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Truth suffers from too much analysis

Archive for November, 2011

What Time is It?

Posted by allzermalmer on November 13, 2011

Around the year 397 A.D.-398 A.D., the Christian philosopher St. Augustine talked about time in his book Confessions. In chapter 11 of his book he says, “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.” Time seems so obvious to us, yet at the same time it is hard to explicate what exactly time is. Once we do explicate what time is, we find that we come to contradictions or absurdities. Some, like Immanuel Kant, says that time is a condition of experience that our minds impose on things. Some, like J. Ellis McTaggart, says that time does not exist!

For the sake of this blog, and to cut through many of the discussions on time, and I will specifically deal with McTaggart ‘s Proof of The Unreality of Time. The conclusion of his work is that time is an illusion, or just an ideal. Some people try to avoid this conclusion of the unreality of time. Therefore, they try to come up with positions that can avoid this, yet there are some problems with these positions that try to escape the unreality of time, and what some of them allow for. Now McTaggart lived from 1866 to 1925, and was a philosophy teacher at Trinity College in Oxford. He was part of the Hegelian Idealist movement in Great Britain during this time. McTaggart had his paper, The Unreality of Time, was published in the philosophical journal Mind Vol. 17, No. 68, in 1908.

The philosophy of time is a very complex subject, and it is a subject that has had many things said on it. As a complex subject, there have been contradictory views on time. We have some views of time that it is absolute or relative, and these two contradict each other. We have that time as something that is objective and exists independent of minds, or that time is a product of minds. Time had a beginning, or that time has always existed. Because of these contradictory positions, some held that time does not exist or that it is something that does not exist in an independent world of us, which is the position that Immanuel Kant held. Thus, he said that time is a precondition that our minds impose on our experiences. Others, like McTaggart, have held that time does not exist at all, and would seem to agree that it is an illusion of the mind.

McTaggart has been a philosopher that has brought much food for thought on the philosophy of time. His paper on the illusion of time has helped present two standard views of time, and this has lead to much debate on the view of time. My point of this paper is to go over his view on time, and some of the consequences of it. As I go over some of the consequences of these different views of time presented in his paper, I shall also introduce some ways in which we epistemologically try to deal with these view, and how they can tell us how to work with the views of time.

Now, when someone makes a statement, it is typical for one to ask that person, “What evidence do you have to support your statement?” When we ask for evidence, we usually want something that is observable, which means that we want something that is related to our sense experience. This is where we want the position to come back to a sense experience, since we can verify that the statement is correct. Thus, we can call this verificationism, and state it like this: A statement is true if and only if it is directly based on the senses. Therefore, I can say, “The moon will be blacked out in 5 minutes”. We wait five minutes, and we see if we have the sense experience where the moon is blacked out. If we do make that observation, then we say my statement is verified. If we do not make that observation, then we say my statement is not verified.

Besides verificationism, we have another position called conventionalism. For example, a cubit was defined by the human body parts of an Egyptian royal member as the length of an arm from the elbow to the extended fingertips. This was taking the standard from which a cubit was to be based, and it was employed. They defined was a cubit was based on a standard, and that standard was applied throughout the land. Thus, they made a cast from the person elbow to the tip of their fingers. This became the set standard, and was the convention from which a cubit was set. If something did not meet this standard, it is said not to be a cubit. Therefore, we can define a convention: There is a convention if and only if there is an agreed upon standard. Thus, if I make the statement, “This is a cubit”, and we find that it does not agree with the standard that is accepted, then it is not a cubit. We find that science works with conventions, like those of measurement. We have defined the convention of a meter based on the speed of light, and this has become an accepted convention that scientist employ.

Now, going back to McTaggart’s philosophy of time, he comes to tell us that time is an illusion. He develops an argument to lead to this conclusion, and presents three views of time to do this. In the end, he says that each of them is contradictory, and so that time does not exist. These views of time are the two that are held to today. Therefore, in order to avoid that they lead to contradictions or are false, we try to save them by modifying them. He came up with three series of time, and they are, respectively, the A-Series, B-Series, and C-Series. Each of these plays a part in his argument. The part about his argument is that it is an argument that makes few assumptions, and leads to what he says are contradictions. Because of this, he is lead to the conclusion that time is an illusion and that it does not exist.

Positions in time are considered to be showed in two ways. (1.) ‘Earlier than’ and ‘Later than’ to some other position, and (2.) each position is either past, present, or future. This forms the foundation of McTaggart’s argument, and presents us two theories of time. The first point is a permanent and objective, and the second point is not considered permanent since it relies on change. From these distinctions, McTaggart thinks that the second is the fundamental point of time, and what he thinks a show that time is unreal. He calls the first position the B-Series of time, and he calls the second position the A-Series of time.

We have events as positions in time. These are the things that come to directly make up the A-Series or the B-Series. Without events, we have no series of time. We can imagine it as a dot on a line, since this grabs our attention to a certain part of the line, and this can be an event for anything that happens in time. These form the fundamental part of time, since time is nothing without an event. From events, time expands out to either an A-Series or B-Series, or both.

When we look at the A-Series of time, we have past, present, and future. For example, there is the past in which I started writing this paper. There is the present of me typing words for the paper now. There is the future of me finishing this paper, and getting in A for it! There is a language for this, which is the tensed language. The tensed language follows like this: I started this paper in the past; I am writing this paper in the present; I will finish this paper in the future.

When we look at the A-Series of time, we have ‘before that’ and ‘after that’. For example, John F. Kennedy died after World War II; John F. Kennedy died before Barack Obama became president; Barack Obama was born before the Persian Gulf War; Barak Obama was in the White House as President after Iraqi Freedom.  We call the B-Series language the tenseless language.  It gets rid of tensed language, and forms a new way to talk about events.

With the A-Series of time, things come into being and go out of being. We can look at it like life, since people are born and die. When they person is born, they come into being, and when they die, they go out of being. However, with the B-Series of time, under the analogy of a person, they never go out of being. They always exist within the B-Series of time, and never leave the event that they occupy, since it is permanent.

So, say that we have the events A, B, and C. If we take the A-Series of time, A would be the past, B would be the present, and C would be the future. These events only exist for a little while, and move out further from the present. However, taking the B-Series, these events always exist and always exist in relation to one another.

McTaggart says that the A-Series is more fundamental than the B-Series. We can wonder how this is, and he gives us one answer. The A-Series is what we directly experience, and it is always present to our awareness. We never experience anything else but the present, and the B-Series is something that we never experience. We also find that we have events going from future, to present, to past. We feel and see this flow with our senses. I have a pain in my thumb, and then I no longer feel it after I take a pin killer. The pain is no longer in the present, and so it is no longer felt by me.

What we go on to find is that the A-Series is fundamental since we can derive the B-Series from the A-Series. However, we cannot do it otherwise. We cannot derive the A-Series from the B-Series. Therefore, we find an asymmetry between the A-Series and the B-Series. Say that we accept the B-Series, and then we cannot derive what event is in the present, like what event we are now experiencing. So take the example of the event of pain in my thumb, which we can label X. I would not be able to know when this event will be present within the B-Series. I we have the permanent events of A, B, C, and X. We find that C is before X, and X after C. We also find that X is after A, B, and C. From this, I cannot tell which event is going on now in the present, I can just see what relations are shared.

Now we can abstract from the A-Series and create the B-Series. From the past of A, the present of B, and the future of C, we can say that they are all permanent. Therefore, when I no longer experience A, and A moves further and further from B, I can say that it still exists in permanent relation to B. We form a mental image, and keep these events in relation to one another, even though they are no longer experienced. They are no longer in the present.

Now, with the A-Series and B-Series, we find there is a direction of time. It is constantly moving forward. Thus, we can find it looking like this, –A—-B—Cà. We see the arrow moving forward, yet with the B-Series, the events never change their relation to one another. With the A-Series, we also find things changing, and moving forward with the future becoming the present, past, far past, etc. As McTaggart says, “The B-Series, however, cannot exist except as temporal, since earlier and later, which are distinctions of which it consists, are clearly time-terminations. So it follows that there can be no B series where there is no A series, since where there is no A series there is no time.” (pg. 461 of Mind Vol. 17, No. 68)

McTaggart goes on to bring up a time series that does not involve temporal change, and he calls it the C-Series. The C-Series would look like this, A, B, C, D, E, F, G, H, I, J….Z. There is no arrow pointing one way or another, and so there is no change within it. The events cannot be altered from one to another, as if B switches places with D, or any event with another. This would be a universe that is unchanging, and yet if there were to enter change, then it would automatically become a B-Series. Thus, from the A-Series, we can derive the B-Series, and from the B-Series, we can derive the C-Series. Thus, we can derive the C-Series from the A-Series. We can derive the B-Series from the C-Series by pointing the temporal arrow either forward or back. Therefore, this is the situation: The A-Series is what we experience, and we can abstract from the A-Series and create the B-Series; from the B-Series, we can abstract even more and form the C-Series; however, we cannot derive the A-Series from the C-Series, since we cannot derive the A-Series from the B-Series.

Now we can wonder, How do we verify the B or C-Series? We cannot have an experience to show that the future exists in permanent relations to one another, or that the future actually exists. In order to have an experience of the B-Series or C-Series, we would require being outside of the time. We would need to take a “Bird’s Eye View” of things, and be detached from the time series itself. We have to be on the outside looking in. Now we typically think that our experiences take place in time, and so would have to be outside of time to verify it.

The main problem with this idea is that all of our experiences take place in the present. We can verify this from the beginning, and this is even how we come up with our idea of time. Once we come to recognize that something is going on through experience, we imagine that there is something around the corner waiting for us, which we call the future. This obviously does not come from experience, since that would mean that we are experiencing the present and the future, at the same time. We take the example that I am walking down a street, and I see that there is a turn coming up. I am not experiencing that there is something around the corner, so I do not know that something is there. However, I can imagine that something is around the corner, and think that there is something around there. I verify this when I come to the corner and turn. When I make the turn, and find something is there, like say more buildings, I have verified that something is there.

As we saw before, we can create the B-Series/C-Series from the A-Series, but we cannot create the A-Series from them both. In other words, we can deduce the B & C-Series from the A-Series, but we cannot deduce the A-Series from the B & C-Series. This means that we cannot deduce the present from permanent events. Thus, we find that we have created these abstractions in order to deal with our experiences. Because we have created these things, we have created them in order to help order our experiences and orientate ourselves for action. Therefore, we act as if the future exists and we are moving towards it.

