Green Cars

My thoughts exactly, from a hilarious review of the new Honda Insight:

"Of course, I am well aware that there are a great many people in the world who believe that the burning of fossil fuels will one day kill all the Dutch and that something must be done.

...

But what about the eco-cost of building the car in the first place?

...

The nickel for the battery has to come from somewhere. Canada, usually. It has to be shipped to Japan, not on a sailing boat, I presume. And then it must be converted, not in a tree house, into a battery, and then that battery must be transported, not on an ox cart, to the Insight production plant in Suzuka. And then the finished car has to be shipped, not by Thor Heyerdahl, to Britain, where it can be transported, not by wind, to the home of a man with a beard who thinks he’s doing the world a favour.

Why doesn’t he just buy a Range Rover, which is made from local components, just down the road? No, really — weird-beards buy locally produced meat and vegetables for eco-reasons. So why not apply the same logic to cars?"

Death of a Bicycle

A brief change of topic is in order to mourn the loss...

Winning the War on Terror

There is this idea--this justification--that after 9/11, everything changes. That is, with regard to the War in Afghanistan, the War in Iraq, and the greater global War on Terror and its efforts at home, the events of September 11, 2001 must effectively restructure our way of life. And furthermore that the ways in which we have previously understood rights and both justice of war and justice in war are now subject to new rules and a radically different conception of what is and is not permissible. For the Bush administration this has meant justified expansion of the use of security forces and the armed services both at home and abroad; for Benjamin Netanyahu it means curtailing some civil liberties and basic rights to assume “an active posture against terror”; for Howard Zinn it means retooling America’s foreign policy to end the military superpower status and reinvent ourselves as the global humanitarian superpower.

Still for others it may be a nonsensical idea in a time when, after 9/11, everything ought to stay the same, with respect to the inalienable rights that lie at the foundation of the Constitution, and out of respect for the fact that, while quite large in scale and totally unjust, terrorism should not be seen as a new threat or as suddenly a more worthy foe now that America has been attacked. In other words, terrorism has long been a tool of fanatics, well known to the US government, and has cost many thousands of lives elsewhere, and should be addressed as such, if there is to be a “war on terror”. Asserting that everything now changes has been perhaps so easy for America to do in part because of what the world granted immediately after the attack in terms of sympathy for the American people and authority in bringing justice to the attackers. That the hijacking of planes was inexcusable was proclaimed virtually across the international board, and in some ways may have led to the posture of the US that it had free reign over the war and was justified on a unlimited basis because of the grotesqueness of the attack. However, once the war began, and the effort extended to the entire notion of terrorism instead of a more narrowly defined goal of only justice against the perpetrators the obvious inconsistency arose whereby the United States had to define terrorism in ways that exempted its own actions that could have fallen under most definitions of terrorism.

Eqbal Ahmad, in an address given in October, 1998 at the University of Colorado at Boulder, pointed out at length this fact that terrorism has not been adequately or officially defined by the United States. He outlined what he called the “official approach” to terrorism, and one of those points is the fact that “the official approach to terrorism is a posture of inconsistency”. Terrorism is approached not intellectually, he contends, but emotionally, where “officials don’t define terrorism because definitions involve a commitment to analysis, comprehension, and adherence to some norms of consistency”. The reasons for this are obvious enough, as public support for military response and might are not aroused by intelligent discourse but by emotional outrage. Not to mention that since the US has at times supported terrorists in Central America and the Middle East against governments, it becomes clear that a strict definition of terrorism would not serve well in a war that is supposed to be about the very eradication of the thing itself.

The other reason for the US avoidance of specific definitions of terrorism is that terrorists change. And not the terrorists, really, at least not always. More specifically, their respective strategic positions with respect to the United States is what is known to change. Where the Zionists in Gaza were terrorists, they became freedom fighters, and where Osama bin Laden was a US ally and became its foremost enemy. This inconsistency is facilitated by the whimsical and shifting notion of what makes a terrorist a terrorist. Indeed, the US has supported any number of objectively terrorist regimes in the name of the lesser of two evils or national self interest all over the world, as Ahmad explains in great detail.

