Monday, February 12, 2018


It seems to be logically possible for there to be an exact copy of you, say d-you, because it seems that such a thing might exist in a parallel space-time. D-you would be physically and mentally identical to you; but it would not, of course, be you. Now, we naturally assume that none of us have been instantaneously swapped with such doppelgangers. We can never have any reason to think that any of us might have been swapped; but, that is because such swapping would be undetectable, and that is why we cannot logically rule out the logical possibility of such swapping.

Indeed, you cannot completely rule out the possibility that you are such a doppelganger, because you would have exactly the same memories, exactly the same sense of being yourself. There would be absolutely no empirical difference; the only difference would be semantic: reference intended to be reference to you would fail to be such reference, were it to d-you, for example. And of course, knowledge would be lost, e.g. if I saw d-you at a bus-stop then I would not know that you were waiting for a bus. But of course, I would know that you were waiting for a bus if I saw you at a bus-stop (and you were waiting for a bus). There is no loss of knowledge caused by not ruling out the logical possibility of d-you. We simply assume that such swapping does not happen.

Note that we do not just think it unlikely (and similarly, we do not just think it unlikely that we are brains in vats, or being fooled by demons, and so on and so forth). We do not know for sure that there are no such doppelgangers, and we do not even know for sure that there are unlikely to be any (we can have no evidence for such unlikeliness). But clearly, we are assuming that there are no such things (and nothing else of that rather wide-ranging kind). That is just an obvious empirical fact about our beliefs. (We might not notice it, because being fooled by a demon would be like being a brain in an evil scientist’s vat, and a brain in a vat is like someone having a very long vivid dream; and maybe it is only highly unlikely that you are in a coma right now.)

Thursday, February 08, 2018

Truth in Dreams

In the Cartesian argument (for Skepticism) from dreaming we are to assume that if we were dreaming, then were we to see hands in that dream, those would not be hands; but of course, they would be dream-hands in a dream-world, and so why should dream-reference to them fail? If we think of someone dreaming about hands, then clearly those are not real hands; but, were this a dream (not a dream-within-a-dream, which is what our "dreaming" would refer to), then what is meant by "real hands" within that dream would be dream-hands. You might wonder if that would be the case, had we fallen asleep having already learnt the meaning of "real hands" in the real world; but presumably we learnt the meaning of "real hands" in this world, and were this a dream then that would be a dream-world. Might we have learnt the meanings of our words in some higher realm? But, as soon as we clarify such worries, say in some Moorean way, by describing what is meant by "external thing," we tie the meanings of our words to this world: worrying about that problem resolves that problem!

Wednesday, February 07, 2018

Lots of Misprints?

I've seen quite a few misprints recently, e.g. top of page 159, and again on page 169, in Maddy 2017 (" 'Proof on ..." instead of " 'Proof of ..."), just before she got to Moore's reason why pointing to each of his hands was a proof that there are two hands (and hence that there are external objects, and hence an external world), which was that he could similarly prove that there were three misprints on a certain page by:
taking the book, turning to the page, and pointing to three separate places on it, saying 'There's one misprint here, another here, and another here'
Maddy 2017: 164 (Moore 1939: 147) Although of course, while that proves that there are three misprints, it does not prove that there are three misprints. And while you might agree with Moore that those were misprints, that would not amount to a proof that they were. Moore, you will recall, does not have to show that there are two hands, nor even that there are two hands, he has to show the externality (so to speak) of such things as hands, which is more like having to prove (not just assume) that it is indeed a bad thing to have lots of misprints.

Tuesday, February 06, 2018

What do Philosophers do?

I'm half-way through Maddy's 2017 (a walk through the modern history of Skepticism), where she describes a weakness of the Argument from Dreaming: although we would not be knowing the world were we now dreaming in the ordinary way, we can rule that out in quite ordinary ways; and whereas we cannot rule out that we are dreaming in some extraordinary way (e.g. a life-long coma), why should we rule it out? Such things are unheard of! Furthermore, maybe this is a dream-world, and my hands dream-hands within it; what of it? It is far from obvious why the fact that I don't know much about the fundamental substance of my hands should get in the way of my knowing that I'm typing this with them because they exist (whether that is in a way that is to some unknown world much as dreams are to this world, or some other way).

