How can you know what the ... area says? — Michael

I can't, but since it's not shown, I can only assume.

I don't see anything underhanded here. Do you? — Michael

Yes. The underhanded bit is in the blacked out "..." area.

What evidence is there that Obama tapped Trump's phones whether legal or illegal? Do you just believe it because Trump tweeted it? — Michael

I didn't say I believe it. I said I wouldn't be surprised if it actually happened.

How so? Because Obama was wary about informing members of Trump's administration that they were under investigation? I hardly count that as a conspiracy. — Michael

Yeah, because he was conspiring into what information to share and what information to withhold from the President-elect of the United States.

Was this a joke, or do you actually believe that Obama (illegally) tapped Trump's phones, as Trump's tweets claimed? — Michael

I don't care whether it's "legal" or not. That is irrelevant to me. Pretty much anything that someone does with the authority of the state (which makes the laws) can be portrayed as legal.

I'm not sure, but I wouldn't be surprised if Obama's administration or the FBI listened in to Trump's phones.

Huh? Are you saying that Obama wire-tapped Trump, that the media knew this, that the media lied about it, and that the video above shows this? — Michael

Yes >:)

And what properties do we imagine a being than which none greater can be imagined to have? Is "existence in reality" one such property? Then we're imagining X, not X-e. — Michael

Yes, that comes later in the argument, where we see that if God is the being than which none greater can be imagined, then existence must also be one such property, CONTRARY to (1), which is an assumption that is later rejected in the conclusion.

What lies? — Michael

You know, the so-called "Trump lies" about Obama wire-tapping him, etc.

We don't observe light rays or curvature of space in the way we see cells through a microscope, though. We observe other phenomena about which light rays and curvature of space are explanatory theories. — Janus

I disagree. We can set up experiments where we send a beam of light in a straight line passing by the sun and the set up detectors on the other side to see where the beam lands. If it lands not in a straight line, but in a curve, then we have seen the light rays bendings. We don't see the curvature of space, but the curvature of space is that which explains the bending of the light rays, just like atoms (which we don't see) are what explain phenomena such as brownian motion, which we do see. You are a pragmatist, so how did the Peirce go - the whole of the effects is the whole of the conception, or something of that sort, anyways.

Are you saying that Kant would have denied that any physics experiment could reveal that spacial geometry was not Euclidean? — Perplexed

Yes, I'm quite sure he would have. If he found out about non-Euclidean geometry, he would have tried to re-adjust his theories.

And I actually agree that we cannot carry out the argument, but not because the argument is faulty, but rather because of our finitude. As radically finite beings, we cannot form the idea of God in our understanding. So we cannot have the idea of God in the understanding that is presupposed in order to carry out the argument. Nevertheless, the argument does an excellent job at displaying our finitude, and providing us with something to attach our faith to - our hope for something unseen, that our minds are incapable of grasping.

I know that's not what the argument claims. That's the problem. The argument is wrong. We imagine God to be real, even if he isn't. — Michael

No we don't. We just become aware that God existing in reality is greater than God (existing only in the understanding). That's not the same as imagining a non-existent thing as existing.

The assumption is "God doesn't exist". — Michael

No, that's not the assumption. The assumption is that God exists in the understanding (not in reality).

5) implies that the bit in brackets is X-e, which is wrong. — Michael

No, it's not wrong - it actually is X-e in (1).

1) [A being that is imagined to exist in reality ... ] exists in the understanding, but not in reality. — Michael

No.

(1) God exists in the understanding, but not in reality.

Or

(1) A being than which none greater can be imagined exists in the understanding, but not in reality.

That Alvin Plantinga is in any way reputable is an indictment on the intelligence of our species. — StreetlightX

Platinga is not reputable in anyway.
He's a total nut case. — charleton

These statements say more about you than about Plantinga. It's okay to disagree with someone, but I don't see why you insult his intelligence. He is a reputable, published scholar, a professional philosopher with a PhD from Yale, who also studied at Harvard and other prestigious institutions. On the other hand, I'm not sure where the two of you learned philosophy.