What Ahmad aims at is the idea that if terrorism is to be confronted or defeated it must be understood, not simply hated. His position is that terrorism absolutely has causes, and that the US has historically ignored causes or justifications of any sort and instead shouted down the very idea to say that terrorism is blind, without cause or reason, that terrorists do not have a legitimate position and that the only goal of terrorism is barbarism. Ahmad certainly does not seek to justify terrorism as a legitimate means of communication or resistance, but it is still the case that understanding the motives of the terrorists must be understood if war is to be won against the very option of terror itself. Certainly there is an element of Islamic fundamentalist terror that can be understood as hatred of the West, but to dismiss every action and idea as causeless is to exacerbate the hatred such groups would have for America. The official response to terrorism that Ahmad discussed was given before the September 11 attacks, and deals largely with the historic approach taken by the US government toward terrorism. The fact that it was delivered before the attacks means, of course, that it does not speak to the notion that now everything changes, but perhaps addresses the fact that there remains an overarching issue long ignored and now realized that terrorism as a tool must never be acceptable.

But given that the terrorist attack on 9/11 happened, and with such incredible means and results, a new discussion has begun to take place. While of course ignoring other examples of terrorism, the discussion has been scaled down to specifically Islamic fundamentalist terrorism. What Benjamin Netanyahu has called for is “an active posture against terror” by the United States. What this means, among other things, is that the U.S. ought to seek out terrorists with increased security measures, increased interrogation, limited freedoms for its citizens, and a different set of ideals--one that emphasizes the responsibility to confront terror by means of “overwhelming technological and logistical advantages” over and above any imagined absoluteness of rights and liberties. It means government intelligence watching for terrorist activity day and night, monitoring fringe groups and “employing preemptive surveillance, search and seizure, interrogations, detentions, and prosecutions” whereupon there is evidence of terrorist activity.

This position has been taken by a great number of those on the political right, as well as the Bush administration with the likes of the U.S.A. Patriot Act which, although complicated, allows for many such measures to be employed at the discretion of the government and its information-gathering agencies. It seems like a common sense position at times, and in some respects is--curbing our security forces unnecessarily would certainly be inadmissible. But what seems striking is that the same people who generally do not support government intervention into things like the markets because of the government’s patent inefficiency and bureaucratic, cumbersome nature suddenly give full faith and credit to the same government as if those issues will cease to be. That somehow the government will be effective and precise in this department--and in it alone--is obviously flawed. This becomes even more so when the intelligence is part of Homeland Security, which is often just local authorities without proper training and the wholesale firestorm against any idea which seems to be out-of-bounds, whether it is a terrorist group or not. Simply pointing to behaviors in which terrorists might engage (even pamphleteering or indoctrination) does not expose terrorists necessarily.

Netanyahu properly points out that we have never had absolute free speech, and may have some reasonable restrictions placed upon it. For him, this extends to any number of other rights, and their being stunted by the government in the fight against terrorism is necessary. He claims that to not limit these freedoms and risk not defeating terrorism is to also deny basic human rights; those that are under attack when terrorism strikes. So it becomes in this sense a trade-off. Either rights are monitored during security concerns or terrorists may have an easier path to terror, which will also limit freedom. This argument is not without merit, but seems problematic for the very reason that those who have access to security and intelligence will inform the public about what the dangers are, and the public will be forced to believe the government, handing in its claims on rights, therefore leaning squarely on the government for what they previously held claim to not because the government granted it to them, but because God did. Those rights that the Constitution exclaimed could never be taken away are now doled out by the government only when it is safe to do so, effectively silencing the public during times of war. Duty and subordination are simply sold to the public because of a terrifying and eminent threat--emotion over intellect--and limited social institutions like religion and the press will have a difficult time holding accountable those at the top.

