allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Prediction’

False Hypotheses & True Predictions

Posted by allzermalmer on June 23, 2016

In logic, a conjunction is a logical connective that connects two separate propositions. For example, say we have the propositions ‘The Golden State Warriors won the Western Conference Championship of the NBA in 2016’ and ‘The Cleveland Cavaliers won the Eastern  Conference Championship of the NBA in 2016’. We can represent each of those propositions, respectively, as P and Q.

The logical connective of conjunction would combine each of these two separate propositions together. Each of these propositions would be known as a conjunct that makes up a conjunction. Conjunct of P and conjunct of Q make up the conjunction of ‘Both The Golden State Warriors won the Western Conference Championship of the NBA in 2016 & The Cleveland Cavaliers won the Eastern Conference Championship of the NBA in 2016’. This can be represented as ‘P&Q’.

A conjunction is only true when each conjunct is true. A conjunction is false when either one of the conjuncts is false or both conjuncts are false. In the example presented, it is true that both teams won the Conference championships in 2016. So the conjunction is a true proposition.

Logic tells us that from false hypotheses, or hypothesis, that true predictions follow from it.  Suppose that P means ‘The Golden State Warriors won the NBA Championship in 2015’ and that Q means ‘The Golden State Warriors won the NBA Championship in 2016’. From these two propositions, we can form the conjunction of ‘Both The Golden State Warriors won the NBA Championship in 2015 & The Golden State Warriors won the NBA Championship in 2016’. This can be represented as ‘P&Q’.

Taking ‘P&Q’ as a hypothesis, we can prove that some propositions follow from that hypothesis. One of these propositions that follow is P.  So from the hypothesis of ‘Both The Golden State Warriors won the NBA Championship in 2015 & The Golden State Warriors won the NBA Championship in 2016’ that it necessarily follows by rules of logic that ‘The Golden State Warriors won the NBA Championship in 2015’.

Suppose ‘P&Q’ then necessarily follows ‘P’.

The hypothesis presented is false, P&Q is false. One of the conjuncts is false, Q is false. One of the conjuncts is true, P is true. So the conjunction is false. But from this false hypothesis, we find that a true conclusion follows from it.

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Determinism and Predicting Machine

Posted by allzermalmer on November 13, 2012

This is a copy of the article Determinism and Predicting Machine by Daniel Gogol. It appeared in the philosophical journal Philosophy and Phenomenological Research, Vol. 30, No. 3 (Mar., 1970), pp. 455-456

“Determinism is sometimes thought to entail the theoretical possibility of total knowledge. A strongly deterministic position is, that all physical events conform to a set of laws, and that if sufficient data were given about the state of the universe at a given instant, the occurrence or non-occurrence of a given future event could be deduced from these laws. Related to this strongly deterministic position is the question of the theoretical possibility of building a machine to predict the future.

We present an argument whose outcome is that it is impossible for a certain type of predicting machine to exist.

Assume that a machine could exist, called machine M, such that there is some amount of time, t hours, and some distance, d feet, such that the machine would correctly answer any question given it as long as the question had a “yes” or “no” answer and was about the occurrence or nonoccurrence of a physical event within t hours and within d feet of the machine. Assume also that the machine’s answer would consist of some physical event occurring within t hours and within d feet. For example, it might be built to type “yes” or “no”, depending on the correct answer to the question.

Now suppose that the machine were asked the following question: “Will the machine M answer ‘no’ before answering ‘yes’, and at some time during the next t hours?”

Now since this is a question with a “yes” or “no” answer about future physical events occurring within d feet and within t hours, the machine will answer “yes” or “no” within the next t hours. But if it answers “yes”, then the correct answer is “no”, and if it answers “no”, then the correct answer is “yes”. Therefore, by assuming the existence of a machine with certain properties we have been led to a contradiction, so we must reject the existence of such a machine as a logical impossibility.

Of course, the philosophical implications of the impossibility of such a machine are sharply limited. The argument used does not show, for instance, that a machine could not be built which could deduce whether or not any given physical event would occur within 24 hours. But such a machine could not also have the property that it always provided the answer within 24 hours.