The B-Series becomes a convention that we accept, and we try to view the world through that lens of the B-Series. However, when we are viewing something, we are always viewing it in the present, and so are viewing it through the A-Series. We do this since, as has been stated before, we always view it, or experience things, in the present. The conventions that we create are very useful to us, and so we accept them as true when they are useful. However, it does not follow that because something is useful that it is true. We can give a simple argument like, If a cat then an animal. Now all we know is that it is an animal. It does not logically follow that since it is an animal that it is a cat. It could be a human or a dog. With this in mind, we overlook this problem and say that it is true because we find a consequence to be true. We find that it is useful.

Now we have a problem if we say that the future exists permanently. As I already pointed out before, we cannot know this without stepping outside of time to verify it, and to do so, as some might say, is impossible. Nevertheless, the other problem is, as has already been pointed out, will take place in the present. The second is that there is no real test that we can make to show that the B-Series is false, since all tests will take place in the A-Series, or the present. Thus, since we can neither verify nor falsify, it is not amendable to experience. However, because it does not meet either verification or falsifiability, this does not mean that we should disregard it. What it does mean is that it makes for a useful convention. We can act, and think, as if it does exist and the world is like the B-Series.

What the convention of the B-Series does, as a convention, is build up another world that is not really a world of experience. This is an abstract world of our thoughts, and not one of our experiences. From this abstract world, we can build other things within it. From this convention, we can apply it to the world of experience. When we apply it to the world of experience, we are trying to help it order the chaotic world of experience, and become a guide to the world of experience. Similar to what Ernst Mach says in his Analysis of Sensations, “The…task of science is to provide the fully developed human individual with as perfect a means of orientating himself as possible.” Instead of saying “science”, we can take him to say “the B-Series”. Thus, with that change, we get this, “The…task of the B-Series is to provide the fully developed human individual with as perfect means of orientating himself as possible.”

Conventions are things that are accepted by a specific community of people, or people in general. These conventions are developed, not because experience shows them, but because they make it easier to deal with experience and organize it into a methodological pattern. The pattern helps orientate ourselves in the world of experience, and are thought instruments that help us think of the world through a certain lens. It has pragmatic value to use, yet it does not have support directly from the senses. It is not verifiable. Thus, we can act and think as if it is true and is how reality is. The only reality, though, is the one of the senses, which is in the present.

As a metaphysical theory, the A-Series is verifiable and the one that is given to our senses. Thus, it is in line with experience, and makes for a good metaphysical theory. The B-Series, as a metaphysical theory, is just as good as the A-Series. The only problem is that it does not fit with experience, but it does open up a new metaphysical world that we can apply to the world of experience. Thus, as a metaphysical theory that contradicts experience, it is a convention that is very fruitful to apply to experience and orient ourselves in the world.

The thing that makes the A & B-Series adequate is that they have a temporal arrow. This temporal arrow is something that is based on our senses. We find that things change, and they move in a certain direction. Because of this, it is implemented into our theories of time with the A & B-Series. Therefore, as a convention, we try to not abstract too much from experience to form these theories. Thus, the B-Series does not abstract the arrow of time, yet the C-Series does abstract more than the B-Series. Thus, since more of experience is left out of the C-Series than the B-Series, we can say that what holds for the B-Series holds for the C-Series. However, the C-Series is even further from experience than the C-Series. However, this does not mean that the C-Series does not make for as good a convention as the B-Series. Thus, we can hold to the C-Series as if it were true as well.

Take this example. In our experience that we find that when we let a ball fall from our hand that it falls to the ground. We find this happens every time we let go of the ball. This will be held within the B-Series. Now, with the C-Series, we can retrodict and predict. It does not matter if we are going forward, predict, or going backwards, retrodict. Thus, we find that time can move forwards or backwards, and the C-Series makes a great convention to see what will happen, or actually did happen. However, we cannot verify what did happen if there was no experience of it. Thus, it makes for a good convention as well.

So let us recap. (1.) Experience only supports the A-Series, since all experience is in the present. (2.) The B-Series abstracts from the A-Series. (3.) The B-Series is not verifiable by the senses. (4.) The B-Series makes a good convention to work with. (5.) We can act as if the B-Series is the correct view. (6.) The C-Series is further from experience than the B-Series. Thus, we find that the A-Series is faithful to experience, and the B-Series is faithful to a useful convention to think of reality as if it is true. Thus, as a useful instrument, we can use it to orient ourselves and build a world-view that is in line with it. However, because it is useful as an instrument, and acts as if it is true, does not give us good ground to think it is true.

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Facts, Constructions, and Hypothesis

Posted by allzermalmer on November 10, 2011

This blog will be about a chapter in Walter Terrance Stace’s book calledTheory of Existence and Knowledge. This blog will be based on chapter 7, which is called Facts, Constructions, and Hypothesis.  This chapter is also related to posts on the Construction of the External World, and you can read the first one here.

There were six constructions in constructing the external world. And of these six, they can be broken down into two.  These two are Unificatory Constructions and Existential Constructions.

Unificatory Constructions:  Of the six mental constructions we employed to create the external world, three of them fall under the term of Unificatory Constructions. The second, third, and sixth mental construction were of the Unificatory sort. Here’s all three of them.

2.) That the corresponding presentations of different minds are identical, and that there are not many universes, but only one.

3.) That the presentations of a mind may continue in existence unperceived by that mind, provided that some other mind perceived them.

6.) That the different senses we may perceive the ‘same’ objects, and that the worlds of the different senses are, in general, identical with one another.

The characteristic of these three, and Unificatory Constructions in general, are that they don’t postulate new existence, but reduce the number of existences. For example, we find that we have many different things, but we reduce them to a few things to connect all these things together.

The second construction will identify your purple with my purple. my world with your world, and the private worlds of all minds with one another. This helps reduce the multitude of worlds to one world. Instead of having as many worlds as minds, there’s only one world. From many to one, which is a reduction.

The third construction identifies my purple now with your purple in a later moment. When I look at something, I know it exists through experience. But when I don’t look at something, I don’t know that it exists. With the third construction, following the second, we know that there’s only one world and what I see is similar to what you see. When I don’t see something, but you see it, it still exists and is similar to what I would see when I turn to look at it. It reduces the many successive world to one.

The sixth construction reduces all the different senses to combine into one thing, which would be what we call objects. The bird gives me a visual sense, but this visual sense isn’t the same audible sense of the bird. Neither does the taste or smell. But we combine these different senses to the “same” thing. This reduces the many to one.

Unificatory Constructions rest on two principles.
(1.) Principle of Superfluous Existences: Existences that make no difference to either knowledge or practical activities, and may be treated as if they were non-existent; they’re irrelevant to the mind’s purposes, either theoretical or practical, they can be cut out of the universe.
(2.) They Can’t be Proved: They’re not facts, but serviceable fictions, and they’re not inferences from facts. One unificatory construction can serve as an inference from another construction, like the third construction is an inference from the second construction. One construction can serve as a premise to lead to another construction.

Existential Constructions: Of the six mental constructions we used before, three of them were Existential Constructions. They are as follows..

1.) The presentations of one mind bear to the corresponding presentations of other minds the relation of resemblance.

4.) That presentations may exist when no mind is aware of them.

5.) That there exists ‘things’ or ‘objects’, which are not identical with presentations; and that the presentations are ‘qualities’ of the ‘things’; and that the ‘qualities’ may change while the ‘things’ remain the same.

What is common to these three, and one of the characteristics of some of our mental constructions, is that the imagination will invent the existence of some fictions that aren’t given in experience or infered from experience. We try to model these existence off of our experiences, and they’re made out of the materials of experiences we’ve had. But this asserted existence is never actually experienced, and are presented in a hypothetical type of proposition (If…then).

When we make a hypothetical type of proposition when expressing the existence of something never experienced or inferred from experience, the antecedent is something that we can never perceive it’s existence. This antecedent existence is something that we can never experience, and wasn’t experienced in the first place or inferred from what was experienced in the first place. And these things are mental constructions, or fictions.

Unificatory Constructions and Existential Constructions were employed to help build the external world, and they had two things going for them at their basis. There were six mental constructions used, which broke into unificatory and existential, and it all served for simplicity and consistency.

The first, second, fourth, and sixth constructions were all done for simplicity. With the first, we decide to take other people having perceptions to our own. It’s simpler to think that they’re similar than dissimilar. Both are equally ‘true’ and workable for intellectual and practical action.

With the second, we decide to think that our perceptions are approximately identical and believe in one universe instead of many. This goes from many different worlds for different people, but they’re all part of the one world. The one over many carries some sign of simplicity.

With the fourth, we decided to think we think that things go on existencing when we’re not experiencing it. Instead of having one universe going out of existence when people aren’t experiencing it is, and then having a new universe when experincing it, the same one universe continues on when not experincing it.

With the sixth, we decide to say that all our different senses give us information on “thing”. The world of the different senses become unified. The world of the apple feel, apple sight, apple taste, apple smell, hear it.

The third and fifth construction served for another use besides simplicity. They were used for consistency. The mind created this theory of the common world, which went against the facts that contradicted the theory. Because there’s a difference between our various minds and experiences. The third and fifth construction reconcile the differences with the theory of the common world and get rid of the inconsistency with mental constructions.

“We find again and again in the history of knowledge repetitions of this procedure. The mind, having invented a construction for the purposes of simplification and convenience, meets with new facts which do not square with the constructed belief. It is forced either to retrace its steps,  abandon the ground which it has gained, and give up the construction or even the system of constructions (which may well constitute a large bloch of its scheme of knowledge), or, in order to avoid this, it is compelled to manufacture new constructions or systems of constructions which will reintroduce harmony and avoid contradictions. In this way human knowledge grows as well as by the accumulation of new facts and inferences.”

From the epistemological analysis already set up, there’s two different kinds of existence that should be recognized. It’s (1) factual existence and, (2) constructive existence.

Factual existence is the existence of whatever is, has, or will be actually perceived by any mind, at any time or place. An example is that the existence of the computer while it’s being perceived by you or anyone else is a factual existence. But more explicitly, the existence of a visual presentation called the “computer”, the touch of the thing called the “computer”, and etc, are factual existence. When we say that no one is perceiving the computer, we supposed by the mind to think that it’s still there, it is a constructive existence.

What is actualy being experienced is the factual, which means that having the visual experience of the computer, that has factual existence. But when not touching the computer, it is given a constructive existence. When not tasting it, it has a constructive existence. But we go to think that at all times, whether the computer is experienced or not, there is a ‘thing’ behind the experiences and different from them, and this  is a constructive existence.