Netanyahu believes that anti-terror measures and limited rights for a time are successful ways to combat the evil of terrorism, and he points out the various countries around the world who have done so. Britain, Germany, Italy and France, he says, have all established anti-terror guidelines and systems that many would see as a denial of civil liberties. They all had a moment of clarity that forced their hands, so to speak, and although this particular argument was made prior to 9/11, Netanyahu would presumably conclude that we should now have reached America’s moment; that after 9/11, everything changes.

Professor Howard Zinn has proposed a vastly different approach to the whole notion of fighting terrorism. Writing early on in the War in Afghanistan, and even before the War in Iraq or the greater War on Terrorism, he saw in the fight a just cause, but a patently unjust war. Our techniques and methods of bombing cities was tantamount to terrorism itself, killing innocent civilians and displacing entire cities at a time. Without entering the messy business of what justice in war truly means, it is sufficient to note that the U.S. has, at times, engaged in the killing of civilians that, even if necessary or unavoidable for some cause or another would be regarded as a terrorist activity by many around the world. Zinn’s conclusion is that our military presence and tactics have incited much of the anger toward us, and a committed policy of humanitarianism over militarism would quell many of the angers and hostilities of the world. We stop fighting evil, perhaps, with the goal of removing some of its fuel and take an absolute stance on the moral high ground in not engaging the terrorist.

Both strategies seem to fly in the face of what America’s foreign and domestic policies have hoped to achieve. We have typically fought evil abroad (if reluctantly), and protected rights at home (except, of course, for Japanese Americans in WWII and other isolated but unacceptable moments of thievery of rights). And while both seem to distinguish themselves from the norm in unsavory ways, they both also hold an appeal to most people. Many have granted the government the power to do what needs to be done and given away certain freedoms. Many others are sympathetic to the idea that we could use defense spending on humanitarian aid and more positively affect the world. That this would do anything to stop the hatred of terrorist organizations though is, of course, debatable. One strategy has the proven techniques of anti-terrorist campaigns in its corner, the other the high-flown hopes of changing the terrorist mindset and removing American forces from areas which could be perhaps better served food than bombs.

Richard Falk wrote just days after the 9/11 attack that the military would need to exercise restraint and diligence in defeating terrorism because its nature means that it is “a war without military solutions... a war in which the pursuit of the traditional military goal of ‘victory’ is almost certain to intensify the challenge and spread the violence.” Falk is identifying the same type of issue as Ahmad in the need for America to seriously entertain the notion of causation in terrorist threats and attacks. He also lobbied for the type of multilateralism that would embrace sympathy from the world instead of the type of unilateralism that would undoubtedly turn the tide of support to anger and resentment. What happened is what Falk feared, a sort of military overreaction.

In addition to multilateralism and United Nations Security Council authorization, Falk argues that “if retaliatory action fails to abide by [international law and the just war tradition]...then it will be seen by most as replicating the fundamental evil of terrorism...as violence directed against those who are innocent and against civilian society.” This is of course a similar argument to the one made earlier by Howard Zinn, that our just cause becomes an unjust war when it displaces and disregards communities and makes casualties of innocent civilians. Even the most staunch of those against the UN and against the need of a world community for self defense should find attractive the notion that America would continue to uphold those things it aims to stand for, that make it worth defending in the first place. World support both militarily and monetarily would likely stem from America upholding the sanctity of innocent life and justice in war. Certainly the Bush Administration called upon the world for support against the terrorist regimes, and Falk further suggests that “a struggle against global terrorism even in its narrowest sense would require the most intense forms of intergovernmental cooperation ever experienced in the history of international relations.” Reducing the sole burden from America of defender of Western values like secularism and pluralism, freedom and democracy would be advisable and welcomed, but would require a different approach with regard to how Washington viewed the world beforehand.

Winning the War on Terrorism has become so vague and complicated a notion that its justification for continuance is as shady as ever. Winning the war might mean becoming less militarized and more humanitarian; it may mean limiting freedoms for a time to militarily strike the ability of terrorist cells to operate. Or it may, on the other hand, mean entirely reconfiguring the way the US views terrorism. It might mean that we no longer respond unilaterally to terrorism and that we consider it something to be understood, not as a viable means but as the reaction to something in the world, valid or otherwise. It might mean the assured destruction of all known terrorist camps and supporters, but that meaning would perpetually struggle with the simple fact that ideas do not often die with people, and the underlying contempt would almost certainly persist.