Also, our argument does not show that a machine could not be built to answer all but certain special questions, such as the one in our argument. but it would seem that if a complete set of physical laws did exist, such that the answer to all questions of a certain type could be deduced from a sufficient data, then a machine which provides the answers should be theoretically possible, so that the fact that it is not possible destroys some of the plausibility of the idea that such a complete set of physical laws exists. If such a complete set of laws does exist, then it is a “physical” impossibility to build a machine to collect sufficient data and make the necessary deductions fast enough to have the properties of machine M.

Our argument about machine M applies to other possible universes as well as our own, and in different possible universes machine M may be impossible for different reasons. We could divide possible universes into the following two classes:

(1) Those possible universes in which there does not exist a set of physical laws such that any given future physical event can be logically deduced if there is sufficient data about the present physical state of the universe.”

(2) Those possible universes in which there is such a set of physical laws, but it is a physical impossibility to build a machine with the properties of machine M.

 

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How Science is Done

Posted by allzermalmer on September 23, 2012

This comes from the book Biology 6th edition by Raven and Johnson. It is from page 7 to page 9.

“How do scientists establish which general principles are true from among the many that might be true? They do this by systematically testing alternative proposals. If these proposals prove inconsistent with experimental observations, they are rejected as untrue. After making careful observations concerning a particular area of science, scientists construct a hypothesis, which is a suggested explanation that accounts for those observations. A hypothesis is a proposition that might be true. Those hypotheses that have not yet been disproved are retained. They are useful because they fit the known facts, but they are always subject to future rejection if, in the light of new information, they are found to be incorrect.

Testing Hypothesis

We call the test of a hypothesis an experiment (figure 1.4). Suppose that a room appears dark to you. To understand why it appears dark, you propose several hypotheses. The first might be, “There is no light in the room because the light switch is turned off.” An alternative hypothesis might be, “There is no light in the room because the light bulb is burned out.” And yet another alternative hypothesis might be, “I am going blind.” To evaluate these hypotheses, you would conduct an experiment designed to eliminate one or more of the hypotheses. For example, you might test your hypotheses by reversing the position of the light switch. If you do so and the light does not come on, you have disproved the first hypothesis. Something other than the setting of the light switch must be the reason for the darkness. Note that a test such as this does not prove that any of the other hypotheses are true; it merely demonstrates that one of them is not. A successful experiment is one in which one or more of the alternative hypotheses is demonstrated to be inconsistent with the results and is thus rejected.

As you proceed through this text, you will encounter many hypotheses that have withstood the test of experiment. Many will continue to do so; others will be revised as new observations are made by biologists. Biology, like all science, is in a constant state of change, with new ideas appearing and replacing old ones.

figure 1.4

This diagram illustrates the way in which scientific investigations proceed. First, scientists make observations that raise a particular question. They develop a number of potential explanations (hypotheses) to answer the question. Next, they carry out experiments in an attempt to eliminate one or more of these hypotheses. Then, predictions are made based on the remaining hypotheses, and further experiments are carried out to test these predictions. As a result of this process, the least unlikely hypothesis is selected.

Establishing Controls

Often we are interested in learning about processes that are influenced by many factors, or variables. To evaluate alternative hypotheses about one variable, all other variables must be kept constant. This is done by carrying out two experiments in parallel: in the first experiment, one variable is altered in a specific way to test a particular hypothesis; in the second experiment, called the control experiment, that variable is left unaltered. In all other respects the two experiments are identical, so any difference in the outcomes of the two experiments must result from the influence of the variable that was changed. Much of the challenge of experimental science lies in designing control experiments that isolate a particular variable from other factors that might influence a process.

Using Predictions

A successful scientific hypothesis needs to be not only valid but useful—it needs to tell you something you want to know. A hypothesis is most useful when it makes predictions, because those predictions provide a way to test the validity of the hypothesis. If an experiment produces results inconsistent with the predictions, the hypothesis must be rejected. On the other hand, if the predictions are supported by experimental testing, the hypothesis is supported. The more experimentally supported predictions a hypothesis makes, the more valid the hypothesis is. For example, Einstein’s hypothesis of relativity was at first provisionally accepted because no one could devise an experiment that invalidated it. The hypothesis made a clear prediction: that the sun would bend the path of light passing by it. When this prediction was tested in a total eclipse, the light from background stars was indeed bent. Because this result was unknown when the hypothesis was being formulated, it provided strong support for the hypothesis, which was then accepted with more confidence.

