Proof of substance

The proof of substance shows that the universe is not entirely empty. Some people will think this goes against what the Buddha taught, but the Buddha chose to be neutral on the issue of whether anything was endowed with substance, or a “self.” And by self he meant identity. As in his example, even a cart, when examining its parts, the substance of the cart cannot be found, or no part of the cart is the cart itself, and since the cart is made of parts, none of which is the cart itself, the cart has no substance, it is only an amalgamation of parts. So the argument goes.

Now my proof of substance does not go against what the Buddha taught, because it is merely a proof that substance exists. And this proof doesn’t matter much, because a Buddhist should strive to notice emptiness, especially in oneself. This striving can be successful, and we will see how substance is fundamentally connected with ignorance. And how the existence of substance is merely the existence of ignorance, and ultimately results in the first noble truth: the existence of suffering.

1 The first step of the proof is asking: “Is this a question?”

It is like asking if ignorance exists. We cannot decide if it is or isn’t, because deciding would resolve its ignorance, but resolve it in the opposite way we decided: if we decide that it is a question, whether it is a question is no longer in question. After all, how can this question be, if its being were not in question?

2  The next step of the proof is asserting that “is this a question?” while it is undecidable on whether it is a question, is still a tangible thought.

What kind of thought we have when we ask “Is this a question?” is not known. This leads to the third step of the proof:

3 Because “Is this a question?” cannot fit in any form, and it exists, the only option for it is to be substance.

“Is this a question?” cannot necessarily be a question. If it isn’t then what is it? It seems that there isn’t any other kind of “what” it could be, and so it lies outside a what question, even though we know that it is. This is the fundamental ignorance.  As you can see, it is fruitless to argue over whether it exists or not, which is what the Buddha said of the doctrine of self (by which he meant substance). Asserting “is this a question?” is a question yields a paradox, so it may be best to let this question remain in question. In either case, it may be going too far to assert that it is something. After all, a thing is a “what” and this ignorance cannot be categorized or partitioned. Yet it persists.




Fund Me: Barnhurst News

One project that has been knocking around in my mind for many years (12+) is a news filter that is publicly filtered. By publicly filtered I mean that people are in charge of how a search yields news results, not a mathematical algorithm, not elite editors. I am sure this idea has been thought of before and the reason I think it isn’t already out there is there are powerful people in America who don’t want people to be able to consciously filter their news for themselves. So, I will probably need to hire a lawyer at some stage during this project.

The main innovation is that the program will have more than just a simple “like” way to vote on news. The facebook system is still one-dimensional even though you can choose “laugh” “cry”, etc. For this news filter you can react to a news article more than once using the following dimensions (at first)

Scales (instead of binaries) on the following: “about people vs about institutions” “Democratic vs Republican vs(?Anarchism?)etc” “asks a lot of questions of the reader or tells them statements” “How factual vs how interpretive” (and a separate discussions of the facts and the interpretations available for comment) Also just a rating of how much they liked/disliked the news article. Perhaps you could add the conventional classifications “world, local, science, etc” In addition, I’d like to have people offer and vote on other classifications. Also they can vote on news outlets and filter according to that as well, and the votes could be revealed publicly, so people actually know where most others are getting their news, or like getting news.

There will be two settings: an entry setting that allows you to vote on any news article online, and the other setting is the search setting, that allows people to search based on these votes putting in the search criteria (the same criteria that is voted upon in the entry setting).

Here is a very preliminary sketch. Depending on the amount of donations I can make this much better or hire to work on it.

This is where you come in. I am putting a donation button below, donations will let me know how much time I should devote to this project, and how easily I can argue with my wife that time should be devoted to it. I promise to do this project, and that it will remain 100% free to use. However how pretty, how streamlined, and how much time it takes to finish this project depends on the donations I receive. Thank you

click the link and type in zweihanderdawg at gmail dot com to donate to my paypal. Thank you.


and the most expensive, in that it takes the largest bite out of your donation, is a gofundme:

Using terms inconsistently

So, I feel the need to defend the uses of of “=” and “Screen Shot 2016-08-19 at 2.33.44 PM“. Mainly because I am differentiating uses of Screen Shot 2016-08-19 at 2.33.44 PM but not differentiating uses of “=”. If I differentiated, say the identity “A=A” from the identity “B=B” it would mean not that these were different identities, but that there were two kinds of identity. That is a can of worms I am not ready to open yet. But the choice makes more sense if you think of the concept of equals, including identity, as being the opposite of making distinctions, which is what identifying kinds of identity is. This is what makes equals universal, while not-equals is always special, even though I am aware that this undermines the concept of difference, making (allowable) inconsistencies in my previous post.

