What I'm aware of is this: every abstract idea is basically mined from the concrete.Your numerical example is perfect for demonstrating that: an idea pulled out of sets/collections of concrete objects. If so then zero must be an abstraction of sets that contain no members. Infinity, being more of a concept than an actual number, is to me, simply an extension of finite concrete sets, understandable in terms of the never-ending process of adding elements, say adding 1 to the preceding element, to a preexisting set. — TheMadFool

Your suggesting that: since concrete objects entail abstract objects, that all abstract objects entail concrete objects. That does not follow; it commits the fallacy of affirming the consequent.

First order abstractions are formed by considering multiple objects of the world that have some common features, and mentally discarding the features that distinguish them. Second order abstractions are mentally constructed by extrapolation of first order absteactions - they don't necessarily have instantiations in the real world. Consider extrapolating from squares to cubes, to tesseracts, and beyond to higher dimensional analogues of cubes. They can only exist in the world if the world actually has that number of spatial dimensions.

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. — Wayfarer

Yes, I assume that the images in our mind are different from the objects beyond our minds. Only you have access to your mind's contents; the content is subjective, and it comes to exist solely through mental activity, and ceases to exist when your mind ceases to exist (or sooner; you don't remember all the details of all your past experiences). This is different from objects of the external world, which exist independent of minds - they have objective existence.

And the problem with your theory of numbers, is that it fails to account for the 'unreasonable efficacy of mathematics in the natural sciences' — Wayfarer

The objects of the world are states of affairs whose constituents have relations to one another, and these relations can be described mathematically. I'm not saying the rekations don't exist, I'm just saying they don't exist independently of the states of affairs in which they are instantiated.

Does it really make more sense to suggest the relations exist independently, and the states of affairs that exhibit them have some sort of ontic relation to those platonic objects? The efficacy of math is not dependent on it.

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".

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.

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.

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.

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.

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.

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.
.

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).

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 think no beliefs are properly basic, because foundationalism is false, — Pfhorrest

You disagree with foundationalism, but do you have any other particular system for evaluating the reasonableness of your beliefs, and the beliefs of others?

Do you think belief in God can be rational? If the answer is yes, then Plantinga's Reformed Epistemology may be irrelevant to you. If no, then please describe your basis for thinking that.

If Bernie runs, even if it were more likely that he would lose to Trump, there's still a good chance Bernie will win. Let's call that chance x%.

That means there's a (100-x)% chance the status quo will change in the opposite direction.

A risk-based approach means Bernie is the only viable candidate. — Benkei

You are giving weight to changing the "status quo" and it seems you are saying Bernie, and only Bernie can possibly do that.

What specific status quo changes do you seek?

Are my big issues at all relevant to you? Do they fit into, or out of, the status quo? They are: rescuing Obamacare and improving access to affordable health care, judicial appointments (which indirectly protect abortion rights), comprehensive immigration reform, and social security reform. I overlap with Bernie supporters in also wanting to make it easier to climb out of poverty (which I did, growing up in the 1960s-70s). I give the edge to Bernie only on that last point, but I have low expectations about what he could possibly accomplish. I very much like his voting record, but he hasn't gotten any revolutionary bills to pass (he's the principle sponsor on a total of 7 bills that passed, during his 13 years in the Senate).

That seems to suggest he did not believe there are laws of nature, because these entail necessitation. Perhaps he had a Humean view of regularities rather than law.

Personally, I’m even more convinced that the game is rigged... to put it bluntly. Thoughts? — 0 thru 9

I don't think anyone, or any group, has rigged it. Nature is taking its course, and voter complacency (regardless of reason for it) helps define the course.

It's a de facto ologarchy, but one can't just blame the "oligarchs". The populace has the power, but to exercise it they'd have to take the time and make the effort to learn more. In another thread, I complained that voters are stupid. Someone wisely corrected me - it's not stupidity, it's that people don't have the time and resources to learn and get involved. Nevertheless, the latent power is there, so responsibility is shared.

said that the future does not exist because it is indeterminate; — aletheist

There are components of the future that are determinate, for example: the positions of the planets with respect to the sun, at this exact time tomorrow. Does this determinacy mean it exists?

