π day is 3/14. But today is super π day: 3/14/15. To celebrate it properly you must do so at 9:26 A.M. or P. M. Years ago, as a student of electrical engineering, I memorized π this far out: 3.14159.
The decimal expansion is non-terminating. But that is not what makes it an irrational number. What makes it irrational is that it cannot be expressed as a fraction the numerator and denominator of which are integers. Compare 1/3. Its decimal expansion is also non-terminating: .3333333 . . . . But it is a rational number because it can be expressed as a fraction the numerator and denominator of which are integers (whole numbers).
An irrational (rational) number is so-called because it cannot (can) be expressed as a ratio of two integers. Thus any puzzlement as to how a number, as opposed to a person, could be rational or irrational calls for therapeutic dissolution, not solution (he said with a sidelong glance in the direction of Wittgenstein).
Yes, there are pseudo-questions. Sometimes we succumb to the bewitchment of our understanding by language. But, pace Wittgestein, it is not the case that all the questions of philosophy are pseudo-questions sired by linguistic bewitchment. I say almost none of them are. So it cannot be the case that philosophy just is the struggle against such bewitchment. (PU #109: Die Philosophie ist ein Kampf gegen die Verhexung unsres Verstandes durch die Mittel unserer Sprache.) What a miserable conception of philosophy! As bad as that of a benighted logical positivist.
Many people don't understand that certain words and phrases are terms of art, technical terms, whose meanings are, or are determined by, their uses in specialized contexts. I once foolishly allowed myself to be suckered into a conversation with an old man. I had occasion to bring up imaginary (complex) numbers in support of some point I was making. He snorted derisively, "How can a number be imaginary?!" The same old fool — and I was a fool too for talking to him twice — once balked incredulously at the imago dei. "You mean to tell me that God has an intestinal tract!"
Finally a quick question about infinity. The decimal expansion of π is non-terminating. It thus continues infinitely. The number of digits is infinite. Potentially or actually? I wonder: can the definiteness of π — its being the ratio of diameter to circumference in a circle — be taken to show that the number of digits in the decimal expansion is actually infinite?
I'm just asking.
Now go ye forth and celebrate π day in some appropriate and inoffensive way. Eat some pie. Calculate the area of some circle. A = πr2.
Dream about π in the sky. Mock a leftist for wanting π in the future. 'The philosophers have variously interpreted π; the point is to change it!'
UPDATE: Ingvar writes,
Of course the ne plus ultra pi day was 3-14-1592 and whatever happened that day
at 6:53 in the morning.
So we have one yearly, one every millennium, and one
once.
I Ain't Superstitious, leastways no more than Howlin' Wolf, but two twin black tuxedo cats just crossed my path. All dressed up with nowhere to go. Nine lives and dressed to the nines. Stevie Ray Vaughan, Superstition. Guitar solo starts at 3:03. And of course you've heard the story about Niels Bohr and the horseshoe over the door:
A friend was visiting in the home of Nobel Prize winner Niels Bohr, the famous atomic scientist.
As they were talking, the friend kept glancing at a horseshoe hanging over the door. Finally, unable to contain his curiosity any longer, he demanded:
“Niels, it can’t possibly be that you, a brilliant scientist, believe that foolish horseshoe superstition! ? !”
“Of course not,” replied the scientist. “But I understand it’s lucky whether you believe in it or not.”
It "drives him crazy" that people say 'at the end of the day.'
(Now why did I use double and then revert to single quotation marks? Because I went from quoting a particular person to mentioning a phrase in widespread use, but not quoting any particular person. There is no need for you to be so punctilious. Just don't call me inconsistent.)
I predict that the current controversy will soon be forgotten and Hillary will bounce back more formidable than ever. She looks tired, but she is as hungry as ever. She has Ambition written all over her. Do not underestimate her. The rumors of her imminent political demise are greatly exaggerated. Mark my words! I hope to hell and Hillary that I am wrong.
For a leftist, politics is her religion. That's the advantage they have over us. We are at the Conservative Disadvantage.
One of the reasons I gave this weblog the title Maverick Philosopher is because I align neither with the analytic nor with the Continental camp. Study everything, I say, and drink from every stream. Reverting to the camp metaphor, when did the camps become two? In dead earnest this occurred when Heidegger burst onto the scene in 1927 with Being and Time. I agree with Peter Simons: "Probably no individual was more responsible for the schism in philosophy than Heidegger." (Quoted in Overgaard, et al., An Introduction to Metaphilosophy, Cambridge UP, 2013, 110.) It is not as if Heidegger set out to split the mainstream whose headwaters were in Franz Brentano into two tributaries; it is just that he started publishing things that the analytic types, who had some sympathy for Heidegger's main teacher Husserl, could not relate to at all.