Brute insistence does not a discussion make. — StreetlightX

Sure, but I didn't insist. I merely quoted you saying that:

That a cake 'exists in the understanding' means precisely that the cake doesn't exist, or rather, what exists is the 'understanding' of a cake. — StreetlightX

And then explained that the existence of a cake in the understanding does not "mean precisely that the cake doesn't exist", because it could very well exist.

I've given reasons why the formulation is grammatically suspect, reasons which you've not addressed. — StreetlightX

Your so-called "reasons" mask presuppositions that you have not bothered to make transparent.

the understanding of the cake, and not the cake, is the subject of the sentence. — StreetlightX

For example, as if there was no connection between "the understanding of the cake" and "the cake". "The understanding of the cake", for example, exists in the cake. That is why experiencing the cake can help me form the concept of the cake in my understanding. You are adopting what looks like a form of nominalism, that entirely divorces the two, such that saying something about the one has no bearing on the other.

Brute insistence does not a discussion make. — StreetlightX

Sure, of course it doesn't. Neither does calling something a sophism repeatedly, saying that even a 10 year old could understand it, deriding people who hold those views, etc. make a discussion. That might be a monologue though, which helps you feel that you're right and your opponents have nothing useful to say. It kind of betrays the purpose though - if you're so confident, there's no need to deride the opposition.

It also has nothing to do with the syllogism at hand, so has zero import on the argument. I will ignore any argument by you that invokes this pseudo-distinction. — StreetlightX

At first, you said it has everything to do with the syllogism:

As for the hand waving distinction between 'finite and 'infinite beings', that's just what you're trying to prove — StreetlightX

Now it seems you have suddenly changed gears, now it has absolutely nothing to do with the argument. So it seems to me that you're quite confused. What I said is important, because having an idea of God in the understanding is one requirement for the argument. And part of having an idea of God in the understanding involves understanding the difference between finite beings, and the infinite Being. This was part of the Hegelian criticism of Anselm, that Anselm never actually clarified the concept of God.

I'm saying that if we imagine God to be real then we can't imagine something greater than God — Michael

This part is okay, without the ending.

When we imagine God, we imagine X, not X-e. The ontological argument implies that we imagine X-e, and so can imagine something greater, which is false. — Michael

No, it's not false starting from the assumption of the ontological argument. You keep claiming that we imagine X and not X-e, but that's not what the argument claims.

Now the lies of the media are starting to come to the surface.

Also, if for nothing else, you should also read that article because the ontological argument has played an essential role in philosophy historically. The history of the ontological argument is almost the history of Western philosophy!

My concern isn't with existence being or not being a predicate. — Michael

I know, but that article also addresses your concern.

My concern is with the claim that we can conceive of something greater than God if God doesn't exist (as explained here). — Michael

What do I conceive of when I conceive of God? What do I conceive of when I conceive of this "greater" Being? If there isn't a difference then I don't conceive of something greater than God, and so the premise is false. — Michael

Call X the whole concept of God, including all possible predicates. Now subtract existence from X and call this X-e. The two concepts are existentially equivalent.

The concept of a pizza in the mind is the same as the concept found in an existing pizza (ideally). That doesn't mean that the predicate of existence does not make a difference though. Clearly the pizza in your mind is different than the pizza in reality, even though their concept is existentially the same.

As has been pointed out, the Ontological argument is a sophistic display of thaumaturgical witchery, whereby mere words and definitions are able to conjure concepts into existence. As Cioran writes, "God Himself lives only by the adjectives we add to him." — Maw

Merely repeating something does not make it true.

I will come back to this later, but you really should read that paper, it addresses your concern.

http://www.andrewmbailey.com/ap/Kants_Objection.pdf

Yeah, and the premise is nonsense, or at least worded in a purposely misleading way. — StreetlightX

You think reputable philosophers like Alvin Plantinga would "purposefully" word an argument in a misleading way?

Regardless of that, I don't think the argument is misleading. That a cake exists in the understanding does not tell me whether or not it (being finite) also exists in reality. So, by all means, the cake existing in the understanding doesn't tell me that the cake doesn't exist in reality. It could also exist in reality.