That terrorism is unacceptable has been well established by all reasonable parties in the discourse on justice and war. Without a doubt, the United States was justified in wanting justice and action against its attackers. But not all agree on what exactly should be the appropriate path toward such justice, and now, seven years after the attack the notion that after 9/11, everything changes may be at the end of its road. Although clearly an attack so large means that some things will change. The world has seen terrorism, however loosely and incoherently defined, brought to the forefront of international discourse. Although, for many in the world it was already the case, now America has simply tuned in. Decent people all over the world have hated terrorism and terrorist organizations in the Middle East and elsewhere for many years, but now that America has acted militarily is ways so similar to them they may have invited the same reaction to its shores as against the terrorists themselves.

Richard Falk succinctly summarized that the US could not itself seem to be a terrorist group, or in any way appear to fall in line with state terrorism, while at the same time condemning the terrorist organizations. “Such a double standard,” he wrote, “will damage the indispensable effort to draw a credible distinction between the criminality of the attack and the legitimacy of the retaliation.” We have seen this to be the case, and we shall continue to so long as the flag is permitted to fly that says, after 9/11, everything changes.

The proper response may take parts from all those previously mentioned--curtailed rights, humanitarianism, an understanding of terrorism--but they must all be subordinate to the very idea that, regardless of what is done to the United States--if it is what we have always said it is--that some things ought to change and some things ought not to. There must be a change in the US understanding of the need for world support and there must be some definitions on what winning the war really means. But there must not be a change with respect to how the US approaches justice and there must not be a change in the manner in which its citizens are dealt with. Overbearing security measures and a redefining of freedom in the name of defeating an unknown enemy will never be the means by which a war should be fought or won. To say that now things must change because of the magnitude of that terrible day is to bring into question what the principles this country rests upon are really worth, and to defiantly supersede what the world already knows in terms of terrorism and war. It is possible and desirable that the United States should cling to its vociferously proclaimed standards and ideals and resist the urge to militarily dominate this enemy, thereby winning the war for any and all who hope to continually celebrate upon those lofty and hard-fought mountaintops of liberty and justice for all.

(written in December, 2008)

See also:

Benjamin Netanyahu, Fighting Terrorism. “The Question of Civil Liberties" 1995. Pgs. 27-50.

Howard Zinn, "A Just Cause, Not a Just War" December, 2001, The Progressive.

Eqbal Ahmad, Terrorism: Theirs and Ours. Seven Stories Press, New York, 2001.

Mathematical Truth and Philosophy

Curtis J. Metcalfe
April 24, 2009

There lies at the heart of mathematics an assumed premise that it provides truth. We are taught
that the truth of mathematics is real, absolute, and indubitable. Mathematics, to the dismay of so many students, has right and wrong answers. It has explicit values and formulas. It is true and works at all times and for all people. It is eternal. Isnʼt it?

Math homework has been handed back covered in red ink that proclaims, “Yes!” But how can we
know that the truths of mathematics are, in fact, true? And even if they are, how do we have access to them? And do they give us truth about the world outside of mathematics, or is it merely a closed system, true but vacuous? By exploring first logic and the use of language, as well as the history of philosophy of mathematics, we can move toward the understanding of more complex systems of symbols and probabilities and can see how, in logic and philosophy, we attempt to derive truth from our language in much the same way we derive truth from mathematics and, indeed, vice versa.