If I were were to select two writings that best epitomize the depth of the Continental-analytic clash near the time of its outbreak, they would be Heidegger's 1929 What is Metaphysics? and Carnap's 1932 response, "On the Overcoming of Metaphysics Through the Logical Analysis of Language." (In fairness to Carnap, let us note that his Erkenntnis piece is more than a response to Heidegger inasmuch as it calls into question the meaningfulness of all metaphysics.)
To nail my colors to the mast, I take the side of Heidegger in his dispute with Carnap and I heartily condemn the knee-jerk bigotry of the thousands upon thousands of analytic types who mock and deride Heidegger while making no attempt to understand what he is about. The cynosure of their mockery and derision is of course the notorious sentence
Das Nichts selbst nichtet. (GA IX, 114) The Nothing itself nihilates.
This is the line upon which the analytic bigots invariably seize while ignoring everything else: its place in the essay in question and the wider context, that of Being and Time and other works of the early Heidegger, not to mention the phenomenological, transcendental, existential, life-philosophical, and scholastic sources of Heidegger's thinking.
Now, having called them knee-jerk bigots and having implied what is largely true, namely that the analytic Heidegger-bashers are know-nothings when it comes to Heidegger's philosophical progenitors, and thus having paid them back in their own coin, I will now drop all invective and patiently try to explain how and why Heidegger is not talking nonsense in the essay in question. This will require a series of posts. It will also require some attention and open-mindedness on the part of the reader as well as some familiarity with the two essays in question.
Heidegger's Alleged Violation of Logical Syntax
For Carnap it is obvious that existence and nonexistence are purely logical notions, more precisely, logico-syntactic notions. The sentence 'Cats exist,' for example, does not predicate existence of individual cats. It says no more than 'Something is a cat.' But then 'Cats do not exist' says no more than 'Nothing is a cat.' This sentence in turn is equivalent to 'It is not the case that something is a cat.'
'Nothing,' then, is not a name, but a mere bit of logical syntax. Carnap calls it a "logical particle." (71) And the same goes for 'something.' If I met nobody on the trail this morning, it does not follow that I met somebody named 'nobody.' (Bad joke: I say I met nobody, and you ask how he's doing.) If nothing is in my wallet, that is not to say that there is something in my wallet named 'nothing.' It is to say that:
It it not the case that something is in my wallet It is not the case that, for some x, x is in my wallet For all x, x is not in my wallet ~(∃x)(x is in my wallet) (x) ~(x is in my wallet).
The above are equivalents. It should be obvious then, that in its mundane uses 'nothing' is not a name but a logico-syntactic notion that can be expressed using a quantifier (either universal or particular) and the sign for propositional negation. By a mundane use of 'nothing' I mean a use that presupposes that things exist. Thus when I assert that nothing is in my pocket, I presuppose that things exist and the content of my assertion is that no one of these existing things is in my pocket. (Don't worry about the fact that it is never strictly true that there is nothing in my pocket given that there is air, lint, and space in my pocket.)
I think we can all (including Heidegger) agree that in their mundane uses, sentences of the form 'Nothing is F' can be translated, salva significatione, into sentences of the form 'It is not the case that something is F' or 'Everything is not F.' The translations remove 'Nothing' from subject position and by the same stroke remove the temptation to construe 'nothing' as a name. Not that Heidegger ever succumbed to that temptation.
But now the question arises whether every use of 'nothing' fits the deflationary schema. Is every meaningful use of 'nothing' the use of a logical particle? Consider ex nihilo, nihil fit, 'Out of nothing, nothing comes.' The second occurrence of 'nothing' readily submits to deflation, but not the first. Suppose we write
It is not the case that something comes from nothing.
This removes the quantificational use of 'nothing' in 'Out of nothing, nothing comes' but leaves us with a 'substantive' use. Of course, 'nothing' cannot refer to or name any being or any collection of beings. That is perfectly evident. And Heidegger says as much. But 'nothing' does appear to refer to, or name, the absence of every being. The thought is:
Had there been nothing at all, it is not the case that something could have arisen from it.