As for the hand waving distinction between 'finite and 'infinite beings', that's just what you're trying to prove — StreetlightX

No, we're not. This is something that is involved in understanding the concept of God, so that we can say that such a concept is present in the understanding.

But the premise is that we can imagine something greater. — Michael

The only place where I see the word "imagine" is in your post, not in the argument. The argument merely says that something that doesn't only exist as a concept, and also exists in reality, is greater than something that only exists as a concept.

So we have two different concepts: G1 and G2. — Michael

Sure.

How do these concepts differ such that G2 is greater than G1? — Michael

They don't (at least not existentially)! It's not in differing qua concepts that G2 is greater than G1. Plantinga doesn't claim they differ either, in fact:

And you read me as supportive of ontological arguments and the idea that concepts alone can vouchsafe a being's actuality? — fdrake

You've been spewing a lot of nonsense in this thread, but this mistaken understanding is precisely the problem. You treat God as another being amongst beings - as finite. Sure, for a finite being, concept and actuality are not identical.

God is defined as a being than which none greater can be imagined. — Michael

God is rather defined as maximally great.

If a being that is imagined to exist in reality is greater than a being that is imagined to exist in understanding alone then the first premise of the argument is: — Michael

The being is not imagined to exist in reality. "Imagined" is not a useful word. To exist in the understanding is to exist qua thought & concept (which is similar to your imagination). To exist in reality is to be an instantiation of whatever the corresponding thought or concept is. The argument is not talking about imagining God as existing in reality.

I think it's quite clear that existence in the understanding is not hypothetical - God really exists in the understanding, that is the claim of premise (1).

The point of changing 'is' to 'would be' is to expose the fact that 'existence in the understanding' is hypothetical to begin with. — StreetlightX

Why?

It equivocates on the whole concept of existence, confusing, from the very beginning, ideality and actuality — StreetlightX

That's your mistake. Ideality and actuality are different only in finite beings. But for the infinite being, God, there is no gap between ideality and actuality. So of course, if you treat God as a finite thing - as one more being amongst other beings - then the argument fails. That's precisely the reason why the argument doesn't work for the perfect island.

According to 5) we can conceive of something greater than this. So what are we conceiving? — Michael

No, "God" in (5) refers to the God we have conceived in (1). Greater than that God.

5) doesn't make sense. — Michael

Why not? (3) establishes only that such a being can be conceived, not that it is also greater than God. It is (4) that establishes this. Thus (5) is a conclusion combining both (3) and (4) to tell us that a Being greater (the greater comes from (4)) than God (as conceived in assumption (1)) can be conceived.

'would' must be coupled with an 'if' — StreetlightX

Even if this is granted, the "would" is coupled with the if of God existing in the understanding, not with the if of God existing in reality.

I didn't make it into a non-sequitur. It is a non-sequitur. — StreetlightX

Your version is a non-sequitur, since the conclusion you presented does not follow from the premises.

Leaving aside that you've changed the sentence structure so that it no longer reflects the proposition (1) that it needs to mirror so as to disprove (the entire point of the exercise) — StreetlightX

(1) is an assumption. The conclusion is in accordance with the assumption. That's why we say that it is false that God would exist in the understanding (assumption (1)) and not also in reality.

But, I will grant you this - the atheist does not have to show that the idea of God is incoherent or logically contradictory to deny the argument (as most people think). It suffices to show that the idea of God, (or the Absolute, or call it how you will) cannot exist in the (finite) understanding.

Also, it's something that is exaggerated to think the argument is a sophism, when heavy-weights like even Hegel thought that it is important.

Fixed it. — StreetlightX

No, you haven't fixed it. You've made it into a non-sequitur.