RULES OF LOGIC
To the uninitiated it may seem strange that the most basic element of reason is actually an
argument. But in this way we are not arguing (in the usual sense) so much as arguing for a
conclusion.1 Properly understood, an argument is a defense of a particular position where we use one or more premise(s) to justify our arrival at a conclusion. We can take the following argument for example:
1. All human beings are born, not hatched.
2. I am a human being.
3. Therefore, I was born, not hatched.
So then, (1) and (2) are the premises and (3) is the conclusion. We see that if both of the premises are correct, the conclusion must be correct. It is utterly unavoidable. However, we do not have quite the truth we are looking for yet, since arguments are only (in this sense) defined by their form, not their content. An argument with false premises and a false conclusion, in proper form, is still valid. In this way, an argument cannot be said to be true or false, only valid or invalid. Only statements can be true or false.

This is a fundamental truth of symbolic logic. So to get sentences into a form manageable by a
system of formal logic, we use variables and symbols, whereby a sentence that reads, “either I am awake or I am asleep,” can be represented by, “p or q,” where p represents “I am awake,” and q represents “I am asleep.” Or, written in symbolic form, p∨q, where ∨ is the connective “or.”
Further, if p is true and q is true, then p∨q is true; if either p or q is false, p ∨ q remains true; if
both p and q are false, p ∨ q is false. We will return to the use of symbols later on.

We can set up such universal scenarios as these with truth tables for many other argument forms
and rules of inference, but it is sufficient for our purposes to understand that we can, on at least the level shown so far, use declaratory statements in simple forms, universally replaced by variables and computed in a way that shows the validity of our argument. Nevertheless, we must mind our propositions and carefully examine how we set up our arguments. For example, the argument form if p, then q; and p, therefore q is obviously valid. It is also valid for us to say, if p, then q; and ~q, therefore ~p. However, to conclude either ~p therefore ~q or q therefore p are invalid.2 But, one might wonder, what have we really shown to be true? At most, we have come up with some statements that under some circumstance may be true and at other times may not be. These statements surely are not necessary but contingent on some other set of facts, which is not the way we generally take mathematics to work. Logic, though it can be written in a mathematical form (as we will see with more complexity later), is only superficially related to mathematics in most instances. Clearly we do not place mathematics and language in the same discipline, so there must be differences.

RULES OF MATHEMATICS
Humanist philosopher and mathematician Reuben Hersch calls the method of mathematics
“conjecture and proof.”3 In this sense it is traditionally only mathematics that can claim to have a “proof” of anything, where a mathematical statement is shown to be true, necessarily. We say that 2+2=4 necessarily, and anyone who understand the terms “2” “+” and “4” as (1+1)+(1+1)
cannot deny the fact. But explaining exactly what a proof is can be a difficult if not impossible task, outside of understanding that it is, at least, how one convinces another of a theorem or conclusion.4 So it is this type of proof we are hoping to be able to apply to other areas, where we can show our conclusions in such a way that they are unavoidable, beyond doubt.

HISTORY OF MATHEMATICS AND PHILOSOPHY
The history of mathematics and philosophy, (philosophy of mathematics) is a lesson far too complex to address here. However, a few thinkers in particular can be seen as points on our line worth stopping to consider. The giants in both ancient and modern philosophy have sought to incorporate mathematics into their ideas. Platoʼs idea of mathematical objects existing immaterially in the perfect world of the Forms where the ideal version of everything exists is largely the framework by which mathematicians still work, aware of it or not. The absolute truths of mathematics exist, thought Plato, in the same way the perfect form of every abstract idea does. When one thinks of the color blue, it isnʼt some certain blue, but the very form of blue. Likewise, the idea of table must exist perfectly and immaterially in the realm of the forms in order that we recognize every individual, different table as having those categories essential for tableness. Or, when one has the idea of tiger it is surely not just one individual tiger, so that an actual tiger would cease to be recognizable because of its deviation from that one tiger in our mind. Somehow, we must have a notion, Plato thought, of tigerness, and it must be in the immaterial world of the Forms. Other philosophers like Descartes attempted to arrive at things in life so certain and indubitable, so clear and distinct, as the truths of mathematics, and Spinoza modeled his Ethics in a Euclidian fashion of axioms and theorems. David Hume accepted the truths of math only insofar as they gave vacuous truth, mere tautologies. The truth of 7+5=12 may hold, but gives us no truth about the universe. Math is like a game that we invented with arbitrary rules, so while even if it is true, it is contingent.