The sun rising tomorrow has a factual existence, because it will be actually perceived. The existence of Thomas Jefferson is also factual, because he was perceived. And for epistemology, this is an important distinction between factual and constructive existence. “But for the purposes of all other knowledge it is essential to obliterate and forget it.”

Constructive existence consists of supposing that unperceived things go on existing like they did as when actually perceived. Thus, we have experience of the computer existing when being perceived, and project that type of factual experience into a realm of where we have no experience. Projecting perceived factual existents, into the unperceived constructive existents.

The distinction between constructive and factual existence has only importance for the theory of epistemology, and not with theory or pratice. We can easily go on thinking that the computer exists when we don’t perceive it. But what they are during times when not perceived or if they are, they have no difference to us as practical people. What matters is when it’s there when we turn to it, what else would matter as practical people?

This situations makes no difference to the knowledge of the computers. We know the method of the manufacture of the computers, chemistry, electronics, and physics of operation. Any conceivable knowledge have of the computer remains the same during unperceived existences.

“It is, as we have seen, a logical rule of the mind that it ignores and treats as non-existent superfluous existences, existences which make no difference of any kind either to theory or practice.”

From this, the mind ignores the distinction between factual and constructive existence. We come to lump together all existence together as factual, and this may be regarded as a Unificatory Construction. And the attitude of which the mind takes up in this matter must be regarded as ‘true’.

For the most part, our knowledge has been built on mental constructions. And if we admit this knowledge as knolwedge, and not as false, then we admit constructed beliefs as being composed of truths. So we must take it as true that there’s an independent external world, things exist when no one perceives them, your penny is the same penny as mine, the table you touch is the same as the one that I see. And this forms part of our admitted knowledge of the world.

“These propositions form a part of our admitted knowledge of the world. They are universally accepted as true. Unless we are to do extreme violence to all accepted standards of truth and to all acknowledge conceptions of knolwedge, we must also admit them to be true, and must frame our definition of truth so as to include them.

And these things apply to our common world knowledge. Now let’s consider scientific knowledge to be distinguished from common world knowledge, and we find a similar conclusion as we did common world knowledge (i.e. factual existents and constructive existents).

Scientific knowledge is also composed of mental constructions, like the common world. We should be reminded of the ‘hypothetical’ nature of science. But as has been pointed out earlier, the ‘hypothetical’ aspect is composed of constructions, e.g. atomic theory and electronic theory. If we regard scientific knowledge as true, then we admit that such truth includes constructions.  This admission does not mean that the theories are false.

“We have to take a broad view of knowledge, to regard it in something the same way as we regard the world of art. The world of art is a product of the immense labors of the human spirit. So is the world of knowledge. It has been constructed by countless minds working through countless centuries.”

Truth, therefore, is held to include those constructions which have been built into human knowledge and form permanent parts of it. But this seems to raise a problem: Constructions are fictions, and if all constructions are true, then this destroys the distinction between truth and falsehood altogether. What ever we imagine could claim to be truth, would seem to be allowable. But some constructions are true and some false. (Future blog)

Hypotheses can assert either factual or constructive existences. For example, I now hear a noise behind me, and I conjecture that it’s my cat. I turn around and see the cat doing something with bubble wrap. I conjectured that the cat was behind me doing something to make noises. It’s a hypothesis, and the verification of it was based on me seeing the cat behind me doing something that’s making the noises that I heard. This hypothesis asserts the factual existence of my cat. The cat isn’t a construction but a fact.

Now it’s true that the existence of my visual cat when not being seen is a construction. It could be further said to be true when I say “I believe that the noise is caused by my cat” is not a hypothesis but a construction. But my statement of belief was based on two parts. (1.) My general belief in independent external world existing whether I experience it or not, and  (2.) my belief that among objects of this independent world is my cat which is causing the noise. And once grant an external world, my guess at my cat making the noise is a hypothesis.

At one point there was an invention known as the ether of space, which at the time required to be carrier of the light waves. The ether of space was not only hypothetical, but it was also a construction. It was posited not only the existence of the external world, but it also posited the existence of a new unperceived object.

Hypothesis are as much concerned with factual existence as with constructive existences, and what is usually called the hypothetical nature of science should be called its constructive character.

The character of science is said to be hypothetical, but this can’t mean that all scientific knowledge consists in unverified hypotheses. Hypothesis cease to be hypothesis when it has been verified. It will become known as a theory or a fact. For example, we once found that orbit of Uranus was the way that Newton’s theory was, and we came up with the hypothesis that there was another planet which helped cause the Uranus to be the way that it is, and different from what we thought with Newton’s theory. We eventually came to find this new planet, and this new planet became a fact. So this doesn’t quite to be what is meant by science being hypothetical.

Does this mean science is only concerned with hypothetical propositions? But this seems erroneous. It’s true that science makes very wide use of hypothetical propositions, but they’re intended to advance towards categorical ones.

“Hypothesis is a method of seeking scientific truth. But the truth when found is in no wise hypothetical. Hypothesis is not the end at which science aims-as would seem to be almost implied by such a phrase as ‘the hypothetical character of science’-but merely a means towards its end. And its real ends are the attainment of categorical propositions.”

Let’s use an example, and one dealing with Einstein’s theory and the displacement of Mercury. Einstein frames a hypothetical proposition like this, “If the geometry of space-time is such and such, then the displacement of the orbit of Mercury will be so and so, and rays of starlight passing the limb of the sun will be bent in such and such angle.” We come to know the displacement of the orbit of Mercury, and the bending of the light rays is measured. These facts are found to agree with deductions of the geometry of space-time that was set forth in the hypothetical proposition. And the hypothesis to some extent has been verified. And the hope is to be able to give the categorical proposition ‘The structure of space time is such and such.”

Supposes the scientist has a hypothesis that says that the atom may be described with the characters of mathematical formula like X,Y,Z. It is taken that X,Y,Z is true, and then attempts to deduce known properties of matter as observed in our ordinary life and in experiments. If correct, it shows that hypothesis explains all relevant facts that have been discovered, and if no further tests then it’s probably true. But what is actually hoped is that it is proved true, as far as such proof is possible in science. It is hopped to give the categorical proposition of the nature of the atom actually given is by the formula X,Y,Z. If the hypothesis is proved wrong, then it is hoped to hit the right one and prove the nature of the atom is expressed by the formula of P,Q,R.

So it’s not strictly true to say that scientific knowledge is hypothetical. It aims at being categorical. But it seems that there’s an important truth that science is hypothetical, and that could be that it’s expressing the constructional character of science.

“The essential distinction, then, between hypothesis and construction is that the construction is always a pure creation of the mind, and the existence posited by it, if any, is always a constructive existence; whereas in hypothesis need not possess this character. The existence posited by it may be factual, as is the case with the rat and the planet Neptune. It is true that any hyothesis may sometimes also be itself a construction…So that some hypotheses are also constructions and posit constructive existences. But this is not essential to the character of hypothesis as hypothesis. The existence posited by a construction is always constructive. The existence posited by an hypothesis may be either factual or constructive.”

The results can be summed up as follows:

(1.) A fact is something actually perceived, with qualification that the mind which perceives or knows is itself also a fact.

(2.) Mental constructions are pure creations of the mind and to which no facts correspond.

(3.) Existences posited by hypothesis are either factual or constructive.

(4.) The method of science may be mostly the method of hypothesis, the nature of science truth is not hypothetical. But it’s nature is constructional. And this is probably what is meant to refer to the ‘hypothetical character’ of science.

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Fatalism Arguments

Posted by allzermalmer on November 7, 2011

This is a blog based on an article by Steven Cahn. It is based on an article called Fatalistic Arguments. It appeared in the philosophy journal The Journal of Philosophy, Vol. 61, No. 10 (May 7, 1964), pp. 295-305. It also follows from the blog Fatalism.

The article by Cahn, basically, follows what Richard Taylor presented in his article on Fatalism (which I gave you a link to that I did a blog of).

Crucial Assumpitions: One assumpition is that any proposition is either true or false, and this is the Law of Excluded Middle. Another assumpition is that an agent can’t perform an action in the absence of some conditions necessary for the action. Another assumpition is that a necessary condition is an event or state of affairs which is logically unrelated to X but which is nevertheless such that X cannot occur without it. We say that oxygen is a necessary condition for humans to live, which is that no human can live without oxgyen. But this isn’t to say that it’s logically impossible for a human to live without oxygen.

“given that it is true that a certain event E has occurred, then it is not now within the power of any agent to perform any action A which would, if performed, be sufficient for the nonoccurrence of E-for a necessary condition for the performance of A is the prior nonoccurrence of E.”

One way to sum this up is “The past is unalterable”. This seems pretty straightforeward, and something not really argued against, or something people believe. I can’t alter who my parents were, or when I was born. That’s beyond anything I can control or change.

“given that it is true that a certain event E will occur, then, [Taylor] says in effect, it is not now within the power of any agent to perform any action A which would, if performed, be sufficient for the nonoccurrence of E-for a necessary condition for the performance of A is the subsequent nonoccurrence of E.”

One way to sum this up is “The future is unalterable”. Now this doesn’t seem straightforeward to the way that we typically like to view things. But one analogy should help. We tend to think that the future is alterable, but we don’t tend to think that movies are alterable. When we go to see a movie, we pretty much expect the movie to have an unalterable ending. But from the point of view of the “characters in the movie”, the future isn’t set and is alterable.

The type of reasoning used is helped is based on necessary conditions and sufficent conditions. For any two events or states of affiars X and Y, if X is a necessary condition for Y, then Y is a sufficent condition for X, and vice versa. It doesn’t matter which one occurs first in time, X or Y.

“Being able” and “Knowing how”: But we might have trouble with the way that Taylor uses the term ‘can’. We might disagree that no agent can perform actions in the absence of some conditions necessary for the accomplishment, only certain harmless logical impossiblility. And this has nothing to do with what any agent is able to do.

Here’s what John Turk Saunders had to say on this, in regards to what Taylor brought up:

“My knocking upon a thin wooden door with my fist is a sufficient condition for the door’s shaking. Hence the door’s shaking is a necessary condition for my knocking upon the door. But the door ‘s shaking is not a necessary condition for my ability to knock upon the door.”

But this type of critique misses the point. Taylor did not argue against an agent can know how to perform some act when there’s missing the condition necessary for it’s accomplishment. And thus, in that sense, the person doesn’t have the ability to perform it.