We can say, for example that 1+2=3 and 2+3 = 5 and then that 1+2 Screen Shot 2016-08-19 at 2.33.44 PM 2+3 which in effect means that the two equals signs are for different equalities. No problem there, and the difference is kept with the symbol Screen Shot 2016-08-19 at 2.33.44 PM, which is the way it should be. But how can I defend that there shouldn’t be different kinds of identity, where there should be different kinds of distinctions? Well, is the way that “A=A” any different from the way “B=B”? I would say no. And, again appealing to the intuition: There is a big difference between the way a question is different from a neutron star and the way an lemon is different from a lime. So I am committed to the idea that there are different kinds of differences, but there is only one kind of sameness.

Mathematical Relationship between Logical Pluralism and Vagueness

There can be a pluralism of logics because Screen Shot 2017-09-23 at 10.55.59 PM.png whereScreen Shot 2017-09-23 at 10.57.58 PM is classical negation. This can be justified because  “1 Screen Shot 2016-08-19 at 2.33.44 PM 2″ and “1 is not 2” are basically the same statement. However “not 2” has different meanings in different logics, so 1 Screen Shot 2016-08-19 at 2.33.44 PM 2 means something different in paraconsistent logic (We’ll use DeCosta’s C1), we mark this difference with 1 Screen Shot 2017-09-23 at 10.58.22 PM 2, and claim that the difference between classical negation (Screen Shot 2017-09-23 at 10.57.58 PM) and paraconsistent negation (Screen Shot 2017-09-23 at 10.58.22 PM) is  marked Screen Shot 2017-09-23 at 10.58.10 PM. Hence Screen Shot 2017-09-23 at 10.55.59 PM.png.

I mentioned in a previous post that we cannot generalize this statement into Screen Shot 2016-08-19 at 2.33.02 PMbecause it is a contradiction. Nevertheless, a sense in which Screen Shot 2016-08-19 at 2.33.02 PMis true is the sense Screen Shot 2017-09-23 at 10.55.59 PM.png.

Now, vagueness is the situation where it is not clear if 1 Screen Shot 2016-08-19 at 2.33.44 PM 2. To illustrate, take this curve: graph_avg_weight1

here is vagueness on whether we have two or one “heaps”. This thing could be 2 or it could be 1 and so in a sense 2=1. How is this handled by logical pluralism? Paraconsistent logic would allow that A: “1 is not 2” and ~A: “1 is 2” has a sense in which it is true, while classical logic would explode. The reason for this is entirely based on the difference in negation. C1 creates a new sense each time a true possibility is negated, making the negation of a possibly true row in the truth-table have two senses, one in which the negation is true, another in which the negation is false.

(A Screen Shot 2017-09-23 at 10.57.58 PM ~A) Screen Shot 2017-09-23 at 10.58.10 PM (A Screen Shot 2017-09-23 at 10.58.22 PM ~A)

The point is that how you handle negation changes how vagueness is handled (or not handled). A difference in negation also gives rise to an entirely different logic. Vagueness can be described completely as a failed distinction/negation, so that even though we want “1 is not 2” vagueness makes this distinction fail. A different negation yields a different way distinction fails, but no logic “solves” vagueness completely. This is the mathematical relationship between vagueness and logical pluralism.

This may be made clearer with another example. Vagueness is the situation when a distinction fails, which can be described by the failure to distinguish = from Screen Shot 2016-08-19 at 2.33.44 PM, so Screen Shot 2017-09-28 at 1.30.38 PM.

Now for classical logic if vagueness renders 1 = 2 we can prove Screen Shot 2017-09-28 at 1.30.38 PM, likewise in paraconsistent logic there is no problem having Screen Shot 2017-09-28 at 1.30.38 PM as another non-explosive contradiction. this means in particular that Screen Shot 2017-09-23 at 10.57.58 PMScreen Shot 2017-09-28 at 1.34.47 PM and Screen Shot 2017-09-23 at 10.58.22 PMScreen Shot 2017-09-28 at 1.34.47 PM. Substituting, we get that things can get so vague we can’t tell the difference between Screen Shot 2017-09-23 at 10.57.58 PM and Screen Shot 2017-09-23 at 10.58.22 PM, in other words Screen Shot 2017-09-23 at 10.57.58 PM = Screen Shot 2017-09-23 at 10.58.22 PM. and from our previous statement Screen Shot 2017-09-23 at 10.55.59 PM.png we have Screen Shot 2017-09-23 at 10.58.10 PMScreen Shot 2017-09-28 at 1.34.47 PM and vagueness is now mathematically related to logical pluralism.

