A chapter planned for my Steroids to understand the philosophy, but there will be no lack of space. It is a work-in- progress should be reviewed and corrected.]
We finish our (inevitably incomplete) overview of philosophy by offering ten philosophical puzzles are invitations to extend the study in the directions they suggest
1. Zeno does overtake the tortoise?
Zeno! Zeno cruel! Zeno of Elea!
Hast thou pierced by the arrow winged
Who vibrates, flies, and do not steal! The sounding Shaft gives
and arrow killing me!
Ah! the sun. . . What shadow turtle
For the soul, Achilles still fast
Paul Valery
(The Marine Cemetery)
We know only little about Zeno of Elea (circa 490 - to 425), but what we do know suggests that he possessed an intellect absolutely remarkable.
Zeno was a disciple of Parmenides and was responsible for several extremely ingenious arguments to support the doctrines of his master on the impossibility and the illusory nature of the movement, of change and plurality. Specifically, Zeno, to defend these ideas, put forward in a troubling paradox (Proclus ascribes him 40 in a treaty unfortunately lost), intended to show that our intuitions about these things (movement, change, plurality), that he Parmenides and deny, are, and for good reason, inconsistent.
These paradoxes have since ceased to fascinate and concern of philosophers and scientists. Some of them, affecting the movement had a profound influence on the development of mathematics. They are known by the discussion devotes Aristotle in his Physics and are referred to by the following names: The Dichotomy, The Stadium, The Arrow and Achilles and the Tortoise.
We will concern ourselves here with the latter, probably the most famous, which is presented by Aristotle as follows: "[...] the slowest in the race will never be overtaken by the quicker, for he who pursues must always begin by achieving the point where the fugitive is gone, so that the slowest advance was always something. "What
understand by that? The tradition used to explain the example of a race between Achilles and a tortoise.
Achilles, the hero-footed, is, as we know, all the Greeks, the fastest runner. A race is still held between him and the slow turtle. Good player, Achilles gives the tortoise an advance. These are the basic data of the paradox. Assume for simplicity
Achilles advances one meter per second and the turtle forward two times slower.
Call A the point from which Achilles and the point where B from the turtle. The race begins and soon, in exactly 1 second, Achilles is able to point B. The turtle, meanwhile, advanced from .5 meters and is located at point C, when Achilles reaches the point B, and it is still ahead (but smaller) on the hero. The race continues. Achilles comes quickly to point C. But he took time to do so and during that time, the turtle, too, has advanced. The point here is D, Achilles joined very, very quickly, without doubt, but nevertheless asked the route for some time, during which the tortoise has reached the point E. And the reasoning goes this way, infinitely: and it is Therefore, concludes Zeno, Achilles can never, in a race, catch a turtle when he spent a step ahead.
Everyone knows that Achilles overtake the tortoise: the problem is not there, but in fact to indicate where the error in the reasoning of Zeno Zeno
suggests that the distance between Achilles Turtle constantly dwindling, but after each new stage of the race (in which Achilles reaches the point where the tortoise was in the previous step), it is still a new distance, however small it may be, to travel a distance that corresponds to the distance traveled by the turtle during the same time it takes Achilles to reach the point where it was Achilles will never succeed in overtaking the tortoise, which is still ahead of him in a given distance - which is steadily being eroded, but never completely abolished.
The paradox has inspired many developments in logic, mathematics and physics and some of them can explain what seems at first so paradoxical and cons-intuitive in the reasoning of Zeno.
Achilles travels first unit, that is to say that the meter leads to B. Then a half unit, which leads to point C. Then fourth unit, which brings it in D. And so on
In the language of modern mathematics, the distance it travels is expressed as follows:
1 + 1 / 2 + 1 / 4 + 1 / 8 +1 / 16 + 1 / 32 ... + 1 / 2n + ...
Zeno, we have seen, thinks that will never end. But modern mathematics suggests that we are here in front of a convergent series whose limit is 0. These two ideas - series converges with limit and zero - were unknown to the ancient Greeks and profoundly inhibited their ability to respond Zeno.
But this explanation does not satisfy everyone, and some point out that this series tends to its limit, but never reach it: which was precisely what Zeno's assertion.
2. The current King of France is bald?
Bertrand Russell (1872-1970), logician, philosopher and social reformer, was one of the most influential thinkers of the twentieth century. There is also a leading designer of this analytical method, inspired by logic and mathematics which is practiced extensively in philosophy in the Anglo-Saxon.