The point, rather, was that no matter what an agent might know how to do, they still cannot even do what they know how to do (being able to do it) if they’re lacking some condition necessary for doing it.

Here is what Taylor is tyring to get at, with an example:

“[I]magine an expert pole-vaulter locked in a room with an eight-foot ceiling. Both Taylor and Saunders might agree that an expert pole-vaulter has the know-how or technical expertise to pole-vault twelve feet. In this sense of the word “can” the pole-vaulter can pole-vault twelve feet. What Taylor is asserting is that, given the conditions of the locked room, the pole-vaulter does not have it within his power to pole-vault twelve feet. His know-how is constrained by circumstances that prevent him from exercising it.”

Now Brue Aune made a criticism of the “absurd consequences” of what Taylor said. One of them is that no agent can perform any given action if lacking some condition necessary for it. Here is one of the “absurd consequences”, which Aune thinks to seem that follows.

“If a man should say that he can swim, or that he has the ability to swim, he would surely take it as a poor joke if someone replied, ‘No, you cannot swim: you lack the ability to do this because you are not now in a pool or lake.'”

Now imagine that we reply to this situation, and change it just slightly. Imagine that a man comes up to you and says that he can swim, or that he has the ability to swim. Another person says to them “well then, you can swim under any conditions. Let’s see you swim out of water.” Now this would surely be a joke or an “absurd consequence”. The first one, given by Aune, would be a joke. The second one, given by Cahn, would be a joke. But the first joke asserts an obvious truth, which is that one needs water in order to swim. And this is exactly the type of truth that Taylor uses.

But the second joke is really a joke. The second assumes that when someone says that they can swim, they mean that he can swim at a specific time even if the necessary conditions for swimming are missing. This means, no person takes the meaning of “I can swim”, to mean that they can swim when they lack the necessary condition of water.Thus, we find that the way that Taylor uses “can” fits in perfectly with the way that we use.

The Simple Rejection of Fatalism: Some people, like John Turk Saunders, have pointed out that Taylor’s argument leads to fatalism. It is dismissed as “weird” that the ability to knock upon the door will suffice to make it shake. And this is part of the fatalist position. You cannot perform a given act if there is lacking a condition necessary for doing it, no matter what you might know how to do. This does imply that if I can knock on the door then I shall.

One person, Peter Makepeace, allows Taylor’s argument, like “I cannot make something happen in the future if it is not going to happen.” And the logical equivalent of that statement is “If it is true that a certain event E is not going to happen, then I cannot make it happen.” But if he allows that, then he supports Taylors argument. That’s what Taylor’s argument leads to, and he agrees with that!

Here is what Makepeace takes disagreement over, with an example of what Makepeace doesn’t like.

“If conditions are such that a snowfall yesterday is a necessary condition for the lawn ‘s being snow-covered this morning, then, given that no snowfall occurred, we can conclude not only that the lawn is not snow-covered, but that it cannot be.”

So we shouldn’t speak of the lawn’s state of being snow covered being “within its power”. So we think it’s absurd to add that it’s “consistent with its being able to carry snow, having the ability not to melt it, and so on, and thus being able, in that sense.”

But this isn’t really absurd, but it is an odd choice of words for one to use. We don’t usually, or like to, think of inanimate objects having something “within its power”. But this isn’t a major issue, because we can change examples from animate to inanimate objects. We can change the expression of “within its power” to “within its capability”. Now this just shows that Makepeace repating an error that Saunder’s made, which is disputing what Taylor didn’t claim.

Taylor hasn’t claimed that “the lawn does not possess the capability to hold snow (i.e., to carry snow, not to melt it, and so on), any more than he claims that the pole-vaulter does not have the know-how to pole-vault twelve feet in a room with an eight-foot high ceiling.”

All Taylor is claiming is that given the absence of a necessary condition, the lawn doesn’t have it within its capability to be snow-covered, just like the pole-vaulter doesn’t have it within their power to pole-vault 12 feet in the 8 foot room.

Fatalism and Linguistic Reform: Some have taken problem with Taylor’s use of “within ones power’s”, and still using it in its coneventional contexts. And this is said to lead to the fatalistic conclusion, because doesn’t keep a distinction.  And this means that it’s claimed that Taylor treats “the only events which it is within one’s power to produce are those which occur.”  as an analytic.

But Taylor isn’t using the statement as analytitic. It’s not true by definitions, but it does follow from his argument that the only action one is able to perform are those which he does perform. And this is the conclusion of fatalism.

Is this linguistic reform, that Taylor is trying to do? Perhaps not, and maybe an example could help to figure out what Taylor is saying.

“Consider a violinist, for instance, who has forgotten to bring his violin to his recital and is unable to obtain another before the time of the recital.”

Taylor is not asserting that the violonist could not play the violin, even if, they had a violin in their hands. This is false. What is being asserted is that if at the time of the recital the violinist doesn’t have a violin in their hands, then they can’t play at the time of the present recital. They’d have to be playing imaginary violins, because that’s the only thing that they had. In that actual situation, there was no violin, and so they can’t play a violin when they don’t have what they need to play. We can imagine that one could have gotten one into their hands, and then when they had it they could play it. But the fact is that they don’t have one. No matter of imagination changes that. And Taylor takes “cannot” to mean that people can’t play imaginary violins, and we consider this to be obviously true.

But Taylor admits that there is another way that the word “can” is used, but one way that he doesn’t use it. The way that his notion of “can” is use, is used to mean the notion of “know-how”. Now this is what we mean when we say that the violinist “can” play the violin. They have the know-how, so if one were given to them then they could play it. But Taylor doesn’t use it this way.

And we don’t think that because someone in the past had the “can” or “know-how”, to do something when they lacked it in the past, means that they did it when they lack that necessary condition. But now it’s trying to be applied to the future. But Taylor is using “can” in the way we use it for the past.

Fatalism and Causation: One might try to attack Taylor on causality. For Taylor’s argument isn’t logically related, but then it must be causally related. But Taylor expresses the argument in terms of necessary conditions and sufficent conditions, which involve no temporal relations. And yet causality seems to imply a temporal relation.

“If, for instance, the presence of oxygen is a necessary condition of a certain man’s being alive over a given period of time, then that man’s continuing to live over that period is a sufficient condition for there being oxygen present. But neither of these is logically necessary or sufficient for the other, nor is either the cause of the other. The presence of oxygen may be a causal condition of that man’s continuing to live, but certainly his living is no causal condition for the presence of oxygen-even though it is a sufficient condition for the presence of oxygen.”

One person points out that Taylor doesn’t include logical necessary and susfficent conditions in his arguments. And logical necessity implies physical necessity, and this could be damaging to the argument.

But Taylor only dealt with “physically” necessary or sufficent conditions. But Taylor doesn’t deny that logical necessity implies “physical” necessity, because he doesn’t a stand on this, and isn’t relevant to his argument.

The Nonefficacy of time: Some might claim that Taylor’s assumpition that time isn’t efficacious is ambigious, because time is logically efficaious. But this misunderstands Taylor’s notion of efficacy of time.

“Taylor explains this by noting that the mere passage of time does not augment or diminish the powers or capacities of anything. Abelson, however, seems to equate the sentence “Time is logically efficacious” with the sentence “Time often has a lot to do with the truth of what we say. ” But these two sentences are entirely different. For instance, the sentence “It is now raining” may be true today and false tomorrow. Quite obviously, time has a lot to do with the truth of the sentence. But it is not time which augmented the power of the clouds to produce rain. Certain meteorological conditions did that. Time in this sense is not efficacious.”

Now another person notices that time canot pass without something chaning, and this is taken to be true.  But this has nothing to do with Taylor’s argument. Taylor pointed out that the passage of time “has no causal effect upon anything”. Something must change during a period of time, but time isn’t the cause of the change. A lake is dired up, but not by time. It is by certain meterological conditions or by people emptying the lake. This all happens in time, but time itself is no cause of it.

Taylor thought we could avoid Fatalism by alterting the Law of Excluded Middle. This way, we say that the certain statements about the future might be neither true or false. But Cahn presents Taylor’s argument, but with only slight modification and unaffected by any modification of the Law of Excluded Middle. This argument takes all of Taylor’s originaly presuppositions, all six of them, and will work with his second instance of the naval commander.

1. At time^1 Naval Commander issues order that “will ensure a naval battle the following day”, or if he does not issue order that “will ensure a naval battle the following day”, then he issues order which “will ensure that no naval battle occurs the following day”.

2. His issuing order which “will ensure a naval battle the following day” at time^1 is a sufficent condition for a naval battle occuring at time^2 (assuming time^2 to be exactly one day after time^1).

3. Therefore, a necessary condition for his issuing order which “will ensure a naval battle the following day” at time^1 is the occurrence of a naval battle at time^2.

4. Naval Commander issuing order which “will ensure that no naval battle occurs the following day” at time^1 is a sufficent condition for no naval battle occuring at time^2.

5. Therefore, a necessary condition for his issuing order which “will ensure that no naval battle occurs the following day” at time^1 is no naval battle occuring at time^2.

6. But at time^2 it is true or, if not true, then false, that a naval battle occurs at time^2.

7. If it is true at time^2 that a naval battle will occurs at time^2, then a necesssary condition is lacking for his having issued order which “will ensure that no naval battle occurs the following day” at time^1.

8. If it is false at time^2 that a naval battle occurs at time^2, then a necessary condition is lacking for his having issued order which “will ensure  a naval battle the following day” at time^1.

9. But in either case, a necessary condition is lacking for his having issued one or the other of the two orders.

10. Therefore, one of the orders was such that he could not issue it, and he was forced to issue the order.

Now this argument can be denied, and avoid fatalsim. But we’d do this by saying the argument doesn’t prove that a necessary condition for one of the two orders was lacking at time^1, but that the conditions were only lacking at time^2. Thus, the naval commander didn’t have it within their power to issue ither command. This means that the law of excluded middle was denied to certain statements in the future. But this seems to bring about some problems. Here’s an argument that tries to show that problem.

1. In order to issue order which “will ensure a naval battle the following day” at time^1, all conditions necessary for the occurrence of order which  “will ensure a naval battle the following day” at time^1 must be satisfied at time^1.

2. In order to issue order which “will insure no naval battle the following day” at time^1,  all conditions necessary for the occurrence of  which “will ensure a naval battle the following day” at time^1 must be satisfied at time^1.

3. If order which “will ensure a naval battle the following day” is issued at time^1, then that is a sufficient condition for a naval battle occurring at time^2.