The symmetry between Completeness and Vagueness

The (Problem of the) Heap of Sand is the classical representation of vagueness, where you create an inference: if you take away a grain from the heap then it remains a heap. This is a good inference for a long time, but eventually breaks down due to the vagueness of what a heap is (eventually you will have taken so many grains away that it wont resemble a heap anymore). And you can’t even tell when the inference will break down, exactly. So, as you can see, vagueness has a very precise and non-vague formulation, something similar to this strange property of vagueness (that it is a clear and distinct concept, even though it is a concept about indistinctness) is common for mathematical concepts. That is, mathematical concepts are chosen and defined so that they contain the terms necessary to get round their own difficulties—their faults or cracks, as all concepts are imperfect. Example: “Completeness”.

The difference between vagueness and completeness, is:

1) that the term completeness is in direct opposition to the claim that every concept has a “fault” or “crack”, in this it is a “perfect” term. The definition of completeness, however, must be vague, because the terms used to define completeness all have cracks.

2) The definition of vagueness, by contrast, is perfect, but the term refers to an essential fault of all terms, and is always perceived. (perception is always vague) Vagueness is defined as how the if, then fails— The “heart of logic” (the paragon of precision) and the most reliable way to preserve truth. It is clear and distinct in its description of how the if, then fails. Since each of the terms in the definition of vagueness have cracks, the definition is precise.

The term vagueness refers perfectly to its referent because it is well defined as an indistinctness, the definition of completeness is vague because the term refers to something that can’t be perceived, a perfect whole.

Stuff, and Higher-Order Vagueness

At the heart of real analysis and the study of real numbers is a confusion between points and “stuff,” or how points can perfectly describe distance/space/extension. Put the other way around, how can extension be reduced to points? Or how can we know the extension (with points) of a length/width of an object?

This question is caught up in measurement, and the relationship between word and object. I have seen people give (real) number a privileged position between word and object, but I would argue that number suffers from the same flaws that language suffers from, including vagueness. One reason is there is vagueness in what to call “one” (see the classical “heap of sand” in a previous post), further there is vagueness in when something is countable or uncountable. Electron cloud size to water or human height is uncountable, but what about popcorn or puffed rice? These could be counted, but should we be counting the grains? Should we count water molecules? Should we go back to a particle model for electrons so we can count them? This should comes more pointed when we consider the ancient belief that counting/taking measurements about humans directly endangers them (Feyerabend 1999). Why was it believed that being unsure which side of the microscope you are on endangers?

Vagueness runs right through these issues from the finer points of graduate school mathematics to the ethical issue raised above. And of course it does, since we would like number to draw a clear line between word and object, point and “stuff”. Strangely, insight into these distinctions can be garnered by understanding just how troubling (and what) vagueness is.

Enter higher-order vagueness. Now the question has been put to me “Well the vagueness between, say, “high up” and “not high up”, (this can easily be pictured on a cartesian graph with a line gradually going down from left to right) can be dealt with by adding and third “uncertain” value/region. And the trouble here is, as is well known, that adding a region uncertain only adds two new borderline cases between “high up” and “uncertain”, and another borderline case between “uncertain” and “not-high up”, so that new “higher order” uncertainty regions have to be added for these borderline cases. And now we have introduced new sources of vagueness, etc. Ultimately the pursuit of conquering higher-order vagueness by exchanging borderlines(points) with intervals(stuff/extension) is a vagueness between points and intervals.

As that sinks in, realize that a vagueness between points and intervals is a general problem reproducible anytime vagueness rears its ugly head. If we draw the connections from points to words and from intervals to the “stuff” of objects, we find that the line between words and objects is vague, which is also well known. What is new here is that we found this well known vagueness by investigating vagueness itself in a general way.

To summarize I would say that the vagueness between word and object is an essential or “stock” vagueness that crops up anytime we are in vague territory, and is the heart of analysis of “real” numbers. In this sense, vagueness is an important ultimate concept for mathematics, and it ought to be mentioned in analysis text books that vagueness is what the book is about.



—The following is a tribute to my father, Kevin Barnhurst, who passed a year ago this month–

I decided to make this post a tribute to him.

Dad and I were working on this essay ( when he died.

Dad was a flawed human being, but one comfort is that I almost exclusively remember good things about him, and feel pleasure in remembering him. I know thats good for both of us. We were at odds a lot when I was a kid. I went through a different kind of school system engineered to dumb down the American population, and entered college a logical positivist by default, but underneath all that wash, I was deeply skeptical of my “education”. For dad his family didn’t trust his decision to enter college, and the situation was reversed. For him school was how to become educated, for me what education I have was a result of conversation (with him and many others). I probably would not have gone to college at all if dad hadn’t pushed me hard to apply. That was one of the strange things about dad, he was very forceful, and only made me more stubborn, but he softened later in life and knew how to make his force felt in a strangely soft way.