Developing Theories

Scientists use the word theory in two main ways. A “theory” is a proposed explanation for some natural phenomenon, often based on some general principle. Thus one speaks of the principle first proposed by Newton as the “theory of gravity.” Such theories often bring together concepts that were previously thought to be unrelated, and offer unified explanations of different phenomena. Newton’s theory of gravity provided a single explanation for objects falling to the ground and the orbits of planets around the sun. “Theory” is also used to mean the body of interconnected concepts, supported by scientific reasoning and experimental evidence, that explains the facts in some area of study. Such a theory provides an indispensable framework for organizing a body of knowledge. For example, quantum theory in physics brings together a set of ideas about the nature of the universe, explains experimental facts, and serves as a guide to further questions and experiments.

To a scientist, such theories are the solid ground of science, that of which we are most certain. In contrast, to the general public, theory implies just the opposite—a lack of knowledge, or a guess. Not surprisingly, this difference often results in confusion. In this text, theory will always be used in its scientific sense, in reference to an accepted general principle or body of knowledge.

To suggest, as many critics outside of science do, that evolution is “just a theory” is misleading. The hypothesis that evolution has occurred is an accepted scientific fact; it is supported by overwhelming evidence. Modern evolutionary theory is a complex body of ideas whose importance spreads far beyond explaining evolution; its ramifications permeate all areas of biology, and it provides the conceptual framework that unifies biology as a science.

Research and the Scientific Method

It used to be fashionable to speak of the “scientific method” as consisting of an orderly sequence of logical “either/or” steps. Each step would reject one of two mutually incompatible alternatives, as if trial-and-error testing would inevitably lead one through the maze of uncertainty that always impedes scientific progress. If this were indeed so, a computer would make a good scientist. But science is not done this way. As British philosopher Karl Popper has pointed out, successful scientists without exception design their experiments with a pretty fair idea of how the results are going to come out. They have what Popper calls an “imaginative preconception” of what the truth might be. A hypothesis that a successful scientist tests is not just any hypothesis; rather, it is an educated guess or a hunch, in which the scientist integrates all that he or she knows and allows his or her imagination full play, in an attempt to get a sense of what might be true. It is because insight and imagination play such a large role in scientific progress that some scientists are so much better at science than others, just as Beethoven and Mozart stand out among most other composers.

Some scientists perform what is called basic research, which is intended to extend the boundaries of what we know. These individuals typically work at universities, and their research is usually financially supported by their institutions and by external sources, such as the government, industry, and private foundations. Basic research is as diverse as its name implies. Some basic scientists attempt to find out how certain cells take up specific chemicals, while others count the number of dents in tiger teeth. The information generated by basic research contributes to the growing body of scientific knowledge, and it provides the scientific foundation utilized by applied research. Scientists who conduct applied research are often employed in some kind of industry. Their work may involve the manufacturing of food additives, creating of new drugs, or testing the quality of the environment.

After developing a hypothesis and performing a series of experiments, a scientist writes a paper carefully describing the experiment and its results. He or she then submits the paper for publication in a scientific journal, but before it is published, it must be reviewed and accepted by other scientists who are familiar with that particular field of research. This process of careful evaluation, called peer review, lies at the heart of modern science, fostering careful work, precise description, and thoughtful analysis. When an important discovery is announced in a paper, other scientists attempt to reproduce the result, providing a check on accuracy and honesty. Nonreproducible results are not taken seriously for long.

The explosive growth in scientific research during the second half of the twentieth century is reflected in the enormous number of scientific journals now in existence. Although some, such as Science and Nature, are devoted to a wide range of scientific disciplines, most are extremely specialized: Cell Motility and the Cytoskeleton, Glycoconjugate, Journal, Mutation Research, and Synapse are just a few examples.

The scientific process involves the rejection of hypotheses that are inconsistent with experimental results or observations. Hypotheses that are consistent with available data are conditionally accepted. The formulation of the hypothesis often involves creative insight.

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