that current physics does not establish whether there was, or was not, a past boundary in time.

However, there are hypotheses that do establish a past boundary in time. For example, Stephen Hawking's last paper. There are others that entail a finite past, and none that establish an infinite past - they only fail to establish a physical basis for a temporal boundary.

So there may be a physical basis for a past temporal boundary, and there can be no physical basis for an eternal past. But there is a conceptual problem with an infinite past: completeness. The universe, as it exists at this moment (its current extent, including everything within it) reflects a completed temporal process. Processes of infinitely long duration entail incompleteness at every temporal step. We conceptualize an infinite future as follows: every future point in time, Ti, will be succeeded by a point in time Ti +1. i.e. there is no point in time at which there is completeness. Now turn this around: to reach the current moment would entail a completed infinity, which contradicts this conceptualization. This provides a reasonable conceptual basis for believing the past is finite. This doesn't show it to be logically impossible, but a denial entails a burden to provide a conceptual basis for an infinite (completed) past.

I was referring to that fact that infinity is not a number that is mapped to. That fact doesn't entail an upper bound.

While it is true that abstract concepts only exist in minds as mental entities, minds themselves have no other source of information than the actuality of the external world, so they are all ultimately grounded or abstracted from the real world and are really only extrapolations and variations on the theme provided by the universe itself.

In more poetic language you could say that all we do or think can only be just a reflection of what the universe does and what the universe is. To put it bluntly, a bunch of abstract, meaningless symbols like: 0 = -x + x, can actually have a true metaphysical implication and might be our only way to answer the hardest questions of all, such as “why is there something rather than nothing”, and all about continuity / discreteness and infinity of both time and space.

While it is true that abstract concepts only exist in minds as mental entities, minds themselves have no other source of information than the actuality of the external world, so they are all ultimately grounded or abstracted from the real world and are really only extrapolations and variations on the theme provided by the universe itself. — Zelebg

Indeed the Way of Abstraction is grounded in the real world: first order abstractions are mental creations formed by considering several similar (actually existing objects) and omitting all features except for those held in common. Second order abstractions are formed by extrapolating from first order abstractions - they are abstractions of abstractions, and these are not grounded in existing objects (unless they can also be formed in first-order fashion).

I have an SB in Philosophy. I never studied Philosophy of math. (Though I did take a class on Paradox and Infinity taught by George Boolos.)

In my education, I was always taught that numbers are real, abstract entities. When this was asserted, the professor would typically insert some caveat about how not everyone views numbers in this way, but it was easier to conduct philosophy if you made this assumption. So please let's "bracket" skeptical worries about this, they would say.

I'm sure that when I wrote a paper, I could have adopted either position as a premise without argumentation, and received no red marks, as long as I was consistent wrt to this in my argument.

Personally, I see no good reason to reject numbers as being real, abstract things. In fact, it only seems to make one's life more difficult. There are important questions in Philosophy that I actually lose sleep over, and I don't see how being an anti-realist about numbers is going to help me answers those questions. In fact, it would only seem to make my life more difficult in that regard.

If I'm going to be an anti-realist about numbers, why not also be an anti-realist about chairs, for instance. There are physical things that correspond to our human conception of chairs, but are those things really chairs? Or are they really only just bits of space-time quantum probability wave configurations that we have arbitrarily decided to lump together in a way that does not amount to chairs being "real".

I suppose if I were a "real" philosopher, I might be interested in the intricate minutiae of all the myriad positions and arguments that one can make about exactly it means to be "real". But personally, I guess I'm just a dilettante who is more concerned with the answers to very important questions, like,

(1) "Will that internal Star Trek transporter leave me alive? Or will being transported kill me?" (Wanting to know the answer to this question is actually why I started studying Philosophy, and on the first day of Philosophy 101, Judith Jarvis Thompson pointed at me at the beginning of the class, and asked me why I was here in a Philosophy 101 class. I was too embarrassed by the reason I was there to answer her. Little did I know at the time that this is actually a topic of serious philosophical debate!)

(2) Are p-zombies possible, and if not, what explains the fact that no amount of perfectly good reasoning can convince me that they are not? Well, maybe this really means that interactionism is true and p-zombies can't exist, but interactionism just seems way too problematic.

(3) Why is boiling live babies to death something that I should not do? It seems like an indisputable fact that this is true, but all roads of argumentation that would lead to this conclusion seem to be based on very tenuous premises.