We kept a long tradition of holding protracted conversations in the evenings and into the night. I owe my intellectual development primarily to him, and it is strange how long it took me, all the way to the last few years of his life, to realize what a gift that was and to reach an understanding that allows respect his for work.

Magical Thinking in Mathematics

The goal for today is to prove that magical thinking is rampant in mathematics. First of all lets define magical thinking. I would say that magical thinking is a kind of metaphorical thinking, as in the metaphor “My heart is the sun” only with the added idea that writing these words/making the metaphor exerts towards making the metaphor true to some degree or in some sense. Magical thinking is the claim that saying “My heart is the sun” actually warms my heart.

Now the way that mathematics uses magical thinking is to start with a metaphorical idea of difference. For example, the difference between a “raven” (1) and a “writing desk” (2) metaphorically (not actually) is the difference between the “north star” (3) and the “form of thinking called questioning” (4). It is fairly intuitive that the difference between (1) and (2) is different from the difference between (3) and (4), but mathematics amalgamates all differences together into one concept with metaphor. And it is a particular kind of metaphor that asserts that difference actually works that way.

Even though 3 and 5 are less different (2) than 3 and 9, (6), these differences are not taken into account in the traditional mathematical symbol for difference, the Screen Shot 2016-08-19 at 2.33.44 PM.  Traditionally 3 Screen Shot 2016-08-19 at 2.33.44 PM 5 just as much as 3 Screen Shot 2016-08-19 at 2.33.44 PM 9, so the identity of difference, Screen Shot 2016-08-19 at 2.35.11 PM, is enforced.

Mathematics asserts an ultimate concept “Difference” that is universal—it works for any situation where there is difference, making any difference “complete” and it does so by metaphorically joining disparate differences. Hence, it falls under my definition of magical thinking.

I am doing the opposite of what Derrida did with his Différance. Derrida added senses to difference allowing it a history and to belong to language, I am suggesting that we subtract, or better divide utterly Difference into differences.

The rest of the sciences follow suit, of course, since mathematics is the language of the sciences. My advisor for my M.S. in mathematics once said “mathematics is the poetry of the sciences.”

Politics of Mathematics

Proof by contradiction follows from the law of excluded middle ((p or not-p) is universally true), the characteristic law of classical logic. The basic reasoning of proof by contradiction is: in order to prove p, we prove a contradiction from ~p (not-p).

“G. H. Hardy described proof by contradiction as “one of a mathematician’s finest weapons”, saying “It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”[1] ” Wikipedia on proof by contradiction

Interestingly the United States has become known for using exactly this type of logic ever since the nuclear era began. Of course we have the Cuban missile crisis where Kennedy offered ‘the game’ in this case ‘the destruction of the world’ as a possibility to Khrushchev.

Destruction by climate change has increasingly entered into our calculations, so that during the 2016 elections we were faced with a choice between the republican party (who are blocking the Paris Agreement from really taking off) and Hillary Clinton. And the result seems to be that life in America is so bad that they are willing to try the alternative.

And logic can help, not classical logic, but constructive logic also rejects the Law of Excluded Middle and proof by contradiction. Changing our minds (our reasoning) is a very important ingredient in changing our politics. Constructive logic takes the perspective of building things as more important, more fundamental, than universal or global laws. Because of this, the “world” of a constructive reasoner is only this or that construction, and the progressive stages of continuing construction. In this sense the geography of construction is “incomplete.”

This incompleteness is fundamental and draws the rest of mathematics into reformulation (Bishop 1967). Things like space and time need a new kind of real numbers to describe. If our mathematics were different, the upgrading of nuclear weapons and their resultant destructive power by a factor of 3 would not be considered “an incredible feat of human intelligence” (Noam Chomsky) because we would have a different understanding of intelligence (reasoning power), and empty-headed “intelligent” weapons developers, along with coldly calculating CIA heads would be following different rules. Offering the game would no longer be considered “one of our finest weapons”.