(1) God exists in the understanding, but not in reality (assumption for reductio).
(2) Existence in reality is greater than existence in the understanding alone. (premise)
(3) A Being having all of God's properties plus existence in reality can be conceived. (premise)
(4) From (1) and (2), a being having all of God's properties plus existence in reality is would be greater than God.
(5) From (3) and (4), a Being greater than God can be conceived.
(6) It is false that a Being greater than God can be conceived (by definition).
(7) Hence, it is false that God exists in the understanding, but not in reality. — Alvin Plantinga

As a non-native speaker, your change of "is" into "would be" in (4) seems fair. But this change does not solicit the corresponding change you've added to the conclusion, that's just arbitrary. In fact, the conclusion that follows can probably remain unchanged.

In fact, if we are to make it more exact, the change should be:

(1) God exists in the understanding, but not in reality (assumption for reductio).
(2) Existence in reality is greater than existence in the understanding alone. (premise)
(3) A Being having all of God's properties plus existence in reality can be conceived. (premise)
(4) From (1) and (2), a being having all of God's properties plus existence in reality is would be greater than God.
(5) From (3) and (4), a Being greater than God can be conceived.
(6) It is false that a Being greater than God can be conceived (by definition).
(7) Hence, it is false that God would exists in the understanding, but not in reality. — Alvin Plantinga

Then we account for the hypothetical being, and the atheist has to show that God doesn't exist in the understanding.

You don't disagree that my solution "works" then, though? — Moliere

Actually... I misread your solution initially. At least you seem to understand what the problem is. So here are my comments again:

So, following my second strategy, Euclidean geometry could be interpreted as synthetic a posteriori knowledge while non-Euclidean geometry could be interpreted as syntehtic a priori -- and the same would apply to any other geometry which predicts the events of the phenomenal world. — Moliere

On what grounds do we judge a geometrical proposition to be a synthetic a priori?

That's what I mean. Surely it's sensible that we could be wrong about the form of inuition. So, supposing non-Euclidean geometry is the true geometry of the space we experience it doesn't seem like a large step to say that we were simply wrong before about the form of intuition. At least not to me. If that were the case, then it would just be an empirical concept, though -- since a priori concepts of space are apodeictic. — Moliere

(1) Why is it sensible that we could be wrong about the form of the intuition?
(2) Does the form of intuition belong to our subjectivity? If so, is it possible to be wrong about our own subjectivity?
(3) Can we know whether a geometric statement really is a synthetic a priori with certainty? And if so, how?

I don't think "intuition" in Kant means the same thing as intuitive. Space isn't intuitively obvious to us. Others have been wrong about space -- like Leibniz and Newton, for instance. So while the examples Kant uses are from Euclidean geometry it seems to me that one could modify the philosophy without losing the core of the aesthetic. It's not that something is obvious, but rather that we are able to have synethic a priori knowledge about space due to our knowledge of geometry. If one geometry is wrong then, just like Newton could be wrong, we could understand such sciences as something which wasn't part of our cognitive faculties but was derived from them, and is therefore empirical in that sense (and not synthetic a priori knowledge, but instead rests upon that) — Moliere

I don't follow how "we are able to have synthetic a priori knowledge about space due to our knowledge of geometry". Our synthetic a priori knowledge of space is what we codify through geometry.

I also don't follow what you mean by "space isn't intuitively obvious to us". For example, it seems impossible to imagine 4D space. So is the three-dimensionality of space not something intuitively obvious to us? Could we be wrong about that too? And what would that even mean?

It's not our perception of space that's at issue, I'd say. The propositions of geometry are closely tied to physics, by my reading. Because our intuition follows mathematical laws we are also able to apply those mathematical laws to objects, which are themselves within our intuition.

Strictly speaking it's not perception which intuition is trying to explain, but rather intuition is one half of the elements of cognition which explains how knowledge of objects is possible. Clearly there are relations between perception and cognition, and granted the intuition's description relies heavily upon visual imagery (like a lot of Western philosophy), but the reason why mathematical laws are able to be posited and discovered in the phenomenal world is because our cognition relies upon this form. It sort of explains why we are able to make predictions which are actually caused -- meaning the "necessary connection" between two events -- in the first place, rather than merely the constant conjunction of non-related events believed by force of habit. — Moliere

If I follow you correctly, your point is the traditional Kantian one that the phenomenal world is organised through the a priori forms of space and time and the categories of the understanding - so in this specific case, space doesn't exist "out there", it is just how we represent the phenomenal world to ourselves. In other words, space continues to be transcendentally ideal per your view?

