EXAM review Flashcards
Ancient argument for the infinity of space.
Lucretius’ case for the infinitude of space:
***If the universe has a boundary, there must be something outside of it to limit it. But nothing can be outside the universe.
***Suppose there is an edge and you can stand there and throw a missile. If it goes forward, then there is no boundary and you are not at the edge. If it is blocked, then there is something outside and you are not at the edge.
Ancient arguments for the atomic nature of matter.
Lucretius: the study of changes in matter requires us to accept that the basic parts of matter are much smaller than we have imagined.
When we observe slow changes in nature, we infer that they are cumulative effects of very small changes.
From the effects of slow changes we must infer that there are small parts of matter far smaller than anything that we can perceive.
Example 1: Wind has the power to alter physical things just as water does. Both must be matte run motion. But the wind is not directly perceptible. Therefore the moving matter must consist of parts too small to see.
Example 2: Metal and stone objects are worn by use (e.g. handling, or being stepped on. The effect of much use is cumulative. But no individual action has a perceptible effect. Therefore particles too small to see are being removed from the object.
Example 3: Dripping water, over a long time, can create a depression in stone. Therefore each drop of water must be dislodging imperceptible particles from
“Paradoxes” of infinity: what is paradoxical about infinite sets
The infinite turns out to be the contrary of what it is said to be. It is not what has nothing outside it that is infinite, but what always has something outside it.
A quantity is infinite if we can always take a part outside of what has already been taken. On the other hand, what has nothing outside it is complete and whole. We define something that is whole, as a thing where everything remains intact, and nothing is outside. If you can take something from a whole quantity, however small that may be, then the remaining quantity is not “all”. Nothing is complete which has not ended; and the end is a limit.
It’s not about what is whole, it is about what is not whole but cannot be emptied.
A. Zeno’s “Arrow” paradox:
An arrow must move half the distance to its target. Then it must move half of the remaining distance, then half of that and so on. To reach the target is therefore an infinite task.
B. Zeno’ “Achilles” paradox:
Achilles is the fastest creature on legs. But can’t over take a tortoise who has the slightest head start, when he reaches the starting point of the tortoise the tortoise will always already have moved further.
These paradoxes illustrate the contradiction between our conceptual understanding of motion and perception of motion.
The key to understanding this paradox is to understand that not all infinite sets are the same size.
A paradox of the infinite: (“Russell’s paradox”)
Ordinary set: does not contain itself as an element.
E.g: The set of all natural numbers is not itself a natural number, and so it is not an element of itself.
Extraordinary set: does contain itself as an element: E.g: The set of all sets not mentioned in the Bible is itself not mentioned in the bible, so it is an element of itself.
The set: S: the set of all and only ordinary sets: i.e. the set of all sets that are not elements of themselves. If S is an ordinary set, then it should contain itself as an element since it is supposed to contain all ordinary sets.
But that means that S is an extraordinary set since the extraordinary sets contain themselves as elements.
So S is not the set of ordinary sets, since It contains an extraordinary set (itself).
Example: Barber of Alacala: He only shaves men who do not shave themselves. Therefore, he is a man who does shave men, who shave themselves)
Countable vs Uncountable infinity
The different sizes of infinite sets can be understood through the concept of one-to-one correspondence: by matching all the numbers for set A to all the numbers to set B.
ex. If set a is a line segment of 4 metres, and set B is a line segment of 6 metres. You can match all the points from 1-4 an infinite amount of times. But when you try to match the points that are 4 metres and greater, you will find that you cannot do that because set A is only 4 metres long. Therefore it could be said that set B has more points then set A, despite both lines having an infinite amount of points.
Countable Infinity: A set is countable if it can be placed in 1-1 correspondence with the natural numbers.
Example, every number that can be expressed as the ratio of two whole numbers: it contains every possible numerator and every possible denominator.
Uncountable infinity: are a set of real numbers that cannot be expressed as a whole number ratio.
Pi = 3.1415692635… each decimal expansion continues forever without settling into a repeating set of numbers.
NON example: 0.3333333… because it is not irrational, it can be expressed as 10/3.
Despite the fact that Infinite Sets are not equal shown through understanding one to one correspondence. Attributes like “equal”, “greater”, and “less” cannot be applicable to infinite but only to finite quantities. This is shown through the examples below.