But here's a thought: If some higher power (maybe a UFO) replaced you with a pod-person who was exactly the same as you, physically and mentally, then the people of the world would of course not know, were they to see that person before them, that you were standing there. So, if the underlying substance of the world was such that things were frequently replaced with identical copies, in such ways (and note that we cannot even know that that is unlikely), then our references would frequently fail, and we would end up knowing a lot less about the world than we assume we do. We do assume that such does not happen, but that just means that, for example, it is at best epistemic luck that people know that you are there, when they see you. At worst it is knowledge by assumption, because we do assume as much; which reminds me of Wittgenstein's "hinge propositions," which Maddy will be getting to shortly...

Perhaps we assume that things generally continue to be the same things. Or perhaps we assume that things that look the same are the same. I would not say that we know such a proposition, but maybe we do thereby know propositions that depend logically upon it, such as that I have hands. (Knowledge seems not to be some minimal amount of epistemic luck, but rather the sufficient reduction of certain kinds of epistemic luck, as required by one's context; and philosophy is a context with high standards. In philosophy we tend to accept the force of epistemic closure, because the high standard is logic (or meta-logic).)

Monday, February 05, 2018

Beginning the Resolution

My resolution of the aforementioned paradox begins by observing that apparently timeless possibilities could possibly become more numerous over time; I begin like that because if possible selections become more numerous then that could change the meaning of (3) enough to avoid (5). Furthermore, were that the only logically possible resolution, we could conclude that possible selections do become more numerous; and if the only way they could do that was for a Constructive Creator to do some definitive selecting, then there would have to be such a God. My example of apparently timeless possibilities becoming more numerous was (before I took a break, from conjecturing and blogging here, to take photos and share them via Google+) as follows:

You were always possible, but had you never existed that possibility would have been the possibility of someone just like you; it could not have been the possibility of you in particular were you not there to refer to. Looking back now, we can see that there was always the possibility of you in particular as well as the more general possibility, even before you came into being; but, had you never existed, there could have been no such distinction. Now, Presentism appears to be logically possible; and if Presentism is true then there will originally have been no such distinction, even though you were always possible; the distinction will have arisen when you came into being. So, it appears to be logically possible for apparently timeless possibilities – e.g. the possibility of you in particular – to emerge as distinct possibilities from more general possibilities.

Friday, February 02, 2018

The essence of Cantor's paradox

(1)     There are at least three things (e.g. these three words)

(2)     Given some things, there are possible selections from them (e.g. "these" and "three")

(3)     There are all the things given by reiterating (2), given (1)

Note that each possible selection is a thing, and that it was always possible.

(4)     Given some things, cardinally more selections from them are possible

That is shown by Cantor's diagonal argument.

(5)     There are cardinally more things of kind (3) than there are things of kind (3)

That follows from (4), given (3), but is contradictory, and hence false.

Thursday, February 01, 2018

Logic Needs That Hypothesis

In the Germany of the eighteen-nineties, Georg Cantor discovered the mathematical paradox that bears his name.
He put it down to the ineffability of God, even though he was only studying numbers; they were very big numbers.
But, the mathematical mainstream has since then replaced our natural conception of a collection with formal (or fictional) sets that are better behaved.
Whereas, the natural conceptions are fundamental to our actual thinking; in particular, if we cannot rely on our best thinking about formal sets, then why should formal sets be any better?
Consequently logical thinkers need to hypothesize God: only that allows those conceptions without paradox (as previously posted).
Over the next few posts I aim to scrutinize the elements of this, e.g. the essence of Cantor's paradox, and why we do still need logic (or meta-logic, if we are doing formal logic) even in this democratic and scientific age.

The Problem with Prefaces

Suppose that it says, in the preface to some non-fiction book, that there is bound to be some false statement in the book, even though each statement in the book is believed to be true by the author. That is the Preface Paradox. A first analytical thought might be to regard belief as sufficiently high credence, so that we would not believe large conjunctions of our beliefs (cf. how you will probably not get a 1 or a 6 with one throw of a die, but with three dice the chance is less than 30%); but of course, we very often do (and for other reasons belief is not simply high credence, as recently posted). A more sophisticated response might discover contextualist aspects (e.g. self-reflection upon one's fallibility); but what I am interested in here is how we naturally overlook the following absurd response: Why not say that sets are simply such that sets of beliefs are like that? We could then have all that we want, and nothing that we do not want: we simply put precisely that much into the axioms of set theory! But of course, that would be too easy; what about what sets of beliefs really are? The thing is, that is essentially the mainstream response to Cantor's Paradox (which I shall be posting on in my next few posts). The Preface Paradox therefore shows how absurd the mainstream foundations of mathematics are.