So if it turns out that Euclidean geometry is not the form of intuition it would seem to upend the notion that we have synthetic a priori knowledge of the form of intuition. Same goes for the physics based upon that synthetic a priori knowledge. However, if Euclidean geometry were merely empirical, an approximation of our cognitive faculties as Newton was an approximation, then I'd say that the aesthetic is saved.

So if we don't have synthetic a priori knowledge of the form of intuition there are two main questions:

(1) Since the form of intuition is subjective, why don't we have such knowledge? How does acting in the world (empiricism, scientific experiments, etc.) help us gain that knowledge? Aren't we ultimately gaining knowledge about ourselves then?
and
(2) How do we even know that synthetic a priori knowledge even exists if we do not know when we have it? How can we know if a piece of synthetic knowledge is a priori (Riemmann) or a posteriori (Euclidean)?

But in either case, it's not how we perceive that's at issue. It's how we are able to know math and why it applies to the objects of our perception in the first place. Kind of a hair-thin distinction, but I'd say it's important because in one case we are dealing with phenomenology and psychology, and in the other we are dealing with the possibility of knowledge which seems to fit more in line with the whole Critique.

To go back to your initial question, your solution doesn't appear like a cop-out, but there are a lot of things to flesh out.

Kant scholar's — Janus

See, I am tired of "reinterpretations" of Kant such as:

Under the understanding of a prioricity at issue pre-Two Dogmas of Empiricism, a priori truths were largely conflated with necessary truths. So, if you could recognize the possibility of the failure of the parallel postulate, that would constitute a falsification of its necessity and thus (given the conflation) a falsification of the claim that it was a priori.

Where Kant went wrong, if this was indeed what he held, was in thinking that our intuition of space and time represented the world as it actually is. Frege famously made the same mistake in one of his later articles, "Foundations of Geometry". — Dennis

From here.

If this interpretation is correct, Kantianism is dead anyway. Schopenhauer would rightly find the notion of a space and time beyond perceptual space and time (the Euclidean ones) abhorrent to Kant's doctrine, and rightly so. If you ask me, such reinterpretations are pathetic, and they exist because people can't abandon a dead doctrine, and try to change it to fit the facts, when it really should be let go of.

This lecture is a good summary of the refutation of Kant's views:

http://faculty.poly.edu/~jbain/spacetime/lectures/13.Kant_and_Geometry.pdf

@andrewk

To further illustrate what imagination is, when I imagine a curved line, I imagine that line curving right in front of my eyes. Basically I see what anyone would see if they were to draw a curved line on a piece of paper. So if someone asks me about extrinsic curvature, that's what it is - that's how you imagine it. Now show me that you can imagine intrinsic curvature in the same way.

Suppose the curvature is very high, such that if you take 10 steps in one direction, you return to the same point where you started. This is a thought experiment, an unrealistic one, but it's useful. Suppose there are a series of poles, 1 step apart, in front of you, with the pole right next to you being red (so that you can keep track of when you return), while the others are some other colors. How would this visually look to you?

I'll describe below how I imagine it, but that's beside my point, which is that I think we don't need to imagine it. I think all we need to cognise the world is the bolded list of items in my previous post, and we get that from any Riemannian Manifold, whether flat or curved. When we use those things in navigating the world we can remain uncommitted as to whether the space is slightly curved or perfectly flat. — andrewk

I will address this later when I have more time.

Now to reply to your specific question. You are right, it is weird to imagine. Here's a couple of ways:

1. Two spaceships set off on a journey, travelling initially parallel and starting 1km apart, going at the same speed and steering straight ahead. If the space is flat they will remain 1km apart. If not, they will subsequently measure that they are getting further apart if the space is hyperbolic, or closer if it is elliptic.