Synthesis of Vagueness and Logic

by Andrew Nightingale, November 14th, 2559

CC: Dr. Khajornsak Buaraphan, Dr. Parames Laosinchai, Dr. Patchayapon Yasri

The problem with Heideggers “enframing” attempt—that science enframes nature and in any frame there the phenomena are still vague—is that certain kinds of vagaries do not entail paradigm shift. “Though discovering life on the moon would today be destructive of existing paradigms (these tell us things about the moon that seem incompatible with life’s existence there), discovering life in some less well-known part of the galaxy would not.” (Kuhn 1970, p 95) However, some vagueness does warrant paradigm shift, because “Ambiguity [between terms and the world], … turns out to be an essential companion of change.” (Feyerabend 1999, p 39)

Precision, on the other hand, is not an argument in favor of a theory because “In fact, so general and close is the relation between qualitative paradigm and quantitative law that, since Galileo, such laws have often been correctly guessed with the aid of a paradigm years before apparatus could be designed for their experimental determination.” (Kuhn 1970, p 29) So that the measurements are predicted with intense precision, and then the experiment carried out is an elaborate, highly overdetermined one that has only one possible interpretation within the paradigm.

Vagueness is apparent to the naked eye, but it is traditionally opposed to what can be grasped rationally. “In general, Leibniz had followed the other great rationalists in interpreting perception as a confused form of thinking. Like Descartes, he had treated the deliverances of the senses as sometimes clear but never distinct.”(Walsh; Edwards Ed. 1972, p 307) However, vagueness is a clear and distinct concept, and it seems that it also is in complete agreement with the “deliverances of the senses.” Thus, in the sense of mathematics that Whewell and others held, vagueness is a truly mathematical one, that is,

“…in mathematics there was no difference between objective reality and subjective knowledge; the human mind was completely in tune with external fact.” (Richards 1980, p 362) Rational thought and empirical observation are brought together into one concept: vagueness. This old idea of mathematical truth has changed drastically now. With Godel’s theorems, it became clear that an absolutist (that is mathematics is absolutely true and unchanging) view became untenable. One stronghold of the old sense in which mathematics is true (Whewell’s) can be found in the mathematician Brouwer’s intuitionism. According to Brouwer (and Kant before him), the experience of time is accessed to fill the empty formalisms of mathematics, giving it meaning and truth. Vagueness is another source of mathematical truth. It may be that vagueness between two things is present in Brouwer’s intuition of a “twoity,” the beginning of intuitionist arithmetic.

What do I mean by vagueness? The ancient representation of vagueness is the problem of the heap of sand. When you have a heap of sand, you have a relatively safe inference that if you take one grain from a heap, then you will still have a heap. As the story goes, eventually taking grains of sand will show this if, then statement to be faulty because you will no longer have a heap of sand. Why does classical “if, then” fail us here? There is an analogue between the heap of sand example and with the calculation of a real number according to a rule. Also, this question gains importance when reflecting that “Logical consequence [the if, then] is the central concept in logic. The aim of logic is to clarify what follows from what. – Stephen Read, Thinking about Logic [99]” (As quoted in Beall, Restall 2006, Kindle Edition) According to Beall and Restall, logical consequence can be clarified in more than one way, giving rise to more than one equally valid (if applied in different situations) formulation of logical consequence. “We must reconcile ourselves to the fact that every precise definition of [logical consequence] will show arbitrary features to a greater or less degree.” (Tarski as quoted in Beall, Restall 2006)” Additionally probability theory is not a solution to the vagueness of logical consequence, because

…probability theory might provide a canon for evaluating degrees of belief, … Nonetheless, probability theory cannot be a complete answer here, for we also make assertions and denials (and hypotheses and many other things besides), and these may also be evaluated for coherence, using the norms of deductive logic. In particular, we hold that it is a mistake to assert the premises of a valid argument while denying the conclusion… (Beall Restall 2006, Kindle Edition)

The solution to the vagueness of logical consequence, rather, lies in logical pluralism. Logical consequence brings true conditions to their true conclusions, but logical consequence itself is conditioned, and ultimately forms the structure of what can be intelligibly conditioned. Since phenomena are inherently vague, and logical consequence is vague until arbitrarily made precise, there is no clear difference between form and substance, ideas and things.

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Beall, J. C., & Restall, G. (2006). Logical pluralism. Oxford: Clarendon Press.

Edwards, P., & Walsh, W. H. (1972). The encyclopedia of philosophy (2nd ed., Vol. 4). New York: Macmillan.

Feyerabend, P., & Terpstra, B. (1999). Conquest of abundance: A tale of abstraction versus the richness of being. Chicago: University of Chicago Press.

Kuhn, T. S. (1970). The structure of scientific revolutions. Chicago: University of Chicago Press.

Richards, J. L. (1980). The art and the science of British algebra: A study in the perception of mathematical truth. Historia Mathematica, 7(3), 343-365. doi:10.1016/0315-0860(80)90028-2