The famous "theory descriptions, "he explains in an article published in 1905, is a good example of what he proposes and she is also generally recognized as the paradigm of analytic philosophy of the twentieth century.
In very simple terms, saying that Russell shows that we are deceived by the language when we imagine that there must be a reference to any corresponding name and that this leads to obvious absurdities in the case of proposals as "L present king of France is bald. " France is not a monarchy and therefore has no king. The proposal is wrong? If they say, then, under the law of excluded middle, the negation - the current King of France is not bald - should be true: that which does not seem to make sense.
Russell's solution is clever and uses logic and analysis. It is to make explicit that the phrase implies the existence of a king of France, and decomposed into statements that may be asserted or denied separately.
If we agree to denote the predicate R "present King of France" and C "be bald," the proposal: "The present king of France is bald 'will be rewritten as follows:
1. There is an x such that Rx;
(There is a person who is king of France.)
2. For all y, if Ry, then y = x;
(There is only one: "the" king of France.)
3.Cx (This person is bald.)
What's Note in formal logic as follows:
x [(Rx y (R yy = x)) Cx]
Mischievous, Russell, who was not wearing Hegel in his heart, suggest that this kind of problem arises for by the Hegelians for whom the present King of France ... wears a wig!
3. Gettier problems call into question the analysis of knowledge advanced by Plato?
Remembering analysis Tripartite knowledge given by Plato.
But a contemporary writer, Edmund Gettier (1927) wanted to show, by imagining cons-examples, that this tripartite analysis of knowledge may be unsatisfactory after all. To do this, he imagined situations where three conditions are satisfied, but which can not be said of a subject S knows that P. This is one of them.
Suppose that Smith and Jones are both candidates to a certain position. Suppose further that Smith has good reason to hold true for the following conjunctive proposition:
(a) It is Jones who will get the job and Jones has ten coins currency in his pocket.
What are the good reasons not matter (say, if you will, the company president told Smith that Jones would get the post and Smith has just see Jones counting money he has in his pocket): the important thing here is that Smith is epistemically justified in holding (a) true.
Smith then epistemically justified in believing that the next proposal, which follows, is true:
(b) The person who gets the job has ten coins in his pocket.
But suppose also that, without his knowledge, it is he, Smith, not Jones who gets the job, and suppose further that he, Jones, also unwittingly, ten coins in his pocket.
Proposal (b) is true, although the proposal (a), from which it was inferred, is false.
Gettier suggests that in this example: the proposal (b) is true, Smith believes that the proposal (b) is true, Smith is justified in believing that the proposal (b) is true.
Yet it is clear that Smith does not know that the proposal (b) is true: firstly because it is true by virtue of the number of coins he has in his pocket and he does not know ; secondly because he bases his belief in the proposal (b) the number of coins in Jones's pocket, he also believes, but mistakenly, be the person who gets the job.
So? Should we rethink the tripartite definition of knowledge?
Many articles are published for further debate.
4. The paradox about the omnipotence of God is it conclusive?
As discussed above, the idea of God was considered inconsistent by many philosophers, for many reasons. Here is one, in the form of a paradox concerning omnipotence. It was designed by C. Wade Savage and he has so penetrated the popular culture that is even mentioned in an episode of The Simpsons. In
Weekend At burnsi's (released in 2002), there is in fact the following exchange between Homer and his pious neighbor Ned Flanders: Homer
: - Hey! I ask you a question. (He grabs a piece of paper) "God Could heat a tortilla in microwave oven until it is so hot that he himself could not eat it?"
Ned: - Of course! although it could ... ... Wow! For a snack coconut, it's a pain in the coconut!
Homer: Now you understand what I must endure.
Ned: Fortunately, I just here a book full of answers. (He pulls out a Bible and hands it to Homer, who flips).
Homer comes to find, at its special way, the intriguing paradox of Wade on the divine omnipotence of God called the paradox of the stone.
Here's how it formulated it in 1967 - where X is any being here:
1. Or X can create a stone that can raise X, or X can not create a stone that X can not lift.
2. If X can create a stone he can not lift, then it necessarily exists at least one task that X can not do, namely lift the stone in question.
3. If X can not create a stone he could not lift, then it necessarily exists at least one task that X can not do, namely create the stone in question.
4. So there are at least one task that X can not do.
5. If X is omnipotent, then X can accomplish any task
6. So X is not omnipotent. All
a snack coconut!
5. Wollheim he discovered a paradox at the heart of democracy?
Imagine a perfect machine that counts the votes of citizens in a democratic society to choose between various options.