Wednesday, January 31, 2018

Does it deny the reality of time?

I'm not saying that. Not at all. I'm saying that there is something in the thing itself which human consciousness perceives in terms of a temporal structure of things. That's all. What it is, the whatever that provokes the human mind to perceive time, is hard to say. But it isn't a one-to-one mapping. Something's there, though; and the way our minds make sense of it is to see it in terms of consecutivity, cause and effect and so on.
Adam Roberts, The Thing Itself, 256

Sunday, January 21, 2018

High credence is Not belief

Imagine a spherical die with thousands of tiny faces. You can roll the die around in your hand, surveying all the faces and thinking, of each face, how unlikely it is to end up on top when you roll the die, but that it might. So, for each face you have a very high credence in the proposition that it will not end up on top, but you do not believe that it will not end up on top.

The Lockean assumption that belief is sufficiently high credence is similarly refuted by almost all of our quotidian beliefs. Consider the view from some window. The chance of any particular arrangement of cars, leaves et cetera is low, and so your expectation of having that view is low. Conversely, your expectation of not having that view, and your credence that you won't have that view, are high. But it is of course not the case that you tacitly believe that you won't have that view. On the contrary, you know that you will probably have some such unsurprising view.

Friday, January 19, 2018

Turri's Maxwell's Car

When Maxwell arrives at work in the morning, he always parks in one of two spots: C8 or D8. Half the time he parks in C8, and half the time he parks in D8. Today Maxwell parked in C8. It’s lunchtime at work. Maxwell and his assistant are up in the archives room searching for a particular document. Maxwell says, “I might have left the document in my car.” The assistant asks, “Mr. Maxwell, is your car parked in space C8? It’s not unheard of for cars to be stolen.” Maxwell thinks carefully for a moment and then responds, “No, my car has not been stolen. It is parked in C8.”
With that example began John Turri's "Epistemic closure and folk epistemology," where he went on to add that:
The epistemic closure principle says, roughly, that if one knows that P, and one knows that if P then Q, and one infers Q, then one knows Q.
Maxwell may have been misapplying logic, when he thought carefully: he recalled that he had parked in C8, rather than D8, and so he thought that his car was in C8 (unless it had, as his assistant noted, been stolen), from which he may have concluded that it was not stolen. (But perhaps he took the low chance of his car having been stolen to be reason enough to think that it had not been stolen. And for all we know the archive's windows looked down on C8.)

Most people think that Maxwell knew that his car was parked in C8 (assuming that it had not been stolen, etc.), but not that it had not been stolen, which contradicts Closure: if Maxwell knows that his car is in C8, and he knows that if his car is in C8 then it has not been stolen (he did seem to know that because he did seem to infer, from it being in C8, that it had not been stolen), then Closure says that Maxwell did know that his car had not been stolen.

Logically, if Maxwell's car was in C8, then it had not been stolen; and the whole point of logic is that logical reasoning takes us from knowledge to knowledge. So it seems to be logical, to go from Maxwell knowing that his car was in C8, rather than D8 (which I think he did know), to Maxwell knowing that his car was in C8 (which most people think he did know), to Maxwell knowing that his car had not been taken out of C8 (which most people think he did not know).

But of course, we can see from this example why that is invalid; and so we also have this insight into why skeptical scenarios are not threats to knowledge (and also why they are). If we are BIVs then we do not have real hands, so how can we know that we have real hands but not know that we are not BIVs? If we are BIVs then we think we have real hands (which is good enough for us BIVs).