We can quite easily, perhaps, feel like Plato might have had a critical idea, but the idea of an
immaterial world presents some problems. How do we interact with it? How do immaterial and
material coincide? Does it not seem just as plausible that we abstract the general idea from the
specific experience? How can we have an idea of a tiger with no specific qualities, yet still call it a
tiger? Even if every mathematical truth is existent somewhere, somehow, how could we ever know it? It seems like there are problems, to be sure. But is the alternative better? Is math only a
game? We could imagine this being so in light of the use of language that is so necessary in
mathematics, but we also realize that mathematics just simply works too well, too often, and
(especially in physics and cosmology) too far away. But let us, for now, consider more deeply how mathematics applies to truth and philosophy and place the former questions on hold.

APPLICATION
So although there is considerable debate about the nature of mathematics and the absoluteness
thereof, we may consider certain axioms and rules in our language as they are used in areas such
as symbolic logic and probability calculus. By using symbols in a system of sentential, deductive
logic, we see a system very reminiscent of algebra. Indeed, “mathematics uses deductive logic to
get its results.”5 What follows will be several examples of each, as well as the mathematic
principles that help make them so.

SYMBOLIC LOGIC
Sentential logic deals with translating sentences with a truth-value into symbols.6 We symbolize
words like and, or, then, not and therefore.7 We can use the variables p and q to represent generic sentences, and constants (A,B,C, etc.) to represent specific sentences. Consider the sentence, “Alfred and Bill are funny.” We could say it differently, that, “Alfred is funny and Bill is funny,” or (A⋅B). If we say “Alfred is funny and Bill is not funny,” (A⋅¬B). Or, “Alfred is not funny and Bill is not funny,” (¬A⋅¬B) or (¬A⋅B). So the sentence “Alfred is funny or Bill is funny” is symbolized as (A∨B) and “Either Alfred is funny or Bill is funny, but not both is {(A∨B)⋅¬(A⋅B)}. Here one will notice the use of brackets and parentheses just as in an equation in algebra, and for the same sort of purposes. For example, (6× 2)÷3 ≠ 6×(2÷3). In the same way, (A⋅ B)∨C≠ A⋅(B∨C). To see what this looks like in predicate logic (where a property is ascribed to some individual entity), we can use the following argument.8

1.A temporal world exists. Te
2.God is omniscient. Og
3.If a temporal world exists, then if God is omniscient, God knows tensed facts. Te⊃(Og⊃Kg)
4.If God is timeless, He does not know tensed facts. (Tg⊃¬Kg)
¬(¬Kg)
5.Therefore, God is not timeless.
∴¬Tg

By assuming the truth of the statements, we can test for the validity of the argument. So, for
example, in (3) we see that if Og, then Kg, and since we established the truth of Og in (2) and the
first half in (1), then (3) is valid. In (4) we have if Tg then not Kg, but since we established in (3)
the truth of Kg, we can deduce (5), not not Kg, and therefore (6) not Tg.
Notice we have not determined the truth or falsity of the argument, only the validity. The validity of an argument is shown “if and only if it is not possible for all of its premises to be true and its conclusion false. If all premises of a valid argument are true, then its conclusion must be true also.”9 The conclusion is inescapable. So even though the truth of each premise may be dubitable, as long as it follows this form and these rules and the conclusion follows logically, it is valid. We can show one more example, also from an argument in Dr. Craigʼs “Timelessness and
Omnitemporality” where t represents any time prior to creation and n some finite interval of time:

1.If the past in infinite, then at t God delayed creating until t+n. Ip⊃Dg
2.If at t God delayed creating until t+n, then He must have had a good reason for doing so.
Dg⊃Rg
3. Ip⊃Rg
4.If the past in infinite, God cannot have had a good reason for delaying at t creating until t+n.
Ip⊃¬Rg
5. (Ip⊃Rg⋅ Ip⊃¬Rg)
6.Therefore, if the past in infinite, God must have had a good reason for delaying at t and God
cannot have had a good reason for delaying at t. Ip⊃(Rg⋅¬Rg)
7.Therefore, the past is not infinite. ∴¬Ip