Galileo’s example of Roots and Squares. If there is a sample of 100 numbers, then there are 100 real numbers and 10 squares. It would be sound to say that there are more real numbers than squares. The same cannot be true about an infinite set. If you have an infinite amount of real numbers. Then you have an infinite amount of squares, despite the fact squares appear less frequently than real numbers.
The same could be applied to the concept of two number lines, one being longer than the other. Even though one segment is longer than another, there are infinite points one each line. Even though one segment is larger, than the other, you cannot say something is greater than infinity because that is incomprehensible.
Example 3: salt and water example, if we were taking water out of the infinite well, there is an infinite amount of salt and water, although salt appears much less frequently then water.
Laplace’s view of the role of probability in human reasoning:
From a complete description of the state of the universe at any moment, and the complete laws of nature, the state of the universe at any other moment, past or future, could be deduced with certainty.
Probability theory: given that there are n possible outcomes, and no circumstances that favour any one one over the others, the probability of any outcome is 1/n.
How to understand determinism in space and time:
Everything in the universe is a particular physical state at any given time. The laws of nature determine how the state at any one moment evolves into the state at any future moment.
Example: If you know the positions and velocities of all the planets in the solar system at a certain time, you can predict their future positions.
You can even “retrodict” their positions in the past.
Laplace’s account of determinism:
“Laplacian determinism”, in classical world: if you know the position and momenta of all the particles at a given time t, you could deduce the trajectories for the future for the entire future or past.
Laplace’s Demon: an being of a higher intelligenvce that would be able to know all past and future events if it knew the postitions and velocities of all atoms in the Universe. The demon would be able to embrace in single formula the movement of the greatest bodies and those of the tiniest atom.
In Laplace’s world, everything is predetermined and there is no chance, no choice, and no uncertainty.
Hume’s explanation of the origin of our idea of causal necessity:
All of our reasoning about necessity in nature comes from our understanding of how effects follow causes, which we learn only from their regular conjunction:
Hume’s idea that philosophical disputes about free will arise from disagreements about words:
When a philosophical debate has continued inconclusively for many centuries, we have to consider the possibility that it is a merely verbal dispute, i.e., a dispute in which opposing arguments are based on different understandings of the fundamental terms being used.
Perhaps if we agree on careful definitions of philosophical terms such as “liberty” and “necessity”, we can avoid the endless and pointless dispute on the topic of free will.
Hume: before we consider whether human behaviour is a matter of “free will or “causal necessity”, let’s ask: What do we mean by causal necessity at all? Why and when do we think that events in nature happen because they are caused by other natural events?
Hume’s view of the compatibility of free will and determinism:
According to Hume, we have to think of unpredictable human actions the way we think of unpredictable natural events. If we know all the circumstances, we could predict human behaviour as well as we do any other natural phenomenon.
Hume’s view of unpredictability in nature follows that of Laplace: your ability to predict accurately depends on the completeness of our knowledge of all the factors involved in determining outcomes. Our ignorance limits us to probabilities.
Therefore, according to Hume, we have the same basis to attribute casual necessity of human action that we have to attribute it to nature in general: the regular convictions of cases and effects we observe.
All of this means that, whether they admit it or not, all philosophers accept the necessity of human behaviour in the only meaningful sense of that term. Human behaviour follows natural laws along with the rest of the natural world.
Free will and moral responsibility according to Hume.
The true meaning of liberty: The ability to act in accord with one’s will, instead of being constrained, by whatever circumstances, from acting according to one’s will. This is the foundation of our sense of moral responsibility, moral praise and blame.
The false meaning of liberty: the ability to act in a way that is not determined by prior causes. This is essentially random behaviour, for which no one can be held responsible.
If the true meaning of liberty is to act in accordance to one’s will, and one’s will is predetermined by natural causes. Then free will and determinism are in fact, compatible.
Hume’s account of why human actions seem more distinct from natural events than they really are:
The causes of human actions are usually hidden to us.
Hume: The same kind and degree of necessity that we can observe in natural events — i.e, the regular association of cause and effect - is observable in human events.
From the uniformity and predictability of human behaviour, through history, we see evidence of this regularity and necessity.