One of these citizens, a democrat and conscientious thinking after mature consideration, that option A is preferable: it is then that choice in the machine. But others prefer B, which is of course inevitable in a democracy.
The machine records all votes and it is finally the option B was chosen. Our
democrat in this case seems to be a paradox. He must think simultaneously in effect a A part that is the option to follow, since that is the conclusion he reached after reflection on the other hand B is the option to follow, since that is the choice of the majority and it is a Democrat. This conclusion generalizes
course, and democracy seems able to drive, at least in some cases, all supporters of a minority position to have two opposing views of what should be done.
This analysis was presented in 1962 by Richard Wollheim (1923-2003), who sees a paradox at the heart of democracy. Is this the case? Is it important? And if the answer to both questions is yes, is it possible to resolve this paradox?
We always debate ...
6. The debate between free will and determinism is it a mystery?
Grab you a small object like a pen. Tension then the hand that holds it away from you, fist and palm down. Open the fist. The object falls to the ground.
Nobody is surprised: this body falls in line with what we tell our best-established physical laws, according to all that we know of how the world and its fall was planned even before it is released.
This fall is an illustration of most of this vast determinism that governs the universe and that the same causes produce the same effects. Again: no one is surprised.
... otherwise the person (or) a philosopher who wants to know why the hand that held the object, the body that owns this hand, this whole area surrounded by skin that we call a person escape this universal determinism. Because if asked, that person will insist that it is freely obeyed our request, made this subject and let fall. Or at least it's free it generally acts.
But here is taking a doubt meditating on the impact it had on inevitably place of birth, genetic background, her childhood, she made the meetings, the society where she lives, social class. And if it was, too, subject to universal determinism?
And yet our current notions of morality and our laws are based on the idea that although at least some cases we are responsible for our actions and that we choose: in other words we have free will .
So? Free will or determinism? Great ingenuity has been made on this issue with potentially huge implications.
Others believe that just as the problem of the mind, we are here before a mystery that will remain forever inaccessible to our poor minds.
7. The analysis of Sartrean bad faith is satisfactory?
The founder of psychoanalysis, Sigmund Freud (1856-1939), set a principle of psychic determinism at the heart of this discipline.
In its first version of the sychanalyse called first topography, Freud describes a dynamic the human psyche in which he distinguishes three levels - the unconscious, the preconscious and the conscious. According to him, drives (including libido or sex drive) located in the unconscious, seek to express the subject's consciousness. Repressed by censorship, they manage to deceive the vigilance and appear, albeit distorted, in the conscious life of the patient where they can be analyzed as evidence of an internal conflict. Freud studied in that phenomena such as dreams, missteps and lapses: under the principle of psychic determinism, all these manifest content can be understood as distorted versions of a latent content that appears to consciousness after the experience of censorship. Freud offers a famous fable to understand what he means. "Suppose that in the conference room, in my quiet and attentive audience, yet it is an individual who behaves so as to disturb me and disturbs me by inappropriate laughter, chatter or by typing its feet. I declare that I can continue to profess well, and thereupon some listeners will stand strong and, after a brief struggle, the character will at the door. It will be "repressed" and I can continue my conference. But for the disorder does not recur, if the deportee would try to enter the room, people who came to my aid will lean their chairs to the door and form as a "resistance". If we now carries on a psychic events in our example, if one of the conference room the conscious and the unconscious in the hall, this is a pretty good image of repression. "Freud goes on to say that the intruder, angry, try to get back into the room, as required by disguising himself or by entering through the window.
Jean-Paul Sartre (1905-1980) was in turn based his existentialist philosophy on the premise of full freedom of human beings by virtue of which I can always choose - and the absolute responsibility that entails. Psychoanalysis, then very popular, for it represents a possible refutation of his hypothesis of free human. Sartre confronts two times.
First, he argues that the notion of unconscious and those of censorship and repression presumed unconscious, are jointly inconsistent: in order to operate on instincts, censorship must decide those it leaves access consciousness and those it represses, while these impulses, by disguising himself to deceive the censors, testify that they intentionally pursue a project: all this, Sartre concludes, involves consciousness and can not by definition be unconscious.
But how then to account for these undeniable case of intrapsychic problems, since these things obviously we know and that we see, but without seeing and thinking up these actions and that no inexplicable and through a multitude of others? Sartre. And that's where its purpose is the most original, in these cases suggests that consciousness itself with guile, lies to herself, objectifies itself by suggesting that she has no choice. And is acting in bad faith according to Sartre. In the famous pages of Being and Nothingness, he describes this finely subtle mechanism, this art "to form concepts contradictory [...] that unite them in an idea and negation of this idea."