The 'at all' is strictly redundant: it merely serves to remind the reader that 'nothing' is being used strictly. Now could there have been nothing at all? Is it possible that there be nothing at all? More importantly for present purposes: Is this a meaningful question? 'Possibly, nothing exists' is meaningful only if 'Nothing exists' is meaningful. So consider first the unmodalized
There is nothing at all
or
Nothing exists.
These are perfectly meaningful sentences. That is not to say that they are true, nor is it to say that they are possibly true. Suppose they are not possibly true. Then they are necessarily false. But if necessarily false, then false, and if false, then meaningful. For meaningfulness is a necessary condition of having a truth-value. 'Nothing exists,' then, is a meaningful sentence, and this despite the fact that 'nothing' cannot here be replaced by a phrase containing only a quantifier and the sign for negation.
For Carnap, however, the above are meaningless metaphysical pseudo-sentences because they violate logical syntax. If you try to translate the second sentence into logical notation, into what Carnap calls a "logically correct language"(70) you get a syntactically meaningless string:
~(∃x)(x exists).
This is meaningless because 'exists' cannot serve as a first-level predicate in a logically correct language. Existence is not a property of individuals. 'Exist(s)' is a quantifier, a bit of logical syntax, not a name of a property or of any entity. Therefore, 'Nothing exists' is as syntactically meaningless as the ill-formed formula
~(∃x)(∃x(. . . x . . .)).
Two Interim Conclusions
The first is that Heidegger commits no schoolboy blunder in logic. He does not think that a use of 'Nothing is in the drawer' commits one to the existence of something in the drawer. He cannot be charitably read as assuming that every use of 'nothing' is a referring use. The second conclusion is that Carnap has not shown that every occurrence of 'nothing' can be replaced by a phrase containing a quantifier and the sign for negation. He has therefore not shown that a sentence like 'Nothing exists' is a syntactically meaningless pseudo-sentence.
Heidegger Partially Vindicated
But now the way is clear to ask some Heidegger-type questions.
I showed above that 'nothing' has meaningful uses as a substantive, uses that cannot be eliminated by the Carnap method. And I suggested that 'nothing' could name the total absence of all beings. If this total absence is a possibility, as it would be if every being is a contingent being, then Nothing (das Nichts) would have some 'reality,' if only the reality of a mere possibility. It could not be dismissed as utterly nichtig or nugatory. Nor could questions about it be so dismissed.
One question that Heidegger poses concerns the relation of negation (Verneinung) as a specific intellectual operation (spezifische Verstandeshandlung) to Nothing:
Gibt es das Nichts nur, weil es das Nicht, d. h. die Verneinung gibt? Oder liegt es umgekehrt? Gibt es die Verneinung und das Nicht nur, weil es das Nichts gibt? (GA IX, 108)
Is there Nothing only because there is the Not and negation? Or is it the other way around? Is there negation and the Not only because there is Nothing?
I grant that with questions like these we are at the very limit of intelligibility, at the very boundary of the Sayable. But you are no philosopher if you are not up against these limits and seeking, if possible, to transcend them.
The True Gentleman is the man whose conduct proceeds from good will and an acute sense of propriety, and whose self-control is equal to all emergencies; who does not make the poor man conscious of his poverty, the obscure man of his obscurity, or any man of his inferiority or deformity; who is himself humbled if necessity compels him to humble another; who does not flatter wealth, cringe before power, or boast of his own possessions or achievements; who speaks with frankness but always with sincerity and sympathy; whose deed follows his word; who thinks of the rights and feelings of others, rather than his own; and who appears well in any company, a man with whom honor is sacred and virtue safe. – John Walter Wayland
The differences that divide us most deeply are bred in the bone before they are born in the brain. This truth warrants a healthy skepticism concerning the prospects of political 'dialog.'
A recent article bears the title, "The vast right-wing conspiracy is still real. Also, the media is really stupid." The first sentence reads, "Let me start by admitting, upfront, how truly fucking boring I find the Hillary Clinton e-mail story."
I stopped right there.
Suppose Mrs. Clinton broke no law. Her imprudence alone in conducting official business while Secretary of State using a private e-mail server is a strong argument against her. It smacks of an imprudence born of arrogance and of a sense of high entitlement as if nothing she does nor how she appears can impede her progress to her rightful place. If anyone understands that the world runs on appearances, it is the politician. What level of chutzpah does it then bespeak that she appears not to care that people find out what she must know they will find out?