Why do we see the latter as so unlike the former, i.e. as not subject to causal necessity?
It is because the causes are usually hidden from us.
Hume’s argument against the principle that all events are determined by the will of an all-powerful deity:
Hume: To explain human behaviour as determined by a Diety raises additional problems of its own:
This is the long standing “problem of evil”: if the gods have pre-determined all human activity, then the responsibility for evil rests with them.
God is omnipotent and perfectly good. If he is perfectly good, then he would eliminate evil as far as he could. But there is evil in the world. SO, there is no God.
Alternatively, humans can be held responsible for evil, and the gods excused, only on the presumption of free will.
Daniel Dennett’s view of what is illusory about the notion of free will:
The fact that humans are self-examining creatures. We are able to change by self-examination that may have been determined by pre-existing causes, but we are able to look inside.
“If determinism is true, the future is set - and this includes all our future states of mind and our subsequent behaviour. And to the extent that the law of cause and effect is subject to indeterminism - quantum or otherwise - we can take no credit for what happens. There is no combination of these truths that seems compatible with the popular notion of free will.”
What we think we experience as an act of will that causes our behaviour is in fact an effect of prior causes. We have the illusion that in any situation in which we act, we might have done otherwise. But we could n’t have done otherwise in the same circumstances, as an outcome of the same causal chain.
Dennett believes Harris treats the self as a “dimensionless point” that is a passive observer to the see of brain operations. This is very incorrect as Harris therefore ignores the “self educating, self-manipulating, self-exploring aspects of human mental activity” in the common-sense notion of free will.
Humanitarian argument against free will: the illusion of free will causes us to assign moral blame or praise for conditions, and action, over which people have only the illusion of control.
For the sake of social and psychological health. We should treat behaviour as having deterministic causes instead of the result of free choice (HARRIS).
Dennett’s view of what is right about the common-sense notion of free will
“Folk” beliefs about human agency, even though they sometimes sound naive, are usually understandable as sound principles that reflect an underlying “compatibility” view.
The scientific argument against free will: to the extent that the world’s events unfold according to deterministic laws of physics, even the events: “in our minds” are just physical events in our brains that are determined by earlier chains of events (Sam Harris)
To the extent that the world is governed by indeterministic laws of quantum mechanics, mental events are less predictable, but still the products of purely physical processes: We still don’t deserve any credit” for our choices, since they are brought about by purely physical processes.
As Dennett is a compatibilist, this is correct, as our will is determined by pre-existing causes. However, that does not mean that humans are not responsible for their actions. As long, as those actions do not arise from external coercion, humans are responsible for their actions as they had the liberty to act on their will, even if it was determined by pre-existing conditions.
Connection between free will and moral responsibility
The sense that for any human action “I could have done otherwise”, is an essential part of moral judgement and personal (emotional, psychological) development.
Philosophical motivation for skepticism
Some basic non-skeptical attitudes:
Empiricist foundationalism: The senses provide the ultimate criteria for justifying belief.
Rationalist foundationalism: The sense give subjective or even deceptive appearance, and only reason provides a foundation for certain knowledge.
Mysticism: individuals can have private access to revealed truth not necessarily accessible to others.
Authoritarianism: Certain persons (the pope) are empowered to know and speak the truth on fundamental matters.
Some basic skeptical attitudes:
Dogmatic skepticism: Nothing can be known. Nothing is true. All human claims to knowledge are false.
Pyrrhonian skepticism: Certainty is impossible, so the wise person should suspend judgement about theoretical matters.
Probabilism: Human inquiry can’t arrive at the absolute truth, but can at best reach probable conclusions.
The importance of oppositions to Sextus’s skeptical argument
The weakness of Pyrronhian skepticism and Sextus’ argument is the problem of infinite regress. Any rational argument myst depend on the premise. And these premises must be deduced from other premises. And those must be deduced from other presumes.
The weakness of his viewpoint, is that his attitude of systematic doubt inevitably leaves skepticism unable to prove its own conclusions. Skepticism must be careful to avoid self-contradiction, because the rule that everything is susceptible to doubt may itself be susceptible to doubt.
In order to avoid an infinite regress, we can simply choose a principle as an axiom and so refuse to justify it. But since the axiom cannot be deductively justified, it is arbitrary.