(3)is not found in the argument explicitly, but is established by Hypothetical Syllogism from (1) and (2), where, if Ip then Dg and if Dg then Rg therefore (3) if Ip then Rg. And similarly, (5) is the addition of (3) and (4). In this way we could say symbolic logic looks like algebra. But could we say it has anything to do with numbers, or is it actually only a superficial similarity? To see a system of logic and philosophy that deals with mathematics in a more numerical way, we turn to probability.

PROBABILITY CALCULUS
Properly understood, a probability is the likeliness of something happening or not. In mathematics and philosophy we use probability calculations to determine how sound a belief is or how likely some outcome or another is. A probability will have a value between 0 and 1, with 0 being impossible and 1 being certain. What probability calculations give us, then, is a quantity with which to asses truth. Perhaps this is what we are looking for. First, consider the probability that two dependent events will have a certain outcome. We can write it in the following way to say that the probability of B given A equals the probability of B and A over the probability of A.
Prob (B| A)=Prob(B∩A)/Prob (A)

There are some general rules to consider 10:
1. Restricted Conjunction Rule
Prob (A⋅B)=Prob (A)×Prob (B)

2. General Conjunction Rule
Prob (A⋅B)=Prob (A)×Prob (B| A)

3. Restricted Disjunction Rule
Prob (A∨B)=Prob (A)+Prob (B)

4. General Disjunction Rule
Prob (A∨B)=Prob (A)+Prob (B)−Prob (A⋅B)

5. Prob (A⋅¬A)=0

6. Prob (A∨¬A)=1

7. Prob (¬A)=1−Prob(A)

But a more complicated probability is the inverse probability of Bayesʼ Theorem, which, in itʼs
general form is

Prob (q| p)= Prob (q)×Prob (p|q) / [Prob (q1)×Prob (p|q1)+…+ Prob (qn)×Prob (p|qn)]

But what does all of this probability calculus amount to? What does it give us? In their argument
against the claim that the fine-tuning of the universe can be used as evidence for an intelligent
designer, Michael Ikeda and Bill Jefferys have given the following argument in the form of
probability 11:

Prob (F&L&¬N)=Prob (L| F&¬N)Prob (F|¬N)Prob(¬N)<<1

What this says is that the probability of the conditions in the universe being life-Friendly, and the universe existing and containing Life and that the universe is not governed solely by Naturalistic laws equals the probability of the universe containing Life given that the universe is life-Friendly and not governed solely by Naturalistic laws times the probability of the universe being life-Friendly given that the universe is not governed solely by Naturalistic laws times the probability that the universe is not governed solely by Naturalistic laws is all less than 1. That the sentence is complex and far from our task at hand is obvious, but what must also be true is that, given all the multiplication of the probabilities, for it to be less than 1, at least one of Prob (L| F&¬N), Prob (F|¬N), or Prob (¬N) is quite small.12 In other words, some of the values (such as L) have a known value (in this case, 1). The entire argument is in fact conditioned against that value. With this argument Ikeda and Jeffereys hope to show that in any case the Prob (¬N) is very small, or that Prob (F) is also small. Whether they are correct (or on which count) is of course debatable (we are dealing in probabilities here), but it is clear that they are using the inverse probability to show their position.