4. Therefore, a necessary condition for the issuance of order which “will ensure a naval battle the following day” at time^1 is the occurrence of a naval battle at time^2.

5. If order which “will ensure no naval battle the following day”  is issued at time^1, then that is a sufficient condition for no naval battle occurring at time^2.

6. Therefore, a necessary condition for the issuance of order which “will ensure no naval battle the following day”at time^1 is no occurrence of a naval battle at time^2

7. But at time^1 it is neither true nor false, according to those who wish to deny the law of excluded middle, that a naval battle occurs at time^2.

8. In order to issue order which “will ensure a naval battle will occur tomorrow”  at time^1 all conditions necessary for the issuance of that order must then be satisfied, and one of those conditions is that a naval battle occurs at time^2. But this condition is not satisfied at time^1. Therefore order which “will ensure a naval battle will occur tomorrow”  cannot be issued at time^1.

9. In order to issue order which “will ensure no naval battle will occur tomorrow” at time^1, all conditions necessary for the issuance of that order must then be satisfied, and one of those conditions is that no naval battle occurs at time^2. But this condition is not satisfied at time^1. Therefore order which “will ensure no naval battle will occur tomorrow” cannot be issued at time^1.

10. Thus, neither order which “will ensure a naval battle will occur tomorrow” nor order which “will ensure no naval battle will occur tomorrow” can be issued at time^1.

What this argument shows is that we can avoid the conclusion of Taylor’s argument by rejecting the Law of Excluded Middle with regards to certain statements about the future. But if we do this, then we’re led to dney that any action can occur. But this conclusion is even stranger than Taylor’s argument that leads to Fatalism.

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Fatalism

Posted by allzermalmer on November 6, 2011

This blog is based on a paper done by the philosopher Richard Taylor. The paper is called Fatalism, and was in the philosophical journal The Philosophical Review, Vol. 71, No. 1 (Jan., 1962), pp. 56-66.

Richard Taylor first starts out by stating what a Fatalist is suppose to be.

“A Fatalist-if there is any such-thinks he cannot do anything about the future. He thinks it is not up to him what is going to happen next year, tomorrow, or the very next moment. He thinks that even his own behavior is -not in the least within his power, any more than the motions of the heavenly bodies, the events of remote history, or the political developments in China….A fatalist, in short, thinks of the future in the manner in which we all think of the past. For we do all believe that it is not up to us what happened last year, yesterday, or even a moment ago, that these things are not within our power…”

Now he sets up six presupposings, which are supposed to help to lead to Fatalism. And most of these presuppositions are very common, which is what makes the argument interesting.

First Presupposition: A statement is either true or false.  [Law of Excluded Middle]

Second Presupposition: If any state of affairs is sufficient for the occurrence of some further condition at the same or any other time, then the former cannot occur without the latter occurring also. [Sufficient Condition]

Third Presupposition: If the occurrence of any condition is necessary for the occurrence of some other condition at the same or any other time, then the latter cannot occur without the former occurring also. [Necessary Condition]

Fourth Presupposition: If one condition or set of conditions is sufficient for (ensures) another, then that other is necessary (essential) for it. Or, if one condition or set of conditions is necessary (essential) for another, then that other is sufficient for (ensures) it. [Logical implication of 2nd and 3rd Presuppositon]

Fifth Presupposition:  No agent can perform any given act if there is lacking, at the same or any other time, some condition necessary for the occurrence of that act.

Sixth Presupposition: Time is not by itself “efficacious”; that is, that the mere passage of time does not augment or diminish the capacities of anything and, in particular, that it does not enhance or decrease an agent’s powers or abilities.

First Situation: Now let’s imagine that I wake up in the morning, and I find my newspaper at the doorstep. I pick it up and go to sit at the kitchen table. I open it up to look at the headlines of the newspaper. It’s assumed conditions are such that only if there was a naval battle yesterday does the newspaper carry a certain kind of headline, or if it carries a certain different sort (shape) of headline, this will ensure that there was no such battle. Like either it says there was a naval battle, or there wasn’t any naval battle.

Now I know I’m either going to see the headline with a certain shape (i.e. Naval battle) or I won’t see the headline with a certain shape (i.e. Naval battle). And each shall be represented like this:
X=see the headline with a certain shape
~X= don’t see the headline with a certain shape .

We also two more statements, with their own meaning:
Y= “A naval battle occurred yesterday”
~Y= “No naval battle occurred yesterday”

If I perform X, then my doing that will ensure that ~Y. Or, if I perform seeing the headling with a certain shape, then my doing so will ensure that no naval battle occurred yesterday. If I perform ~X, then my doing that will ensure that Y. Or, if I perform not seeing the headline with a certain shape, then my doing that will ensure that a naval battle occurred yesterday.

Now I come to wonder if it was up to me what headline I read when I open up the newspaper, to see the headlines.

I might come to think, “It’s within my power to do X, and it is also within my power to do ~X.” Or, in another way, “It’s within my power to see the headling with a certain shape, and it is also within my power to do not seeing the headling with a certain shape.”

Now this comes off as false, because if it were up to me which one to do, then it would also be up to me whether that naval battle took place or not. This would imply me having the power over the past, and I don’t plainly posses this power.

1. If “a naval battle occurred yesterday” is true, then it is not within my power to “don’t see the headling with a certain shape”.[Reason: for in case “a naval battle occurred yesterday is true”, then there is, or was, lacking a condition essential for my doing “not seeing the headling with a certain shape”, the condition, namely, of there being no naval battle yesterday.]

2. But if “no naval battle occurred yesterday”, then it’s not within my power to see “a headline with a certain shape”. [Reason: same as the reason above.]

3. But a naval battle occurred yesterday or no naval battle occurred yesterday.

4. Therefore, either it is not within my power to  “see the headling with a certain shape”, or it is not within my power to “don’t see the headling with a certain shape.”

This, basically, says that the sort of headline that I read depends on what took place yesterday, or in the past. And what happened yesterday or in the past isn’t up to me. We’re all fatalist when it comes to the past, or it seems that we are. “Don’t cry over spilt milk.”

But there is nothing self-contradictory with thinking that, if I did open up the newspaper and saw a certain shape, then I brought about a naval battle. This is another way of saying that me looking at the headline on the newspaper, and it having a certain shape, that I’ve ensured that there was a naval battle. But I can’t see the headline with a certain shape unless there was a naval battle yesterday.

Second situation: Assume that I’m a naval commander, and I’m going to give my orders for the day. Now assuming the totality of other conditions prevailing,  if I issue a certain kind of order, then it will ensure a naval battle. If I issue a different kind of order, then it will ensure no naval battle. We know that I’ll either issue the first type of order or issue the second type of order.

Here’s a certain symbolic representation:
O= “issue certain kind of order M”
~O= “don’t issue certain kind of order M”
H= “a naval battle will occur tomorrow”
~H= “no naval battle occur tomorrow”

So, if I “issue a certain kind of order M”, then it will ensure that there’s “a naval battle tomorrow”. If I “don’t issue certain kind of order M”, then it will ensure that there’s “no naval battle tomorrow.” But is it up to me which sort of order I issue?

A fatalist would disagree that doing either proposition is within your power. But most of us typically think that it is within our power to do either proposition. For we typically think it is up to the naval commander, with the totality of other conditions prevailing, whether there is a naval battle or no naval battle. The commander, after all, gives the order to do it, and we think that it’s within his power to give the order or not.

But the same formal argument presented for the first instance can be presented for this, the second, instance.

1. If  “a naval battle will occur tomorrow” is true, then it’s not within my power to “don’t issue certain kind of order M”. [Reason: for in case “a naval battle will occur tomorrow” is true, then there is, or will be, lacking a condition essential for my doing “don’t issue certain kind of order M”, the condition, namely, of there being no naval battle tomorrow.]

2. But if “no naval battle occur tomorrow” is true, then it’s not within my power to “issue certain kind of order M”. [Reason: same as for above.]

3. But either “a naval battle will occur tomorrow” or “no naval battle will occur tomorrow.”

4. Therefore, either it is not within my power to “issue certain kind of order M” or it is not within my power to “don’t issue certain kind of order M”.

Another way to say this is, the order you issue depends on whether “a naval battle will occur tomorrow”. By our fourth presupposition, it is a necessary condition for “issue certain kind of order M”, while no naval battle tomorrow is equally essential to “don’t issue certain kind of order M”. Now we might have trouble with this, but we didn’t have trouble when the same type of inference and rules were used with the first situation, with the headline of the newspaper.

Considerations of Time:  Some might object by saying that no condition can be necessary for any other before that conditions exist. However, the fifth and sixth presuppose don’t allow for this.

“Surely if some condition, at any given time, whether past, present,
or future, is necessary for the occurrence of something else, and that condition does not in fact exist at the time it is needed, then nothing we do can be of any avail in bringing about that occurrence for which it is necessary.”

In order for me to be a U.S. Senator, it is necessary that I be at least 30 years old. Past, present, or future, it’s necessary that I be at least 30 years old. If I’m not at least 30 years old, then I can never be U.S. Senator. Being at least 30 years of age is the necessary condition of being U.S. Senator, and I can’t be a U.S. Senator if this condition is never met.

“And if one should suggest, in spite of all this, that a state of affairs that exists not yet cannot, just because of this temporal removal, be a necessary condition of anything existing prior to it, this would be logically equivalent to saying that no present state of affairs can ensure another subsequent to it.”

We would be in a strange  position if we would deny the necessary conditions of states of affairs that don’t exist yet. And this is usually what we do with things in the future, by us thinking that we will either give the naval command or we won’t give the naval command. And this means that what happened in the next second will not be ensured by what happened in the previous second.

“All that is needed, to restrict the powers that I imagine myself to have to do this or that, is that some condition essential to my doing it does not, did not, or will not occur.”

“What restricts the range of my power to do this thing or that is not the mere temporal relations between my acts and certain other states of affairs, but the very existence of those states of affairs themselves;”

We would come to recognize that these states of affairs already exist. All these state of affairs exist, but they don’t exist for us right now. Imagine that you have a long line of dominos, all set up and orderly. You come to focus on one domino. This is basically the position that we’re in. All the dominos lined up are the “states of affairs”, past, present, and future. The present domino is the one that we’re focused on. There’s the one’s in the past which we say exist, and then theres also be the ones in the future which we say exists. We don’t think that we can change the past, and this also follows with us not being able to change the future.