What about you? Will the governments of the world be our hero in the battle against climate change? — NOS4A2

The odds are against governments eliminating the problem, but there's a good chance governments can produce meaningful benefits - so it's wothwhile to push.

Well, I’d go further and say I oppose government intervention in general. I don’t think we need it to tackle climate change. I do believe that humans can get together and cooperate to solve problems without the coercive force of the government. — NOS4A2

I can respect the libertarian principle that less is best for government, even though I don't embrace it. But where collective action is needed, like climate change in particular, there is no hope for this being solved by a free market or by individuals voluntarily choosing to behave nobly.

If you set aside your belief that action is unnecessary, and accept the premise that action IS needed (hypothetically), would you agree?

Sure, but intuitively - A and B have equal, independent ontological status, and his approach doesn't seem to acknowledge that. Instead, it treats that alternate universe the same as an abstraction -real but not existing.

Also, not to nit-pick, but Trump didn't do shit. — Benkei

That judgment depends on what your priorities are.

And Bernie isn't going to change anything about it. But his political base might if they realise that winning or losing isn't the end of the fight. He seems to be the only candidate that has such a politically motivated base at this time. — Benkei

What happens to them in the likely event that he's ineffectual?

You have a good point but I think Plantinga might argue that a "proper functioning" person cannot sensibly doubt God's existence.

The US needs not only a political shift but a cultural one as well and that's not going to happen with another status quo candidate. — Benkei

Trump has shifted the status quo toward xenophobia, racism, and celebrating inequality, and that will only get worse in a second term. And I seriously doubt Bernie will be able to actually do any more than any other candidate. None of the ambitious policies he pushes are likely to pass. On the plus side, he will be a voice. In my book, getting a voice is not worth the risk of a 2nd term for Trump.

The statement that God exists is not the same as "My hand exists." We don't have direct experiences with God, at least not in the sense that we do with our hands, or even our mothers, fathers, siblings, friends, etc. This would be true even if some people did have direct experiences with God. Why? Because most of us don't have direct experiences with God — Sam26

On the contrary, Plantinga claims that most people DO have direct exprerience - a sense of divinity that produces beliefs about God:


The sensus divinitatis is a disposition or set of dispositions to form theistic beliefs in various circumstancs, in response to the sorts of conditions or stimuli that trigger the working of this sense of divinity. ...this knowledge of God is not arrived at by inference or argument but in a more immediate way. The deliverances of the sensus divinitatis are not quick and sotto voce inferences from the circumstances that trigger its operation. It isn't that one beholds the night sky, notes that it is grand, and concludes that there must be a God....It s rather that, upon perception of the night sky...these beliefs just arise in us. They are occasioned by the circumstances; they are not conclusions of them. -- Warranted Christian Belief, p173-175

This is analogous to seeing a hand, and this producing the belief "my hand exists".

I oppose any Green New Deal because it is uniquely authoritarian and statist. — NOS4A2

By opposing any Green New Deal, does that mean you oppose any government interventiions that are aimed at reducing greenhouse gas emissions?

If yes, do you really believe the free market can solve the problem?
If no, then what sort of interventions do you favor?

That seems problematic, since it makes existence relative, and both A and B have being.

From a metaphysical standpoint, Charles Sanders Peirce drew a helpful distinction between reality and existence. The real is that which is as it is regardless of what any individual mind or finite group of minds thinks about it, while existence is reaction with other like things in the environment. Accordingly, abstractions and other immaterial objects do not exist, but some of them are nevertheless real. — aletheist

Hypothetically, suppose there are 2 "universes" (A and B), the products of independent big bangs, but separated by sufficient space (or dimensionally) that they are causally independent of one another. From A's perspective, does B exist? Is B real?