Thursday, January 18, 2018

50 meanings for "know"

To say that you know something is, basically, to say that you are certain of it; in effect, you are promising that what you say is true. Knowledge is important because we want, as a society, bodies of knowledge that can be relied upon. That is why, when cause for doubt is shown to us by skeptical scenarios, our natural reaction is to doubt that we did have knowledge; although of course, academics cannot conclude that they know nothing. At the other end of the scale consider a boy sitting an exam, who is not sure of an answer but puts it down anyway, and it turns out to be correct: we say that he did know the answer. There are a range of uses of the word "know," and in between those two are all the sciences, and all their applications, and such varied uses of "know" give it a certain inconsistency. The Analytical philosophical analysis of "know" is therefore a cornucopia of papers. Continental philosophers may notice that you can only ever really know what you have yourself made up, however, because the paradigm case of knowledge is, as it has always been, that of a God: proposition P is known by subject S when S's justification for believing P guarantees that P is true. How close you have to get to that ideal, for what you believe to count as knowledge, depends upon the kind of knowledge that it is, the use that you are going to make of it, and so on. We pick up on the use of "know" as we learn English, and I for one have found that good claims to knowledge can be gambles, akin to promises, even though knowledge stands opposed to epistemic luck. More generally, we might disagree about the meaning of "know" without any of us being wrong.

Wednesday, January 17, 2018

Gettier's Smith's Job

Smith applies for a job, as does X. Smith thinks that X will get the job, and knows that X has 10 coins in his pocket, so Smith thinks that the man who gets the job will have 10 coins in his pocket. As it turns out, Smith gets the job, and also has 10 coins in his pocket, and so his italicized belief was true. Since Smith was justified in thinking that X would get the job (his new boss had told him that X would get the job) his italicized belief was also justified; but, it was not knowledge, according to Gettier.

One problem with all of that is that it is a bit obscure what exactly is going on: there was a bit of inferring going on, and as a rule we cannot rely on such things as, for example, epistemic closure: If you know that P, and also that P implies Q, then even if you infer Q, you do not necessarily know Q (there was a good example by John Turri at Certain Doubts). Still, one thing is obvious: Smith's reasons for believing the italicized belief were no part of the reasons why it was true, and so it was not knowledge.

However, because those reasons turned out not to be that good (X did not get the job), there is also a question mark over whether they really were good enough to count as justification in the sense required for knowledge (only a question mark). A statement known to be false was always a statement that could have been false (that really could, not just could theoretically). When we think of knowledge we think of statements that can be relied upon, that are justified in ways that basically guarantee their truth.

Sunday, January 14, 2018

Much Knowledge is Epistemic Luck

In a recent post (linked to here) I observed how we simply assume that we can refer directly to the things around us: we cannot know that their substances are not changing in ways that leave their properties the same, because we can only know their properties. Were their substances changing, reference to them would keep failing (assuming that reference is direct).
     And similarly, we cannot really rule out that we are Brains In Vats: all of our evidence is compatible with our brains having been harvested by aliens (in a real world where such aliens are common) and put into high-tech vats that simulate worldly experiences. While we are unlikely to have been harvested recently (as recently noted (although note that we cannot rule out as unlikely a world where are are frequently, but not too frequently, re-vatted)) it is not unlikely (by the standards of the apparent world) that there are such aliens (what is strange is that we see no aliens).
     But of course, we can and do simply assume that there are not such aliens, that we are not currently asleep in our beds and dreaming, that all of our particles are not always being switched with identical particles, and so forth. It is upon such foundations that our knowledge of the external world is built. And of course, we are not BIVs, we are not dreaming, and so on; or at least, I do assume not. And so we do have knowledge of the external world. But, because those are assumptions, such knowledge is epistemic luck.

Saturday, January 13, 2018

Something like Fake Barns

What is adequate justification for holding a belief? It depends on one's context. A true belief that was well-justified when it was formed might cease to count as knowledge within a stricter setting, such as a court-room or a laboratory. And the famous Fake Barns involve unusual contexts. And of course, one needs to be sufficiently rational. Suppose that I see a red car, in a normal road (no fake cars), for example, and so form the belief that there is a red car. But, I also have a lot of irrational beliefs that there are various objects. When there is a red car, I believe that there is, and I am unlikely to have the belief that there is a red car if there is not a red car, although I am quite likely to have some belief that there is something when there is nothing. (It is easy to think of other examples of true beliefs that might seem at first glance to be justified but which do not count as knowledge because they are held by someone who is in some way unqualified.)