(4) Why is there something rather than nothing? It seems to be incredible that there's all this stuff, rather than nothing at all. (Except for numbers and the like.)

So, all in all, how would rejecting the reality of numbers help me in answering what is really important?

|>ouglas

I’m not sure if that article makes one interesting distinction about the abstraction algorithm called “visual perception”. There are colors, clearly an abstraction of who knows what order, but then, there are lines and shapes, and countable discrete things, not quite abstracted, but rather mapped kind of directly.

That sort of thing hints that geometry may hold the truth and perhaps even all the answers, but unfortunately along also comes everything else with all the non-answers included.

One of my focuses is whether or not physicalism is true. Each of the 4 questions you raised are pertinent to that question. If physicalism is true:
1) the Star Trek transporter will definitely kill you, and then create a replica.
2) p-zombies are possible (I think)
3) objective moral values are not existents, so you need to explore psychology, sociology and evolution to understand why most of us don't want to boil babies alive (btw, I prefer my veal to be grilled).
4) existence (rather than nothingness) may be a brute fact, which may not be satisfying - but does that justify choosing an answer (e.g. "God") just because it doesn't leave you hanging?

The ontological status of abstractions is pertinent to physicalism, because they aren't physical, but abstractions don't actually falsify physicalism because they can be accounted for in the Aristotelian way, as I'm doing: they exist in their instantiations, but do not have independent existence apart from these other than as mental objects.
.

I’m not sure if that article makes one interesting distinction about the abstraction algorithm called “visual perception”. There are colors, clearly an abstraction of who knows what order, but then, there are lines and shapes, and countable discrete things, not quite abstracted, but rather mapped kind of directly. — Zelebg

Setting aside the question of what quailia are, colors are first order - we consider objects that are red, and abstract redness from the memory of those perceptions. The geometrical figure "line" is second order - we may envision a drawing of a line on a page, which is imperfectly straight, and 3-dimensional, and imagine its ideal form as one dimensional. A similar process with 2 dimensional objects.

We form concepts about countable discrete things and extrapolate, but these things can also be abstracted directly from something discrete.

And yet, if space is finite, it's contents are finite - which would entail some upper bound. Current physics indicates that space, and its contents, extends in space through a temporal process (described here). This means the extent can only be unbounded if the past is unbounded (which the article also states). — Relativist

The article says quite clearly, and more than once, that we don't know whether the universe is spatially finite or infinite. We can estimate a lower bound on its size, but not an upper bound. The simplest topology consistent with our observations at large scales is an infinite, flat space; this is what the most common current cosmological model posits (so-called FLRW model). However, there are also closed topologies that are consistent with the same observations.

As for your conceptual anti-infinitist argument, this is an old and surprisingly persistent confusion. Quentin Smith had a nice analysis of this and several other such arguments in a 1987 paper Infinity and the Past.

As for your conceptual anti-infinitist argument, this is an old and surprisingly persistent confusion. Quentin Smith had a nice analysis of this and several other such arguments in a 1987 paper Infinity and the Past.

Involving infinity neither side of the argument can be semantically valid. One side wants to count from the beginning where there is no beginning, and the other side has to say something like “infinite amount of events actually occurred”.

Infinite events could not have occurred, semantically, they would have to be still occuring, just like infinite future events can not ever occur by some point in future time and instead would have to still be occurring at every point in time, by definition.

Infinity is a concept defining indefinite, there is no reason to expect any logical / semantic manipulation of such a concept can squeeze some definite or meaningful answer out of it. We need to be asking other kinds of questions, it seems, if there is any actual answer to be found at all.

If one apple exists on a table there is one apple. If zero apples exist on a table there are zero apples. zero exists.

As for infinite, there are infinite real numbers and only time will tell whether infinite exists. How much do you want to bet that infinite exists? A penny?

We can talk about infinity in percentages though. For example, if time and space are infinite, would there be more planets that are completely identical or those that are different in some way? There will be more identical ones. So chances are there is Earth clone planet in the neighbourhood and there your clone is reading this same sentence right now. Don’t you two have anything better to do?

In my thoughts, zero cannot exist. Zero is essentially nothing, and nothing cannot be. On the opposite end, infinity seems to be a human construct to represent things that extend past our comprehension. There would, probably, be no way to ever know if the truth is finite.