“The fact that there is going to be “a naval battle tomorrow” is quite enough to render me unable to  “don’t issue certain kind of order M”, just as the fact that there has been a naval battle yesterday renders me unable to “don’t see the headline with a certain shape”, the nonoccurrence of those conditions being essential, respectively, for my doing those things.”

Causation: This problem is presented without any reference to causation. Thus, bringing up causation, like it only working from backwards to forwards, or past to future. This objection won’t help with what’s being discussed.

The Law of Excluded Middle:  You can reject one of the premises in the second instance. The first two, the hypothetical premises of “If…then”, can’t be denied without having to reject the the second to fifth presuppositions. And none of those presuppositions seem to have any problems, and are widely used. You can reject the third premise in the second instance, but then you’d have to reject the law of excluded middle.

The reject of the laws of excluded middle has been attempted, and there’s no absurdity in doing so. This leaves with either “a naval battle tomorrow” or “no naval battle tomorrow”. This statement is necessarily true, but each one of the disjuncts isn’t a necessary truth. Thus, we can break apart the statement, and have “A naval battle tomorrow” and “No naval battle tomorrow”. Neither of these statements is necessarily true, but possibly/contingently true. We can thus suppose that neither of them are true and neither of them are false. They’re each “possible”, but it only becomes “necessary” when combine them both together.

Now we can replace the third premise in the second instance, and we can employ keeping the two statements apart from each other, other than putting it into the form of law of excluded middle.

1. If “a naval battle tomorrow” is true, then it is not within my power to “issue certain kind of order M”

2. But if “no naval battle tomorrow” is true, then it is not within my power to “no issue certain kind of order M”.

3. But it is within my power to “not issue certain kind of order M”, and it is also within my power to “issue certain kind of order M”.

4. Therefore, “no naval battle tomorrow” is not true, and “a naval battle tomorrow” is not true”.

Now “a naval battle tomorrow” and “no naval battle tomorrow” are logical contradictories, and if either is false then the other is true. But when we look at the first situation, we find no problems and don’t argue about the law of excluded middle. But when it comes to the second situation, and deals with the future, we find that there’s some problem. It looks like a problem, but the logic is the same, and uses the same presuppositions.

Temporal efficacy: It looks that if we want to avoid fatalism, then we’d have to get rid of the first presupposition of the law of excluded middle, and to get rid of the sixth presupposition of Time is not by itself “efficacious”; that is, that the mere passage of time does not augment or diminish the capacities of anything and, in particular, that it does not enhance or decrease an agent’s powers or abilities.

“In fact, it is doubtful whether one can in any way avoid fatalism with respect to the future while conceding that things past are, by virtue of their pastness alone, no longer within our power without also conceding an efficacy to time; for any such view will entail that future possibilities, at one time within our power to realize or not, cease to be such merely as a result of the passage of time-which is precisely what our sixth presupposition denies.”

Some might want to deny the first presupposition and the sixth presupposition, because they think of status of some future things as mere possibilities. This position denies the futures factuality and lack of it’s factuality. And this makes it look like the first presupposition and the sixth are linked together.

The Assertion of Fatalism: 

“Of course one other possibility remains, and that is to assert, out of respect for the law of excluded middle and a preference for viewing things under the aspect of eternity, that fatalism is indeed a true doctrine, that propositions such as (the second instance) are, like (the first instance), never true in such situation as we have described, and that the difference in our attitudes toward things future and past, which leads us to call some of the former but none of the latter “possibilities”, resulting entirely from epistemological and psychological cosiderations- such as, that we happen to know more about what the past contains than about what is contained in the future, that our memory extends to past experience rather than future ones, and so on.”

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Atoms and the Physical World

Posted by allzermalmer on November 5, 2011

This blog is based on Walter Terrence Stace article called Sir Arthur Eddington and The Physical World, in the journal Philosophy, Vol. 9, No. 33 (Jan., 1934), pp. 39-50. The article follows that of Refutation of Realism (which I did a blog on).

He starts out by pointing out the two distinct worlds of the familiar world and the physical world. The first, familiar world contains sticks, stones, stars, colors, sounds, and smells.  The second, physical world, contains electrons, protons, and has no colors, smells, or taste.

The familiar world is suppose to be composed of “sense-data”, and that they only exist in the mind, or are subjective. The physical world is to be composed of something that interacts with us, and gives rise to the “sense-data” that we experience. We reach to the physical world by inference from the familiar world that we experience, to the world outside of it by inference. This means we never come into direct contact with the physical world, like we never see it, touch it, smell it, or taste it. Thus, we only infer from the sense-data, which are ‘in the mind’, to the physical world of electrons and protons. But the electrons and protons aren’t hypothetical entities or fictions (as Eddington might think).

To clear up some of these things, this will not deal with common-sense division of universe of mind and universe of matter. This is to be considered false, because there is a third option. There is the third realm of neither physical nor mental, but what will be called a “neutral” realm. Part of this neutral realm is our sensory qualities, and are neither physical or mental. This is one way to get ride of this division of mind and matter (known as Neutral Monism).

We come to recognize that “Sense-data are the first and the most direct things in our experience; all else is remote inference.” It does not matter if they sense-data are mental or neutral, “in” minds or “outside” of them. What matters is that we don’t attribute these “sense-data” to atoms, because we’re told that don’t have color or anything like that, which are sensory qualities. For we’ll be stuck in a contradictions: “Electrons have color but they don’t have color.”

Let’s take a statement like, “There exists a physical world of protons and electrons which do not possess the sensory qualities. And this world is not in any way hypothetical or fictitious.” And we’ll come to think of it like saying something like the cat is real, the moon is real, the table is real. Come to understand it simply as “existent”.

Now let’s take a look at what happens if we take protons and etc are merely fictitious. We can soften the language and just call them “mental constructions”. This view doesn’t say anything about the validity of science, or the invalidity, nor does it derogates the dignity of it’s claim to teach us “truth”. There existence is more of an ontological question, one of metaphysics. As mathematician and scientist Henri Poincare once said, “It matters little whether ether really exists; that is the affair of metaphysicians. The essential thing for us is that everything happens as if it existed, and that this hypothesis is convenient for the explanation of phenomena.” And physicist Edward Andrade once said, “Whether the man of science regards his atoms as having an ultimate reality or not does not affect the validity of theory; the theory is just as useful in introducing order and promoting discovery if they are merely polite fictions as if they are desperate realities.”

Because we only experience the sense-data, this rules out the suggestion that we can know that atoms exist by perceiving them. They are outside of the sense-data, as the scientist would admit. But we can admit that we perform an experiment and notice that we see a “wavy trail”, and we call that the electron. But we haven’t seen the electron itself, but we say a “wavy trail”. The “wavy trail” was part of the sense-data, but the electron wasn’t. Instead, we come to think that the electron caused the “wavy trail” that was our sense data. This means that the electron would have to be an inference from the sense-data.

Now we could come to wonder how we infer these things from the sense-data. We seem to have the option of causality. What we observe is the effect, and we come to infer the cause from the effects. We notice certain regularities in sense-data, which provide us with the laws of physics or provide the rules of inference. Like “electron caused the wavy trail.”

This can lead us to think that the physical world is the cause of the familiar world, which is the effect of the physical world. In other words, the familiar world we all experience is the effect of the physical world, which is the cause. What we experience is the effect of something else, which we call the physical world.

It shall be assumed that there is some kind of causality, either deterministic or indeterminate, which is how we make the inference from a supposed effect to cause, or from sense-datum to atoms.  The obvious reason we have for believing in the law of causation is based on that observe certain regularities or sequences. When conditions A are met, it is always happens that B happens. This means that when condition A is the case, then B shows up. A is called the cause, and B is called the effect. This leads to the causal law of AB.

But these regularities are found among sense-data. A is a sense-datum, and B is a sense-datum, and any of our other cause and effect relationships ever observed by any human being have been sense-datum. This leads us to the conclusion that the cause of sense-datum is always another sense-datums, and all known causal laws apply solely to the world of sense-data. This means we have no, and could not have, one single piece of evidence for believing that the law of causation can be applied outside of the realm of sense-data, or sense-data can have any causes (like the physical objects) which aren’t sense-data themselves.

A diagram of what is going on here could help out:

A,B, and C are all sense-datum found in the familiar world. The person sees all these things, and sees that B follows A, and C follows B. This leads them to believe that A is the cause of B, and B is the cause of C. It comes to this conclusion of causality by the regular repetition of that order, and through experience. Sense-datum of billiard ball A is found to come into contact with sense-datum billiard ball B. This leads us to conclude that A is the cause of B moving.

But what right do we have, or what reason, to assert that the causes of A,B, and C are a’,b’,c’ (which are physical causes), when they’re never observed behind the sense-data? We have no right to this claim. The law of causation they operate on has never been observed to operate outside of the sense-data, and can therefore have no evidence that it does operate outside of the sense-data. It is sufficent to stick with A being the cause of B. We don’t have to invoke that a’ is the cause of A, when these aren’t part of sense-data, but A is the cause of B is part of the sense-data. We’d have to give two causes for each phenomena, one in the one world and the other in another world. One cause in the physical world and one in the familiar world.

It is not denied that a star causes light-waves, those waves cause retinal changes, the retinal changes cause changes in the optic nerve, which causes movements in the brain cells, and so on.

“But the observed causes and effects are all sense-data, or at least possible sense-data. And no sequences of sense-data can possibly justify going outside of the series of sense-data altogether. If you admit that we never observe anything except sense-data and their relations, regularities, and sequences, then it is obvious that we are completely shut in by sense-data, and can never get outside of them. Not only causal relations, but all other observed relations, upon which any kind of inferences might be founded, will lead only to further sense-data and their relations. No inference, therefore, can pass from what is sense-datum to what is not sense-datum.”

This, in the end, leads to there the fact that atoms aren’t inferences from sense-data. It is not to be denied that there is a vast amount of valid inferential reasoning taking place in a physical theory that contains atoms in it. But from a strict logical sense, there’s no inference from sense-datum to atoms. What does this mean?

“An hypothesis is set up, and the inferential processes are concerned with the application of the hypothesis, i.e. with the prediction by its aid of further sense-data, and with its own internal consistency.”

This means that atoms aren’t inferences from sense-data (i.e. experience), or can validly infer them from sense-data. This means we can’t have any reason to believe that they exist. Or, we at least, no one could know if they did, and means we have absolutely no evidence of their existence.