CONCLUSION
All of these equations and calculuses are examples of the way we can use the form and method of
mathematics in our use of language and philosophy. But what have we learned? Is there anything that can be set in stone? Is anything indubitable? Whether the truths of mathematics are true at all times for all people in all places, (another galaxy?) or whether they are contingently true given some constants such as the gravitational pull or the laws of motion or a certain set of axioms, they seem to at least give us the ability to establish truth if only in limited ways. But does the fact that 2+2 might have a different sum in another possible world qualify it for the scrap heap of subjective judgements? It certainly seems not. So what nearly every philosopher and mathematician has assumed can be held given the fact that we can have such interdisciplinary application of formula and equation. Perhaps, then, it is not the case that mathematical truths must be eternal, but do we have need of such certainty? The conversation tends to drift away from the mathematician on the possibilities of a dualism which does not seem to arise from material causes or the ontological status of abstract and mathematical
objects, even if it is a hidden assumption of the working mathematician. That the mathematician or empirical scientist does not like the conclusion does not, of course, render it untrue, but it may present difficulties that need to be addressed. And indeed, the incredibly specialized and complex mathematics behind these assumptions may be outside the comfort of most philosophers, but one can confidently proceed on both fronts having established that mathematics and logic work in tandem to give us some analytic tools necessary to deduce truths about the workings of the world around us.

FOOTNOTES
1
Alan Hausman, Howard Kahane, Paul Tidman, Logic and Philosophy, (Thomson Wadsworth)
2007, p. 1
2
Antony Flew, How to Think Straight, (Prometheus Books, Amherst, New York) 1998, pp. 35-36.
3
Reuben Hersch,What is Mathematics, Really? (Oxford University Press) 1997, p. 5
4
For a more in depth look at the problems with proof and certainty see Hersh, chapter 4, and for the nature of mathematics see chapter 1. His argument is that mathematics are essentially social
constructs and do not transcend their own limitations and that numbers in our language operate
both as verbs and nouns and cannot have the sort of reliability we normally assign to them in any metaphysical or transcendent sense. The sum of the interior angles of a triangle are only 180
degrees exactly on a perfect triangle, and only on a Euclidian plane. Outside of Euclidian Geometry such a claim becomes dubitable. “Euclidʼs Fifth” axiom, if it is false, changes the very claim about triangles and their interior angles. However, he does not buy David Humeʼs contention that mathematics is “only a game” for various reasons, also external to our discussion. For our study, we will work inside the axioms traditionally set up, leaving the arbitrariness thereof for other discussions.
5
Hausman, et al., p. 21
6
Ibid., p. 22
7
We might, for example, see the following symbols and connectors: and ⋅; or ∨; if/then ⊃; if and
only if ≡; not ¬; therefore ∴
8
William Lane Craig, “Timelessness and Omnitemporality” Philosophia Christi, Series 2, Vol. 2, No. 1, 2000, pp. 29-33. His arguments are found only in the original sentence form, not in symbols, which have been added to show how these symbols work in argument and form.
9
Hausman, et al., p. 17.
10
Ibid., pp. 400-401.
11
Michael Ikeda & Bill Jefferys, “The Anthropic Principle Does Not Support Supernaturalism”, http://quasar.as.utexas.edu/anthropic.html, 2006. The paper is quite long and uses many different probabilistic arguments, only one of which is shown here as a use of the calculus with respect to an argument from philosophy.
12
Each of these gives a different scenario, such that the traditional concept of a deity is undermined with respect to the Anthropic Argument. None of them are particularly important to our discussion, as we are only attempting to show how the calculus applies, bridging the gap between the disciplines.

Kierkegaard On Preaching and Eloquence

from For Self-Examination, p. 3;

He who is going to preach ought to live in the Christian thoughts and concepts--they ought to be his daily life. If that is the case--and it is the intention of Christianity--you also will have eloquence enough and that very thing which is required when you give an impromptu talk. On the other hand, the power of eloquence is fallacious if anyone without otherwise occupying himself with these thoughts, without living into them, now and then sits and laboriously gathers such thoughts together, perhaps in the fields of literature, and thereupon works them together into a well-prepared speech which is then well memorized and excellently delivered both in respect to voice and diction and gesticulation. No, just as one in a well-equipped house needs not go downstairs to get water but has it on tap--one merely turns on the faucet--so that one is a genuine Christian speaker who has the power of eloquence every moment, has the real, true power of eloquence present, right at hand--because the Christ-like is his life.