8. Why such responses to simple problems of trains?
work so-called experimental philosophy today are conducted at the intersection of philosophy and science. Some part of an effort to achieve what some call "experiments" Ethics.
The most famous and most intriguing of them are probably those who have focused on scenarios where people are asked to say what they would do in various situations involving what we call in English a trolley in a French trolleybus or a tram, typically in order to examine their moral intuitions and their eventual consistency. It has done so much research of this kind they are now refers to as "trolleyologie.
Examples.
Scenario 1: You and those threatened by a tram
Imagine the following situation. A
homeless people to the hospital and the doctor who finds that it would consider an ideal donor for five of his other patients, all waiting for a transplant imminent without which each of them will die.
The doctor could he, in this case, take heart from the homeless to give to one of his patients, his liver for transplant to another, her kidneys for a third ... and so on?
Most people think that doing so would be morally indefensible an abomination. If pressed to justify their position, they say you can not kill someone, even if it helps to save five others.
But imagine now a different situation.
You are near a railroad and you see a tram out of control running at full speed, rushing toward five people who did not see - and that the tram will therefore inevitably be killed.
The tram will arrive shortly, however in a place where the switching station near where you are, you will be able to change lanes. The tram then save the five people at risk. Unfortunately, in this case it will go down a road where another person, who will surely be killed.
short, the situation is such that if you do nothing, there will be five victims, whereas if you move a lever switching station, they will be saved - but another person will die.
Various surveys were made and they suggest that the vast majority of people (typically between 80 and 90%) believe it is morally defensible and justifiable to divert the tram to the one person to save five others.
We can see that our ethical intuitions in these two cases seem in tension with each other. In the first case, it is considered unacceptable to kill someone to save five others in the second case, we find it acceptable. Why? How to account for what seems an inconsistency of our moral intuitions?
One reason often cited is that a hospital is a place where you go for treatment. However, in the scenario imagined it would be the person attached to this function (a doctor) that would kill the one that came for care. Kill the patient, in a sense, ruining any possibility of further confidence in the institution and undermines the very foundations. The idea of an institution where you go for treatment is inconsistent with the suspicion that the doctor could see that we will cut you to treat his other patients.
Our intuitions are thus made consistent with the differences between both cases: what are all these other consequences as, for example on the institution, the killing of the homeless who explained that in this case, unlike that of the tram, it is not morally acceptable killing an innocent person to save five people. But
further complicates things.
Scenario 2: You are a fat person and tram
Here now the same scenario with the same tram, but this time with a variation. The tram arrives packaged
thus hurtling toward five people he is about to kill. You always watch the scene, but this time a gateway. Next of you stands a very big person: gold, its weight to it - but not yours - would stop the tram. You would therefore you seize this big person and throw down the bridge to save the five people in danger - which, unfortunately, will kill the big one.
Here, and always with great consistency, the majority of people think it is morally wrong to kill the big one, it was to save five others.
Why this difference if it was acceptable to bypass the tramway - which also killed an innocent person?
This time, it seems that the explanation cited earlier about the homeless can be used: throw the fat person does not have the kind of institutional consequences that had concerned the murder of a patient in a hospital by a doctor. What (s) difference (s) between the two situations can be invoked to explain the divergence of our intuitions?
Traditional morality proposes an answer to this question by inviting us to carefully distinguish between, on one hand, do something that will cause foreseeable harm, but something we do not want to see happen, and secondly intentionally do something wrong - and even if the consequences are the same in this case than in the previous case. Divert the tram is the first case; launch the big one, the second.
But other explanations have been advanced. By using magnetic resonance imaging (fMRI), psychologists have examined what happens in the brains of people experiencing these problems. (More precisely, for this specific research, independent coders rated various scenarios in moral or non-moral and personal or impersonal. The scenario involving the diversion of the tramway was classified as moral-impersonal big one involving the person was classified as a morale-staff.)
In the case, moral-impersonal, where he is to divert the tram by activating a lever, the brain areas associated reflection, reasoning, calculation of consequences and their review are particularly active, for cons, if moral-personal, where he is projecting the fat person, the brain areas associated with emotion are activated particularly.
The question, anyway, is far from closed.
9. Karl Popper (1902 - 1994) he solved Hume's problem?
A branch of philosophy, philosophy of science, is devoted, as its name suggests, the various sciences which are an inexhaustible reservoir of philosophical problems. One of them is rooted in the thinking of Hume.