We can talk about infinity in percentages though. — Zelebg

Novel notion, Z! How would you describe 50% of infinity? :chin:

It depends on what you mean by exist doesn't it? From what I gather existence to you has to be physical - tangible and perceivable through the senses. Existence so defined implies nothing of the mind, let alone numbers, exists. The onus then is on you to show us why you're specifically concerned about infinity and zero. What about their nonexistence is nontrivial?

The article says quite clearly, and more than once, that we don't know whether the universe is spatially finite or infinite. We can estimate a lower bound on its size, but not an upper bound. The simplest topology consistent with our observations at large scales is an infinite, flat space; this is what the most common current cosmological model posits (so-called FLRW model). However, there are also closed topologies that are consistent with the same observations. — SophistiCat

Physics will never be able to prove the past is infinite, all it can possibly do is to show that no past boundary of time has been found.

As for your conceptual anti-infinitist argument, this is an old and surprisingly persistent confusion. Quentin Smith had a nice analysis of this and several other such arguments in a 1987 paper Infinity and the Past.

Thanks for the article. I'd seen it a few years ago, but forgot about it. However, it does not address my argument.

My argument is in the spirit of David Conway’s, in that I utilize the concept of completeness. However, Smith’s refutation doesn’t apply to my argument. I’m not making the bold claim that an infinite past is logically impossible, I simply claim that there’s no conceptual basis for considering it POSSIBLE, and therefore it’s more rational to reject it. An infinite past entails the completion of a sequential process of infinitely many steps, each of which is of finite duration. How can an infinity of days become completed? Our concept of an infinite future entails a process that never ends. This concept isn’t reversible to the past because the past has ended. All Smith does is to assert the past can be mapped to the (infinite) set of negative numbers – a logical relation, that doesn’t account for the process.

If one apple exists on a table there is one apple. If zero apples exist on a table there are zero apples. zero exists. — christian2017

Only in your mind, because you're considering the possible presence of apples on the table. Suppose there were oranges and bananas on the table. The negative fact (there are no apples on the table) provides no information about what DOES exist on the table.

There are no more truths than those entailed by the conjunction of all positive truths, so negative truths are redundant.

It depends on what you mean by exist doesn't it? From what I gather existence to you has to be physical - tangible and perceivable through the senses. Existence so defined implies nothing of the mind, let alone numbers, exists. The onus then is on you to show us why you're specifically concerned about infinity and zero. What about their nonexistence is nontrivial? — TheMadFool

I'm not insisting that only physical objects have existence - I'm open to other possibilities, but I suggest we should be parsimonious in our assumptions of what actually exists in the world. I'd be fine accepting the existence of angels and devils despite being immaterial, if their existence is needed to explain some aspect of the world. I accept the existence of mental objects (exactly what they are depends on what the nature of mind is). On the other hand, abstract objects (all of them, not just infinity and zero) ostensibly exist independently of minds. Where are they? Why include them an an ontology? They aren't causally efficacious, and they can be accounted for without assuming they are components of the world. We need to treat them as existing when doing math, but this utility doesn't force us to treat them as actual, independent components of the world. Math works just fine even if they're just useful fictions.

I'm not insisting that only physical objects have existence - I'm open to other possibilities, but I suggest we should be parsimonious in our assumptions of what actually exists in the world. I'd be fine accepting the existence of angels and devils despite being immaterial, if their existence is needed to explain some aspect of the world. I accept the existence of mental objects (exactly what they are depends on what the nature of mind is). On the other hand, abstract objects (all of them, not just infinity and zero) ostensibly exist independently of minds. Where are they? Why include them an an ontology? They aren't causally efficacious, and they can be accounted for without assuming they are components of the world. We need to treat them as existing when doing math, but this utility doesn't force us to treat them as actual, independent components of the world. Math works just fine even if they're just useful fictions. — Relativist

Infinity exists for the simple reason that if you were to task me to write down all the natural numbers then that would be an instantiation of infinity in the real world.

If I had 5 pennies in my wallet and I gave you all of them then my empty wallet is a real-world instantiation of zero.

As I see it, the concrete precedes the abstract, the latter being derived from the former. Doesn't it follow then that "all" abstract objects will invariably be instantiated in a concrete object?

The abstraction "triangle" that exists in your brain is spatially located in your brain, so it is not the identical object located in my brain. — Relativist

It is no more ‘located in the brain’ than actors are located inside televisions. Rather a rational mind is able to recognize such concepts which however are not dependent on being recognized in order to be real.