3. Set up three space stations 1, 2, 3 in deep space, each firing a laser beam at the next: 1 to 2, 2 to 3, 3 to 1. Each measures the angles between the incoming and outgoing beam. The stations are floating freely, not firing rockets to accelerate. The three angles will add to 180 degrees if the space is flat, less than that if hyperbolic and more than that if elliptic. — andrewk

I don't see how you're imagining anything. To imagine is to create a visual, tactile, or in any case sensory picture or image of intrinsic curvature in your mind. To imagine isn't to come up with some experiments that would prove or disprove the hypothesis.

I keep getting sucked back into these discussions and sometimes they just take up too much time, I don't have much time right now, so...really gotta go... — Janus

Okay, answer when you have time then :P

We cannot directly perceive light rays at all. On account of our explanatory theories about what we do observe we can infer that they are bending. We can further infer that the bending is caused by curvature of spacetime in accordance with other theories. — Janus

We perceive them via instruments, that is still perception. It's like looking at a cell with a microscope - still counts as percieving, even though not directly (I don't see how that is relevant though). Even so called direct perception is mediated through our eyes - if we're color blind, we perceive things differently. So... Whether mediated through eyes, or telescopes or whatever - makes no difference as far as I see it. We basically see that they are bending.

Anyway, apart from that point, do you believe atoms exist? We also infer the existence of atoms from related evidence. So spacetime and its curvature isn't just a theory, it really exists.

I already said it is a hypothetical construct. — Janus

What does it mean that it is a hypothetical construct?

In a way that does not require the space manifold I use to be perfectly flat. — andrewk

How do you imagine a 3D, non-flat space? How do you imagine intrinsic curvature? Hopefully, you won't say that you do via analogy to extrinsic curvature.

Yes and that is the space of human perception. — Janus

What is "human perception"? Is this not the same space as the space in which our bodies act and live? Before you said visual perception - that's not correct. We can have a notion of space through touch alone, for example.

Parallel lines in perceptual space do not meet, otherwise trains could not operate. — Janus

So then this is not visual space - what you see in front of your eyes, but rather something else. You admit that in visual perception, the lines appear to meet at the horizon.

Spacetime, whatever it is, is not that space; that has been my point all along. — Janus

What is spacetime? And how does it relate to the space we intuit?

Spacetime is a hypothetical construct; there is no actual spacetime that we can intuitively understand, as we can our perceptual spaces. — Janus

So what about light rays travelling in straight lines but bending around planets? We cannot perceive that or?

Of course we can; we can intuitively understand them when they are visually represented on two dimensional curved surfaces. — Janus

But we cannot intuitively understand them in three-dimensions, except by analogy, no?

The analogy from curving or warping of two dimensional surfaces into the third dimension (which we can visualize) to curving of three dimensional space into a hypothetical fourth dimension is the only way we can get any notional sense of it; it is not something we can directly represent visually to ourselves at all. — Janus

So then we really don't have an intuitive understanding of it? We have an understanding by proxy of 2D objects curved in the 3rd dimension. Furthermore, I think in mathematics, @andrewk should correct me, the notion of intrinsic curvature does not require the existence of another higher dimension for the space to curve into. So the 2D objects curving in another dimension - that's extrinsic curvature, and we can have an intuition of it. But we can't have an intuition of intrinsic curvature - in the Kantian sense of intuition.

If you think anything can be no other way in Kant's system then I would conclude that you have not read Kant, or if you have, have not understood him. Kant scholar's have been arguing over just what he meant for centuries. — Janus

I am aware there are Kant scholars who disagree - they are free to do so. But those who disagree, do such violence to Kant's system, that it is essentially unrecognisable, or otherwise a Ptolematization. I've seen and read scholars who don't take Kant's transcendental idealism seriously enough, and who buy into Kant's confused idea of the noumenon, and there being a real space out there (that physics figures out), and adapt Kant's ideas to take into account their naturalism, etc. - that's not philosophy if you ask me, that's nonsense. Schopenhauer understood Kant rightly, and at least set the noumenon bit straight, and avoided the pitfalls of naturalism.

If you have any Kant scholar who follows in the footsteps of Schopenhauer and deals with the issue of non-Euclidean geometry, feel free to let me know, and I will look into them.