Consider a scientist who hypothesized that all X are Y. If this was established, we know that the next X we will meet will also be a Y, and we know that if we want to get there, just find X, or make it happen one way or another. These consequences of the establishment that all X are Y are also important because they are the condition of both the explanatory power (I know that Y occurred because X s'état product) and predictive (I can assure that Y will occur since X happened) Science and scientific technology (if you want Y, let X happen). But how have we established the crucial result that "All X are Y"?
The answer to this question is obvious: we have seen many X and we found either that all X are Y (the law: "All X are Y" is so called universal) or that in a given proportion, all X are also Y (in which case the law: "All X are Y" is probabilistic).
Alas! The reasoning of Hume on induction starts down this beautiful building. For starters, the fact that countless observe X were all there can not, logically, to conclude that all X are Y: it is always possible that we will meet tomorrow a cons- example. But it gets worse. The induction is credible only if one assumes that nature is uniform, which, of course, can not be established by our observations of the world, such as are necessarily imitated, our justification of induction is itself based same on induction: what constitutes a vicious circle.
can (and according to Hume, must) be content with that, even admitting that all our knowledge is far more modest and fragile than generally believed and that the boundary between science and non-science or pseudo- science is less clear than we would like.
Karl Popper, for his part proposed an ingenious solution to the problem raised by Hume. Popper suggests that science does not proceed by deduction and induction but it does not seek to confirm his hypotheses or theories but to falsify them. Explain these two ideas. An inductive reasoning
passed the individual (and, ideally, a great many cases the individual) in general: I observe that this swan is white, than another is and, after many observations, I conclude by induction that all swans are white - my observations confirm this conclusion, making it more secure as my observations are more numerous.
Not at all, said Popper. Scientists develop hypotheses or theories from which they deduced the consequences and they are seeking, through observations, falsify, that is to say, to discover that they are false. But if a multitude of observations, say, white swans, can not logically confirm that all swans are white, the observation of a single black swan, New Zealand, where we find, is enough to falsify the hypothesis that all swans are white. A good scientific theory can be deduced from observations that may or may not be falsified. Those that will be rejected and those who are not are provisionally admitted.
Popper's solution, if accepted, solves the problem of Hume by showing that science does not proceed by induction and inductive confirmation. Masi has also other interesting consequences. Consider by exemeple distinction between science and pseudoscience. One and one make assumptions bold, being typically involve observable entities. But those of science, and they alone, are falsifiable in principle: we know that if we watched, we would declare false. Scientific theories (and the scientists themselves) take a risk to the real, that of being rejected and then both houses of scientific honesty and specificity of science. The pseudo-science, however, formulate hypotheses and theories that can never falsify anything and everything confirmed. Popper tidied Marxism and psychoanalysis in many of these theories unfalsifiable and contrasted with the truly scientific theories.
10. Will you live in a machine to happiness?
- Welcome to the Fair happiness, ladies and gentlemen! Ecstasy company is proud to unveil its new Eudaimonix 3000, the machine that makes you happy at last. Sit in the cubicle: you can then attach these electrodes to your head: we close the door and go. You dream of being an author of bestselling novel? To compose music with Paul McCartney? To be renowned surgeon? Eudaimonix through 3000, you will live those dreams and all the others you want. Warning: You will not even know that this is an illusion and nothing that you feel you can not be distinguished from the feelings a person who really lives all these things. Who is to chance? Step right up ladies and gentlemen. Have your life! As you happiness! And for as long as you decide: set a lifetime or a specified time - then you can be unplugged and decide whether or not you take your dream or even change it. It
the philosopher Robert Nozick (1938-2002) who designed such a machine - without naming it or present it well. It sought to highlight something which seems essential for morality. Nozick is the target of hedonism, which identifies the well subjectively felt pleasure, but utilitarianism - at least in versions that can be likened to a form of hedonism or the other.
Nozick think very few people, if anyone, would agree to connect to a Eudaimonix 3000. He puts forward three arguments for this conclusion.
The first is that we do not just want to feel things, but actually doing: and that's because we really do we gain pleasure.
The second is that we not only want to do things but also be a certain type of person - not that inert whose son out of power.
Nozick's final argument is that such a machine we restrict to a "real" designed by humans, without depth or more important than what humans can currently give it and without the possibility of explore any deeper dimensions of reality and discover new experiences.
Some things, Nozick concludes, are important in our lives beyond the experience, even pleasant, to be derived.
So: you log onto the Eudaimonix 3000?
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