Truth suffers from too much analysis

Posts Tagged ‘Conventionalism’

Hume and The Impossibility of Falsification

Posted by allzermalmer on May 5, 2013

Hume’s logical problem of induction as Hume presents it and Popper presents it, deals with contingent statements. The affirmation or the negation of the same contingent statement is possible. Take the contingent statement that “All Swans are White”: It is both possible that “All Swans are White” and it is also possible that  not “All Swans are White”. Logic alone cannot decide if “All Swans are White” is either true or false. So it would be decided by some other way as to wither its affirmation or negation to be true. Hume, and Popper, say that experience cannot show the truth of the contingent statement “All Swans are White”.

“Hume’s argument does not establish that we may not draw any inference from observation to theory: it merely establishes that we may not draw verifying inferences from observations to theories, leaving open the possibility that we may draw falsifying inferences: an inference from the truth of an observation statement (‘This is a black swan’) to the falsity of a theory (‘All swans are white’) can be deductively perfectly valid.” Realism and The Aim of Science

(H) Hypothesis: All Swans are White
(E) Evidence: This is a Black Swan

Hume, as Popper takes him in his problem of induction, showed that we cannot show that (H) is true, no matter how many individual swans that are white we have observed. To show that (H) is true, we must verify every case of (H). (H) is a Universal statement, its scope is that of all times and all places. The universal statement is both omnipresent and omnitemporal in its scope. It makes no restriction on temporal location and spatial location. (E) makes a Singular statement, its scope is of a particular time and a particular place. It makes a restriction on temporal location and spatial location. Popper held that we can know (E) is true, ‘This is a Black Swan’. Thus, we cannot know (H) All Swans are White but we can know (E) This is a Black Swan.

Hume’s logical problem of induction, as Popper takes it, goes something like this:

(i) Science proposes and uses laws everywhere and all the time; (ii) Only observation and experiment may decide upon the truth or falsity of scientific statements; (iii) It is impossible to justify the truth of a law by observation or experiment.


(i*) Science proposes and uses the universal statement “all swans are white”; (ii*) Only singular observational statements may decide upon the truth or falsity of ‘all swans are white’; (iii*) It is impossible to justify the truth of the universal statement ‘all swans are white’ by singular observational statements.

It is taken as a fact that (i) or (i*) is true. So there is no question about either (i) or (i*). So the conflict of Hume’s logical contradiction arises between (ii) and (iii) or (ii*) and (iii*). Popper accepts (iii) or (iii*). So the only way out of Hume’s logical problem of induction is to modify or reject (ii) or (ii*) to solve the contradiction.

Popper thus solves Hume’s logical problem of induction by rejecting (ii) or (ii*) and replacing it with a new premise. This new premise is (~ii).

(~ii) Only observation and experiment may decide upon the falsity of scientific statements
(~ii*) Only singular observation statements may decide upon the falsity of ‘all swans are white’.

Popper rejects (ii) or (ii*), which basically said that only singular observation statements can show that either universal statements are true or false. Popper rejects this because of (iii), and says that Singular observation statements can only show that universal statements are false. Popper believes, as the quote at the beginning of the blog says, that Hume’s logical problem of induction doesn’t show that we can’t show that a universal statement is false by a singular observational statements. But is this what Hume showed to be true?

It does not appear that Hume’s logical problem of induction even allows Popper to escape with the modification of (ii) to (~ii). It appears that Hume’s logical problem of induction does not allow Popper to escape from “fully decidable” to “partially decidable”, i.e.  decide both truth or falsity to cannot decide truth but only falsity.

Take the singular observational statement that Popper gives in the quote, i.e. ‘This is a black swan’. It is a singular statement, but the statement contains a universal within it, it contains “swan”. “Swan” are defined by their law-like behavior, which are their dispositional characteristics, and is a universal concept. These dispositions are law-like, and thus universal in scope as well. And by (iii) we cannot determine if something is a “swan” because of that. The concept “swan” is in the same position as “all swans are white”. They are both universal, and because of (iii) cannot be shown to be true.

“Alcohol” has the law-like behavior, or disposition, or being flammable. So if we were to say that ‘This is alcohol’. We would have to check all the alcohol that existed in the past, present, future, and all places in the universe in which it was located. We would have to light them to see if they catch fire, and thus flammable. Only than could we say that “This is alcohol”, and know that it is alcohol. But to do so would be to verify a universal through singulars, which is impossible by (iii).

In fact, Hume even talks about dispositions and law-like behavior in his talks about the problem of induction. For example, Hume says that “we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them.” Hume is specifically attacking dispositions as well, which means he is attacking universal concepts and universal statements.

“Our senses inform us of the colour, weight, and consistence of bread; but neither sense nor reason can ever inform us of those qualities which fit it for the nourishment and support of a human body…The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers?” Enquiry’s Concerning Human Knowledge

From Popper’s point of view, science can only show the falsity of a universal statement through the truth of a singular statement. The singular statement would have to contradict the universal statement and the singular statement would have to be true.

(h) If it rained then wet ground.
(e) Not a wet ground
(c)Thus, it didn’t rain.

If we assume that both (h) and (e) are true, then we accept a contradiction. Contradictions can’t possibly be true. So we know that at least one of these two must be false. But which one is false and which one is true, (h) or (e).

But how can we show the truth of a singular observational statement when it relies on a universal concept, and universal concepts fall for (iii) just as much as universal statements? Hume’s position of the logical invalidity of of induction, i.e. (iii), also holds not only with universal statements but also universal concepts, i.e. law-like behavior/ dispositional characteristics. How does Popper respond to this?

Popper accepts the invalidity of reaching universal statements through experience, but takes it that we accept singular observational statements based on conventions. We conventionally accept the singular observation statement as true.

Hume’s logical problem of induction shows this:

(H) All Swans are White
(E) This swan is black

Now we may either accept (H) as a convention or accept (E) as a convention, or both as conventions. Popper rejects accept (H) as a convention, because you cannot show that a convention is false. Showing something false is what (~ii) was used to solve the original problem of induction. He wants to show that (H) is false, which is consistent with (~ii), but the only way to do that is if (E) can be shown true. But (E) contains a universal concept and (iii) prevents us from experiencing dispositions or law-like behaviors, i.e. Swan or Alcohol. (iii) applies just as much to universal statements as it does to universal concepts. (E) is based on universal concepts and so has to be accepted as a convention, to escape (iii), in order to show that (H) is false and be consistent with (i) and (~ii). (H) has to have the ability to be shown false to be falsifiable, and not being a convention means it has the ability to be shown false.

Contrary to what Popper thinks, Hume’s logical problem of induction doesn’t even allow you to show a falsifying instance. Thus, following full implications of Hume’s logical problem of induction, we can neither show the truth of a universal statement or show the falsify of a universal statement.

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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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