UPDATE (3/11): Roundup of reactions to Hillary's press conference yesterday. The imperiousness of the lady may contribute to her undoing. That, and her naked ambition. With apologies to William Shakespeare, "Yon Hillary hath a lean and hungry look . . . ." She lusts after the title Hillaria Imperatrix. She would push further the executive overreach of Obama's imperial presidency.
But conservatives beware. Her egregious blunders if not illegalities may not sink her. Nor the vacuousness of her rhetoric. Nor the deviousness of her stealth leftism. The feckless Obama was elected and elected twice. Hillary is not to be discounted. Her base is large and will support her no matter what she does. The next election is not to be sat out. Politics is a practical business; it is always about the lesser or least of evils.
I prefer the more muscular 'lie.' Excerpts from a piece by John O. McGinnis:
Progressivism’s vision of the role of the state conflicts with the system of government envisioned by America’s Founders. The Founders wanted citizens to be free to pursue their affairs individually and in voluntary association; the powers of the federal state were to be tightly constrained. In contrast, the greatest political theorist of American progressivism, Herbert Croly, said that the nation’s “democracy should be focused on an equal sharing of wealth and responsibilities”—an enterprise that demands a larger and more intrusive federal state to enforce. Obama spoke from this tradition on the campaign trail in 2008—most famously, when he told Joe the Plumber that it was “good to spread the wealth around.”
[. . .]
Faced with these constraints, today’s progressives must resort to more misleading and sometimes coercive measures, as they seek to bring about equality through collective responsibility; they must rally support by looking beyond economics, to cultural and social identifications, in a bid to maintain the support of voters with little need for government intervention. They also want to limit the voices of citizens at election time, and thereby magnify the influence of the press and academia, which lean sharply in the progressive direction.
Nothing shows the progressive dependence on subterfuge more starkly than Obamacare, which, by imposing a personal mandate to buy insurance in an effort to bring health care to all, will restructure one-sixth of the American economy.
[. . .]
From its inception, progressivism has posed a threat to constitutional government. It has sought to replace limited and decentralized governance with dynamic, centralized authority in order to force some arrangement of equality on the nation. Because the world has a way of upsetting abstract designs, progressivism depends on empowering administrators to impose its frameworks while disempowering citizens from resisting these coercions. The Obama administration’s push for unilateral presidential authority to disregard the law is thus the logical extension of the progressive program. Opposition to this program requires nothing less than a rededication to our Founding ideals: our nation must be governed by the rule of law, not the rule of an elected monarch or of a legally privileged aristocracy.
While traipsing through the Superstition foothills Sunday morning in search of further footnotes to Plato, I happened to think of James Madison and Federalist #51 wherein we read, "If men were angels, no government would be necessary." My next thought was: "Men are not angels." But I realized it could be the formal fallacy of Denying the Antecedent were I to conclude to the truth, "Some government is necessary." (I hope you agree with me that that is a truth.)
The first premise is a counterfactual conditional, indeed, what I call a per impossibile counterfactual. To keep things simple, however, we trade the subjunctive in for the indicative. Let this be the argument under consideration:
1. If men are angels, then no government is necessary. 2. Men are not angels. ergo 3. Some government is necessary.
A prima vista, we have here an instance of the invalid argument-form, Denying the Antecedent:
If p, then q ~p ergo ~q.
But I am loath to say that the argument (as opposed to the just-depicted argument-form) is invalid. It strikes me as valid. But how could it be valid?
Approach One
One could take the (1)-(3) argument to be an enthymeme where the following is the tacit premise:
1.5 If no government is necessary, then men are angels.
Add (1.5) to the premises of the original argument and the conclusion follows by modus tollendo tollens.
Approach Two
Might it be that 'if ___ then ___' sentences in English sometimes express biconditional propositions? Clearly, if we replace (1) with
1* Men are angels if and only if no government is necessary
the resulting argument is valid.
Approach Three
One might take the (1)-(3) argument as inductive. Now every inductive argument is invalid in the technical sense of 'invalid' in play here. So if there are good inductive arguments, then there are good invalid arguments. Right? If the (1)-(3) argument is inductive, then I think we should say it is a very strong inductive argument. It would then be right churlish and cyberpunkish to snort, "You're denying the antecedent!"
The question arises: are there any good examples from real argumentative life (as opposed to logic text books) of Denying the Antecedent? I mean, nobody or hardly anybody argues like this:
If Jack ran a red light, then Jack deserves a traffic citation. Jack did not run a red light. ergo Jack does not deserve a traffic citation.