The meaning of “suspension” in skepticism
When the skeptic suspends judgement about theoretical matters (such as reality of physical laws, the reality of matter, the reality of time and space, the existence or non-existence of God).
“Suspension is brought about when things are put in opposition to each other. We either oppose objects of experience, to. objects of experience, objects of thought to objects of thought, or a combination of the two.
ex. when we say that a tower appears round from a distance, and square from close on.
ex. snow is white, but snow is frozen water, water is blue, therefore snow is blue.
“the sa could be said about present things we know”
ex. Newton ‘discovered’ gravity. Before Newton, gravity was just a theory hidden in nature, not yet revealed. Similarly, it is possible the opposite of theory now put forward in debate is the hidden nature and not yet not yet revealed. Therefore, we should not verify a theory that seems sound at the moment.
The modes of skepticism
“The same impressions are not produced by the same objects owing to the differences in animals.”
The same impressions are not produced by the same objects owing to the differences among human beings.
The same impressions are not produced by the same objects owing to the differences among the senses.
Owing to the “circumstances, conditions or dispositions,” the same objects appear different. The same temperature, as established by the instrument, feels very different after an extended period of cold winter weather than after mild weather in the autumn. Time appears slow when young and fast as aging proceeds. Honey tastes sweet to most but bitter to someone with jaundice. A person with influenza will feel cold and shiver even though she is hot with a fever.
“Based on positions, distances, and locations; for owing to each of these the same objects appear different.” The same tower appears rectangular at close distance and round from far away. The moon looks like a perfect sphere to the human eye, yet cratered from the view of a telescope.
“We deduce that since no object strikes us entirely by itself, but along with something else, it may perhaps be possible to say what the mixture compounded out of the external object and the thing perceived with it is like, but we would not be able to say what the external object is like by itself.”
“Based, as we said, on the quantity and constitution of the underlying objects, meaning generally by “constitution” the manner of composition.” So, for example, goat horn appears black when intact and appears white when ground up. Snow appears white when frozen and translucent as a liquid.
“Since all things appear relative, we will suspend judgement about what things absolutely and really exist. Do things which exist “differentially” as opposed to those things that have a distinct existence of their own, differ from relative things or not? If they do not differ, then they too are relative; but if they differ, then, since everything which differs is relative to something…, things which exist absolutely are relative.”
“Based on constancy or rarity of occurrence.” The sun is more amazing than a comet, but because we see and feel the warmth of the sun daily and the comet rarely, the latter commands our attention.
“There is a Tenth Mode, which is mainly concerned with Ethics, being based on rules of conduct, habits, laws, legendary beliefs, and dogmatic conceptions.”
“Relativity” as principle of skepticism
Perceptions vary according to circumstances of
Time and place
Physical conditions,
The nature of the objects, and the nature of the individual perceiver.
Conclusion: Contrary to the empiricist, our immediate sensations are no guide to objective circumstances.
René Descartes’ method of doubt:
The “Cartesian skeptical method (“Radical doubt”)
Rules of the “Cartesian method”. Accept nothing as true except what is apprehended so clearly distinct act to be beyond any doubt. Divide each truth into separate parts according to how necessary and possible it is to resolve. Begin with the objects that the simplest and easiest to know (such as doubting the senses), then gradually ascend to such an order if none exist naturally (such as our intellectual beliefs). If you begin to treat all your ideas as false, Descartes thought that you may discover an idea that is unmistakably true.
What Descartes meant by “I think, therefore I am”.
If you assume that you do not exist, then you must also assume that you are not thinking. If there was no way to doubt what you are thinking, then you must certainly exist.
David Hume’s account of conflict between instinctive beliefs and philosophical reasoning
Our senses deceive us.
By instinct, we believe that our senses directly reveal to us the things around us. By philosophical reasoning, we learn that our senses can only provide us with images or signs - internal mental representations of external objects. These objects may be nothing like our images of them, and we can know them only as the causes of our internal mental representations.
Hume’s skepticism about laws of nature
The “Argument from Design” (teleological argument)
All the order that we see in nature represents contrivance (is designed) in order to fulfill obvious purposes. In this respect the profits of nature resemble the intentional products of human intelligence. Since the effects resemble one another, we can reason by analogy that the causes must resemble one another. We can therefore conclude that the universe was designed by an intelligence that resembles but greatly exceeds our own. It was brought into being by a power that resembles, but greatly exceeds our own.