We might wonder the status the atoms have, or the hypothesis that contains them. It doesn’t mean that they’re false and worthless, merely untrue. We don’t come to think that the nautical almanac “exist” except on the pages of the book or in the brains of the people that compiled it or read it. But the natural almanac is “true” as much as it enables us to predict certain “sense-data”, like disks of light at night (i.e. stars). The atomic theory carries a similar function as that of the natural almanac. It helps us make predictions of experiences that we’ll have, and orderly amongst itself.

This view includes making predictions of future things, but it also includes the view to include retrodictions as well, which is making predictions about what happened in the past. For example, we could wonder where Mars was on 8,000 B.C.E. We use our hypothesis, say Newton’s. With this hypothesis, the theory makes a retrodiction of where Mars was around 8,000 B.C.E.

Stace suggests that hypothesis, like the theory of the atoms, are shorthand formula ingeniously worked out by the human mind. And they enable us to predict experiences. He gives us the example of Newton’s “force”.

“Newton formulated a law of gravitation in terms of “forces.” It was supposed that this law-which was nothing but a mathematical formula-governed the operation of these existent forces. Nowadays it is no longer believed that these forces exist at all. And yet the law can be applied just as well without them to the prediction of astronomical phenomena. It is a matter of no importance to the scientific man whether the forces exist or not…But that would not make the law useless or untrue (if Newton’s “force” didn’t exist). If it could still be used to predict phenomena, it would be just as true as it was.”

Instead, we’ve found that Newton’s “forces” couldn’t account for the orbit of Mercury, and a new theory was developed. It was developed based on Einstein’s theory. Einstein’s theory talks about bumps and space bending and creating hills in the space-time fabric. And this helped get ride of Newton’s “forces” in science. But this doesn’t put Einstein’s theory off any better.

“Not only may it be said that forces do not exist. It may with equal truth be said that “gravitation” does not exist. Gravitation is not a “thing,” but a mathematical formula, which exists only in the heads of mathematicians. And as a mathematical formula cannot cause a body to fall, so gravitation cannot cause a body to fall. Ordinary language misleads us here. We speak of the law “of” gravitation, and suppose that this law “applies to” the heavenly bodies. We are thereby misled into supposing that there are two things, namely, the gravitation and the heavenly bodies, and that one of these things, the gravitation, causes changes in the other. In reality nothing exists except the moving bodies, or moving sense-data. And neither Newton’s law nor Einstein’s law is, strictly speaking, a law of gravitation. They are both laws of moving sensedata, that is to say, formulae which tell us how the sense-data will move.”

We tend to think that these things exist, and that is because the human mind hasn’t broken free of the idea that science “explains” things. People weren’t just content with laws that told them planets, as a matter of fact, move in such and such ways. People wanted to know “why” planets moves these ways. Newton replied because of “Forces”. And humanity thought that explained why the planets move in such and such way. That’s because we understand forces, we feel them every time someone pushes or pulls us. This is suppose to have explained by things that are familiar to us in our own experiences. And the same happened with Einstein’s “humps and hills” of space-time.

“But scientific laws, properly formulated, never “explain” anything. They simply state, in an abbreviated and generalized form, what happens. No scientist, and in my opinion no philosopher, knows why anything happens, or can “explain” anything. Scientific laws do nothing except state the brute fact that “when A happens, B always happens too.” And laws of this kind obviously enable us to predict.”

Atoms are said to be in the same position as “Forces” of Newton’s and “Humps and Hills” of Einstein. And so too with the theory of atoms are exactly like them. They’re, in reality, mathematical formulae, and this is the scientific way of stating the atomic theory. This formulae helps to eventually lead to predictions, and these predictions are of sense-data that will appear in given conditions. It will, for example, enable a scientist to predict a “wavy trail”. And the human minds weakness for seeking explanation leads us to think that atoms exist in correspondence with the mathematical formula.

In seeking explanations, we try to come up with causes for events of our experience. And we’ve come to think of causation as a principle of explanation. But we don’t experience atoms as the cause of our sense-data, and so we can’t really say that atoms explain anything. The relation of atoms to sense-data isn’t a relation of cause to effect, but relation of mathematical formula to facts and happenings that enables the mathematician to calculate.

We come to think of these things existing because they give us a “physical” cause for the effects in the “familiar” world. And some scientists cling to the existence of atoms because they cling to explanation. But so did those during Newton’s time that “Forces” existed because they explained things. But it is the imagination that has explained things. It explains things by making them more familiar to us, and more homely. Maybe an example could help with this.

“One of the foundations of physics is, or used to be, the law of the conservation of energy. I do not know how far, if at all, this has been affected by the theory that matter sometimes turns into energy. But that does not affect the lesson it has for us. The law states, or used to state, that the amount of energy in the universe is always constant, that energy is never either created or destroyed. This was highly convenient, but it seemed to have obvious exceptions. If you throw a stone up into the air, you are told that it exerts in its fall the same amount of energy which it took to throw it up. But suppose it does not fall. Suppose it lodges on the roof of your house and stays there. What has happened to the energy which you can nowhere perceive as being exerted? It seems to have disappeared out of the universe. No, says the scientist, it still exists as potential energy. Now what does this blessed word “potential”-which is thus brought in to save the situation-mean as applied to energy? It means, of course, that the energy does not exist in any of its regular “forms,” heat, light, electricity, etc. But this is merely negative. What positive meaning has the term? Strictly speaking, none whatever. Either the energy exists or it does not exist. There is no realm of the “potential” half-way between existence and non-existence. And the existence of energy can only consist in its being exerted. If the energy is not being exerted, then it is not energy and does not exist. Energy can no more exist without energizing than heat can exist without being hot. The “potential” existence of the energy is, then, a fiction. The actual empirically verifiable facts are that if a certain quantity of energy e exists in the universe and then disappears out of the universe (as happens when the stone lodges on the roof), the same amount of energy e will always reappear, begin to exist again, in certain known conditions. That is the fact which the law of the conservation of energy actually expresses. And the fiction of potential energy is introduced simply because it is convenient and makes the equations easier to work. They could be worked quite well without it, but would be slightly more complicated. In either case the function of the law is the same. Its object is to apprise us that if in certain conditions we have certain sense-data (throwing up the stone), then in certain other conditions we shall get certain other sense-data (heat, light, stone hitting skull, or other such). But there will always be a temptation to hypostatize the potential energy as an “existence,” and to believe that it is a “cause” which “explains” the phenomena.”

If the views which I have been expressing are followed out, they will lead to the conclusion that, strictly speaking, nothing exists except sense-data (and the minds which perceive them). The hypothesis truth and value consist in their capacity for helping us to organize our experience and predict our sense-data. But we eventually have to come to the conclusion that the “real” world is the “physical world”. It is the “physical world” that is the illusion, and the familiar world that is the reality. It’s the only world that exists, or ever known to exist.

Science and Hypothesis by Henri Poincare

The Mechanism of Nature by Edward Andrade

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Confirmation (Paradox?)

Posted by allzermalmer on November 3, 2011

This blog is based on something brought up by philosopher of science Carl Gustav Hemple. It’s usually called the Ravens Paradox or Confirmation Paradox. The presentation of the problem originally arose in an article of his called Studies in the Logic of Confirmation (I.). It appeared in the philosophy journal Mind, New Series, Vol. 54, No. 213 (Jan., 1945), pp. 1-26.

“The defining characteristic of an empirical statement is its capability of being tested by a confrontation with experimental findings, i.e. with the results of suitable experiments or “focused” observations.”

This is to tell us that science is concerned with testing our theories against experience, and these experiences are typically of the sensory kind (sight, taste, sound, smell, and touch). This type of thing, empirical statements being able to be be tested based on experiment, is what separates it from statements of math and logic, or transempirical statements.

“Testability here referred to has to be understood in the comprehensive sense of “testability in principle”; there are many empirical statements which, for practical reasons, cannot be actually tested at present. To call a statement of this kind testable in principles means that it is possible to state just what experiential findings, if they were actually obtained, would constitute favorable evidence for it, and what findings or “data”, as we shall say for brevity, would constitute unfavorable evidence; in other words, a statement is called testable in principle, if it is possible to describe the kind of data which would confirm or disconfirm it.”

So the theory has to make predictions of what will happen, or is predicted to happen. This leads the theory to be an empirical statement. But now all empirical statements have to make predictions, whether we can bring them about now or sometime in the future. What they do is tell us that if we bring about certain conditions, then we should observe certain things to happen. But we can’t test them right now, and have to wait for some future time. Even though we can’t test it right now, it is still able to be tested in the future if the technology or situation arises that the statement makes clear. Knowing what the statement predicts, it allows to figure out if the event fits with the prediction (confirm) or doesn’t match with the prediction (disconfirm).

“no finite amount of experiential evidence can conclusively verify a hypothesis expressing a general law such as the law of gravitation, which covers an infinity of potential instances, many of which belong either to the as yet inaccessible future, or to the irretrievable past; but a finite set of relevant data may well be “in accord with” the hypothesis and thus constitute confirming evidence.”

There’s a reason why science can’t prove it’s theories. Science deals with some general statements. General statements, All A are B or If A then B, apply to all times. This means that it holds in the past, even if we weren’t there, or in the future or someplaces we haven’t yet observed or been to. The problem is that it holds for all time (past, present, and future), as well into all locations. But we’re finite beings with a finite amount of time, and finite searching capabilities, which means that we can’t find everything that meets that hypothesis to confirm all of it’s predictions.

“…relevance is a relative concept; experiential data can be said to be relevant or irrelevant only with respect to a given hypothesis; and it is the hypothesis which determines what kind of data or evidence are relevant for it. Indeed, an empirical finding is relevant for a hypothesis if and only if it constitutes either favorable or unfavorable evidence for it; in other words, if it either confirms or disconfirms the hypothesis. Thus, a precise definition of relevance presupposes an analysis of confirmation and disconfirmation.”

Now we go around accumulating all these data from our observations, or creating observation reports. “The squirrel had no tail” or “The counter clicked 15 times when we ran the experiment”, are observation reports or data. But we couldn’t make sense of these reports without some sort of hypothesis. We can’t say that the first sentence disconfirms a theory without comparing how that statement fits in with a theory. But we want to see how to confirm a theory, which involves the relevance of the observation statement in relation to the theory under question. And Hempel hopes to go on to show how we can do this.

“Take a scientific theory such as the atomic theory of matter. The evidence on which it rests may be described in terms of referring to directly observable phenomena, namely to a certain “macroscopic” aspects of the various experimental and observational data which are relevant to the theory. On the other hand, the theory itself contain a large number of highly abstract, non-observational terms such as “atom”, “electron”, “nucleus”, “dissociation”, “valence”, and others none of which figures in the description of observational data.”