Sure, Trump's a symptom of a cancer, but another term will mean it's metastasizing. Metaphors aside, see my prior posts for some of my biggest concerns that are likely to be better under any Democratic candidate.

What do you see about him that's different? — Pfhorrest

Here's a few biggies:

He would be likely to appoint a replacement for Ruth Bader Ginsberg who will have a similar judicial philosophy, and thus retain the right of a woman to control her own body. Trump will replace Ginsberg with someone likely to deny that right.

He would likely support comprehensive immigration reform (including protection for "dreamers"), whereas Trump wants to limit it as much as he can get away with, and would be fine with deporting "dreamers".

He's support measures to protect and extend Obamacare. Trump will do everything possible to kill it.

He is unlikely to interfere in the criminal justice system, while with Trump - interference is standard operating procedure.

There is a significant problem with that in the context of our present discussion, Relativist...one that should be obvious to everyone. — Frank Apisa

You can use whatever definition you like for purposes of your discussion. I was just making a general comment not directly related to what you were saying.

As far as I can tell, he'd be a significant improvement. Is there anything about Blomberg you"d like to ensure I'm aware of?

OK, but that definition of "miracle" doesn't seem very useful. It's useful to have a term that distingushes between events that are physically possible (consistent with the actual laws of nature), and those that are not.

(1) is clearly rooted in a basic belief (no pun intended)
(2) is rooted in basic belief only if there is a God who speaks to humans and we actually have the faculty to hear it.

I'll stress that Plantinga is not endeavoring to prove God. He's just showing that knowledge of God is possible (in the strict sense of "knowledge"), IF God exists.

Yes, I see that I made an error when I asked, "Why think miracles" possible? " and then shifting to "live" possibility. Sorry. But personally, I lean toward physicalism - which would imply miracles are not possible. I'm not committed to physicalism - I'm willing to consider miraculous explanations, but strong evidence would be needed.

So, let me change the question to: Why do you suppose miracles are not a "live possibility"...whatever that means? — Frank Apisa

A live possibility is one that you include in your epistemic analysis, particularly in abductive reasoning - identifying the best explanation for a set of facts.

I don't consider miracles a live possibility because I think physicalism is probably true. I admit to an anti-miracle bias, but I'm willing to reconsider if a good case can be made.

Enough about me, tell me why you think a miracle should be given serious consideration with respect to anything associated with Jesus. i.e. explain why you think miracles are possible, identify when you should consider a miraculous explanation (i.e. it's a live option), and then tell me what sort of evidence would be needed to establish any specific miracle.

There are no consciousness to consciousness connections. You speak words your mind has formulated, the spoken words are transmitted through the air as sound waves, causing the other person's auditory system to react and ultimately interpret what was said.

That's not correct. Platonism involves mind-independent objects. So, how does your triangle exist without consciousness? — 3017amen

Mind independent ABSTRACT objects, right?

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.

Are the foundational beliefs warranted? What about justificatory regress? — creativesoul

That is the general problem with foundationalism. Plantinga addresses this by arguing that beliefs that are "basic in the proper way" (i.e. properly basic) have warrant. The "proper way" is that it was produced by a sound mind, in an environment supportive of proper thought in accord with a design plan successfully aimed at truth.

In a humanistic sense, are you saying that we all are an interconnected consciousness? — 3017amen

Not really. The relations between consciousnesses seems indirect.

No, because the structural properties exist only in the objects that have them. Platonism would entail their existence independent of those objects.

Although it is quite clear that belief begins simply and grows in it's complexity, and is thus accrued in a way, I do not think that happens in a strictly linear fashion — creativesoul

I agree, but we can still analyse any specific belief to determine whether or not it is warranted. A belief that is fully wartanted would rely only on other warranted beliefs, so there are layers upon layers - until reaching the foundation. At any rate, that's the theory upon which foundationalism is based.