Hume’s reply: reasoning by analogy has to be judged by the that we normally apply to cause and effect. But a strong argument requires a strong analogy: the effects have to be “exactly similar” to allow a logical inference to the same cause. If we abstract from our empirical knowledge, then we are incapable of forming any idea a priori of what the universe must be like.
We could imagine infinitely many logically possible universes, but the mind itself would have no reason to prefer any one over the others. “experience alone can point out the true cause of any phenomenon.”
The purposeful arrangement of nature is not by itself an argument for design, except to the extent that experience has shown the two to be connected. All we can say is that there is a principle of order in mind, but not in matter. WE can compare the creation of the universe to the human design and creation of the universe to the human design and creation of objects, but only to the extent that we can see resemblance between the two.
But the disproportion between human contrivances and the universe itself is so great, that inferences by analogy are suspect.
Hume’s account of causal necessity
Correlation does not equal causation. As an empiricist Hume see’s observation as the only source of knowledge. If observation is the only source of knowledge when we observe an outcome of an event, we think that the source must be its cause since we cannot conceive any other impression to which our idea can be traced. Our knowledge about causation is merely inductive, therefore we cannot be absolutely certain of it.
(PREMISE) I’ve seen motion (the effect) follow the hitting of the billiard with a ball (the cause) many times.
(CONCLUSION) Therefore, the ball must have caused this motion.
Since we induce from our observations to find the source of this effect, we cannot say that this cause is certain.
Hume’s “mitigated skepticism”
A recognition of our limits and fallible abilities to learn and to reason about the world. “A tincture of Pyrrhonism leads us to intellectual modesty, and to a just proportion between our convictions and our evidence.
What was new about Newton’s theory of gravity
Law 1: Every body, left to itself, maintains its state of uniform motion or rest until acted upon by a force. “Principle of Inertia”
Law 2: Acceleration is in the direction in which a force is impressed, and is proportional to the magnitude of the force and the mass of the body. “Force = MA”
Law 3: To every action, there is an equal and opposite reaction. “Action = Reaction”
Corollaries 5 and 6: The Newtonian theory of relativity
5: The motions of the bodies in a given space are the same among themselves whether that space is at rest or moving uniformly in a straight line
6: The motions of the bodies in a given space are the same among themselves whether that space is at rest, moving uniformly in a straight line, or accelerated uniformly in parallel directions, by forces that act equally and in parallel directions on all the bodies in the system.
ex. the system of Jupiter and its moons behave as if it is at rest or moving uniformly in a straight line, because the attractive force of the sun acts equally on every part of the system.
Newton’s argument about the fall of an apple
Newton theorized that the same force that caused an apple to fall from a treee was also the force that kept the moon in place.
Newton found that the force that was holding the moon in orbit was the same force that caused an apple to fall. Since the force of the moon is inversely proportional to the square distance from the earth, and the distance from the earth is 60 times the radius of the earth.
Force of moon = 1/60^2 x force of apple = 3600 x Force on apple
The acceleration of the moon is exactly 1/3600 of the acceleration of the fallen apple at the earth’s surface. SO the force acting on the moon is just gravity, but weaker at a greater distance.
Conclusion: BY inductive reasoning, all bodies attract all other bodies, according to their masses and the distance between them.
Gravity is universal.
Newton’s use of his theory of gravity to solve the problem of planetary motion
Because the force holding the moon in orbit obeys the same law as gravity at earth’s surface, it is the same force.
Therefore, it could be said that this law governs the orbits of Jupiter’s and Saturn’s moons, and the orbits of all the planets around the sun. They are actions of the same force. Therefore, gravity is universal.
Newton’s agnosticism about the “cause” of gravity
Newton thought that it was not necessary to know the cause of gravity. He instead thought that the effects of gravity are measurable, through mathematical experiments, then there is a cause and the force can exist independently without a supernatural cause. In an agnostic world where there is no supernatural cause (i.e, God) gravity would still exist because its scientific effects are measurable and mathematically caused. Therefore, planetary motion would still occur.