He want’s to go on to point out that induction can only take us so far in forming scientific theories. Many times, in a theory, it contains terms that don’t come from observation itself. This means that we can’t invoke these terms just from observations, which is usually how induction work. Induction will go from what was observed, to what will be observed. It moves from past happenings to future happenings. This can mean that we predict that because the Green Bay Packers won the Superbowl last year that they’ll win it this year. Or, moving from particulars to a general conclusion (this raven is black to All ravens are black). So there’s another part of theory creation that isn’t based on observation/induction itself. This is based on imagination, and connect these imaginative terms up with observation. Connect the theoretical parts with the concrete parts of observation itself.

Now there is something called, or was called, Nicod’s Criterion of confirmation. It would follow as something like this:

“Consider the formula or the law: A entails B. How can a particular proposition, or more briefly, a fact, affect its probability? If this fact consists of the presence of B in a case of A, it is favorable to the law ‘A entails B’; contrary, if it consists of the absence of B in a case of A, it is unfavorable to this law. It is conceivable that we have here only two direct modes in which a fact can influence the probability of a law…Thus, the entire influence of particular truths or facts on the probability of universal propositions or laws would operate by means of these two elementary relations which we shall call confirmation and invalidation.”

This criterion is based on statements of the form “If X then Y” or “All X are Y”.

Take the simple example of a hypothesis of “All Ravens are Black” or “If Raven then Black”. The hypothesis is confirmed, under Nicod’s Criterion, if the antecedent (Raven) and the consequent (black) are satisfied. This means that we’ve confirmed the hypothesis if we find an object that is a Raven and Black.

The hypothesis “All Ravens are Black” is disconfirmed if the antecedent (Raven) is satisfied, but the consequent (Black) isn’t confirmed. This means that we find an object that is a Raven, but it isn’t Black, which means it could be white.

But this criterion has some shortcomings. One of them is that it only applies to universal hypothesis (All Ravens are Black: ), but it doesn’t work with existential hypothesis (Some Ravens are Black). This means that it doesn’t tell us the criterion to say that an existential hypothesis is confirmed or disconfirmed. It also doesn’t work with psychological hypothesis like “You can fool all of the people some of the time and some of the people all the time.” This means that the criterion doesn’t tell us when we’ve confirmed or disconfirmed an existential hypothesis in conjunction with a universal hypothesis.

But now let’s take a look at a second problem with Nicod’s criterion. Let us say that we have two Statements.

1. All Ravens are Black
2. All non-black things are non-Ravens

Now we have four objects before us to review, and if these statements confirm, disconfirm, or are neutral to the two statements, under Nicod’s criterion.

a. A Raven and is Black::      (confirms 1. but neutral to 2.)
b. A Raven but not Black::   (disconfirms 1. and 2.)
c. Not a Raven but Black::    (neutral to 1. and 2.)
d. Neither Raven or Black::  (confirm 2. but neutral to 1.)

But the problem with this is that is both 1. and 2. are equivalent hypothesis. They are logically identical in their truth-tables. All Ravens are Black is logically identical to All non-black things are non-Ravens. Or, If Raven then Black is logically identical to If not Black then not Raven. This is the logical equivalence of contraposition.

This seems to throw Nicod’s criterion into direct conflict with logic.The way that those statements should be in line with logic when it comes to confirmation or disconfirmation, it would look like this:

a. A Raven and is Black::     (confirm 1. and 2.)
b. A Raven but not Black::  (disconfirm 1. and 2.)
c. Not a Raven but Black::   (neutral to 1. and 2.)
d. Neither Raven or Black:: (confirm 1. and 2.)

This is what leads Hemple to present forward a logical principle to help out with.

Equivalence Condition: Whatever confirms (disconfirms) one of two equivalent sentences, also confirms (disconfirms) the other.”

This is just a logical principle being used to help us have a criterion for determine what counts as confirmation, neutral, or disconfirming for the theory being used.

One of the reasons is that the reasoning processes in creating empirical hypothesis is that they have to be logically consistent (no contradictions). From certain universal statements, you can logically deduce certain predictions for observation.

“an adequate definition of confirmation will have to do justice to the way in which empirical hypothesis function in theoretical scientific contexts such as explanations and predictions, they serve as premises in a deductive argument whose conclusion is a description of the event to be explained or predicted. The deduction is governed by the principles of formal logic, and according to the latter, a deduction which is valid will remain so if some or all of the premises are replaced by different, but equivalent statements; and indeed, a scientists will feel free, in any theoretical reasoning involving certain hypotheses, to use the latter in whichever of their equivalent formulation is most convenient for the development of his conclusions.”

Now here are certain things that follow from the Equivalence Criterion, which is a logical principle used.This principle brings about a necessary condition to say that we’ve achieved confirmation or disconfirmation of a theory.

If Raven then Black is logically the same as If not Black then not Raven.  X–>Y= ~Y–>~X. Now imagine that you hold the hypothesis “All Ravens are Black”. You want to go out and look for things that confirm your hypothesis that you hold. You are probably going to walk outside, and look for things that are Ravens. If it is not Black, then you’ve disconfirmed your hypothesis. Or you find a Black Raven and confirmed your hypothesis. But you don’t even need to go outside to confirm your hypothesis. Just look around your place and see if you can observe anything that is not black and not a raven. I can see a red cup, a blue pen, yellow notebook. This is all confirmation of the hypothesis “All Ravens are Black”. This is usually what becomes known as the Raven Paradox. It makes confirmation of a theory extremely easy, just walk through a grocery store and remember that’s all a confirmation of a All Ravens are Black.

Now there’s one way to try to get around this. One way is to conjoin a universal statement and an existential statement. This means that you put together a statement like “All X are Y” and “Some D are E”. But the problem that we come across is that this isn’t logically acceptable with equivalent statements. This would ruin the way of theoretical arguments, which science relies on itself with it’s hypothesis.

Another way is to say that scientific hypothesis implies an existential statements. This would mean that the Universal statement of “All Mermaids are Green” implies “Some Mermaids are Green”. A statement like “Some Mermaids are Green” means that something exists that is a mermaid and green. But this is no longer the case with the logical square of opposition, in modern logic. Universal statements don’t imply Existential statements. Like, “All Jedi have Midi-Chlorian in their blood system.” This would imply, if we take the suggestion seriously, that “Some Jedi have Midi-Chlorian in their blood system”, which implies that at least one Jedi exists, let alone that Midi-Chlorian exists. This is one reason that modern logic says that Universal statements don’t imply existential statements. They don’t say that what it talks about actually exists.

Another way of dealing with this problem is to say that we should focus only on the “Class of Ravens”. This means that we accept “All Ravens are Black” is our hypothesis, and accept that it’s equivalent to “All non-Black things are non-Ravens”. But we only look for things in the “Class of Ravens”, and see if they’re either black or not black. Now imagine that someone comes up to you and says, “I have a Raven behind my back. Would you like to see what color  it is?” You should say “Yes”, because that’s part of the “Class of Ravens” that your trying to confirm. But now imagine someone comes up to you and says, “I have a pen behind my back. Would you like to see what color it is?” You should say “No”, because that doesn’t fall under the “Class of Ravens”.

But the problem with this is that sometimes, a hypothesis goes beyond it’s class, and works in a purely negative way (i.e. outside of its “Class”). So let’s take a hypothesis All P’s are Q’s. The field of application would be P’s. Take the scientific hypothesis that “All sodium salts burn yellow”, and we focus on the class of “Sodium Salts”. We apply it to something that we don’t know to be a sodium salt or burn yellow. If this thing doesn’t burn yellow, we noticed the absence of Sodium Salt. If it burns yellow, then either we find out it’s Sodium Salt and confirm the hypothesis or find out it isn’t Sodium Salt and find a new thing to study and know it burns yellow.

This isn’t really a logical paradox, but it’s a psychological paradox.

“Our interest in the hypothesis may be focused upon its applicability to that particular class of objects, but the hypothesis nevertheless asserts something about, and indeed imposes restrictions upon, all objects (within the logical type of the variable occurring in the hypothesis, which in the case of our last illustration might be the class of all physical objects). Indeed, a hypothesis of the form “Every P is a Q” forbids the occurrence of any objects having the property P but lacking the property Q; i.e. it restricts all objects whatsoever to the class of those which either lack the property P or also have the property Q. Now, every object either belongs to this class or falls outside of it, and thus, every object-and not only the P’s-either conforms to the hypothesis or violates it; there is no object which is not implicitly “referred to” by a hypothesis of this type.”

This is what we’re logically faced with, but we come to think of Equivalence Criterion as leading to paradoxes. But these paradoxes have nothing to do with logic, or logical paradoxes, but psychological paradoxes.

Now imagine that we’re in a new situation. Imagine that you hold the hypothesis of “All Sodium Salts burn Yellow”. This time you decide to adduce an experiment where you take a cube of ice, and put it over a colorless flame, and find that the flame didn’t turn yellow. This would confirm “Whatever doesn’t burn Yellow isn’t Sodium Salts”, and this statement is equivalent to “All Sodium Salts burn Yellow”. Now this doesn’t obviously look paradoxical, but the other way seemed paradoxical. There’s no logical difference between them, but we take one to be paradoxical and ignore the other one as being a paradox if we accept the other to be a paradox.

“Instead, we tacitly introduce a comparison of H with a body of evidence which consists of E in conjunction with an additional amount of information which we happen to have at our disposal; in our illustration, this information includes the knowledge (1.) that the substance used in the experiment is ice, and (2) that ice contains no sodium salt. If we assume this additional information as given, then, of course, the outcome of the experiment can add no strength to the hypothesis under consideration.”

But we come to think that we have evidence that the hypothesis “Whatever doesn’t burn Yellow isn’t Sodium Salts” is supported by this instance, but it supports “All Sodium Salts burn Yellow”.

We, therefore, seem to be stuck in logical trouble and going beyond what scientist do with their theoretical arguments, if we want to change the confirmation/diconfirmation conditions of Equivalence Criterion.

This leads us to have confirmation for our hypothesis all the time, and have it all around us. With the example of “All Ravens are Black”, it means that everything we see that isn’t a Raven, is confirmation for “All Ravens are Black”. We literally have confirmation for our theories all around us, and see evidence everywhere. The logical point is we have confirmation for our hypotheses all the time.

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