Abstractions do not exist (not in the real world).... — Relativist

I think an objection can be raised here at the outset. The statement about 'the real world' falls for what has been described as the 'myth of the given' - which is, as I understand it, the notion that there is indeed a real world which we know independently of the conceptual processes required for the statement 'there is a real world'. In other words, in respect of this topic, it begs the question, i.e. assumes what it sets out to prove.

I say that such an assertion implicitly pre-supposes a division between the 'real world' which is presumed to exist independently of any conceptual framework, and the purported 'internal world' of ideas, concepts and abstractions, but that this division is really a false dichotomy.

The problem is that as soon as you proffer any judgement of what the real world is, then you're already relying on abstractions. You have your ramified concepts of 'what is real' and how to arrive at judgements about it, and so on - all of which rely on abstractions in some fundamental sense, us being language-using beings. Of course, we don't notice we're doing that, and often it doesn't matter that we don't notice it, but in this case, 'noticing it' is fundamental to the topic itself. So at the outset, I'm questioning this assumed distinction between abstracta and purportedly real objects. Humans look at real objects through a framework of abstracta, such as language, mathematics, and scientific theory. What things are outside of, or apart from, that framework, is in some sense a meaningless question. An oak tree is a perch to a bird, a meal to a termite, and fuel to a fire. To a botanist it is a member of the genus Quercus. What is it, really?

And the problem with your theory of numbers, is that it fails to account for the 'unreasonable efficacy of mathematics in the natural sciences'. This unreasonable efficacy has enabled science to perceive many fundamental things which it could never perceive by unaided sensory experience; because, in some sense, mathematical reasoning both predicts and explains relationships on some fundamental level, then science has been able to deduce mathematical principles with universal applicability. And the empiricist dodge of trying to account for them in psychologistic terms doesn't do justice to this ability.

Real numbers, for example, are real in that they're the same for anyone who can count. The nature of their reality is what is at issue - which is an inconvenient truth for naturalism, which believes that existence has a univocal meaning - that everything that exists, exists in the same way. As soon as you're obliged to say ,'well, it depends on what we mean by "exists"', then you're no longer in the territory of naturalism, and many easy assumptions no longer hold.

Only in your mind, because you're considering the possible presence of apples on the table. Suppose there were oranges and bananas on the table. The negative fact (there are no apples on the table) provides no information about what DOES exist on the table.

There are no more truths than those entailed by the conjunction of all positive truths, so negative truths are redundant. — Relativist

If there are 2 apples on the table, but not 0 or 3 apples on the table then 0 and 3 still exist. What can be applied to 3 can also be applied to 0 atleast in this case.

Infinity exists for the simple reason that if you were to task me to write down all the natural numbers then that would be an instantiation of infinity in the real world. — TheMadFool

You have described an uncomp!etable task,not an existent.

If I had 5 pennies in my wallet and I gave you all of them then my empty wallet is a real-world instantiation of zero. — TheMadFool

Negative facts do not establish what exists.

As I see it, the concrete precedes the abstract, the latter being derived from the former. Doesn't it follow then that "all" abstract objects will invariably be instantiated in a concrete object? — TheMadFool

As I see it, the concrete precedes the abstract, the latter being derived from the former. Doesn't it follow then that "all" abstract objects will invariably be instantiated in a concrete object? — TheMadFool

We can abstractly consider geometrical objects of 4 or more dimensions. That doesn't imply such things exist in the world.

Infinity exists for the simple reason that if you were to task me to write down all the natural numbers then that would be an instantiation of infinity in the real world.

You are referring to the concept of infinity that can not actually exist, by definition. The concept does not represent a thing to exist or not exist, nor it represents a collection or set of things. It represents an unfinished process of counting, and as such whatever it is accounting for can not exist because it is in perpetual state of becoming, just like you can not say a washing machine exists while its parts are still on assembly line and has not been put together yet.

The abstraction "triangle" that exists in your brain is spatially located in your brain, so it is not the identical object located in my brain.
— Relativist

It is no more ‘located in the brain’ than actors are located inside televisions. Rather a rational mind is able to recognize such concepts which however are not dependent on being recognized in order to be real. — Wayfarer

Each TV has its own set of pixel producing devices, and while you and I may perceive nearly identical images, the images in my brain are in MY brain, not yours.

Abstactions like triangles are well defined, that's why we can each consider objects with triangular properties, and engage in the way of abstraction. That does not entail the independent existence of the abstraction, "triangle".