Chapter 1: Language
Language (means of which to convey our thoughts and knowledge) is what makes us different from the rest of the animals, but at the same time language is what causes misunderstanding (too simple = we give the words our own meaning).
The language of science is mathematics: It is precise and rich enough and also is universal.
The language of science is mathematics: It is precise and rich enough and also is universal.
Chapter 2: Mathematics
Kinds of propositions:
- A priori: whose truth/falsity can be shown by pure reason.
- A posteriori: truth/falsity can only be shown after the facts.
- Analytic: propositions after you analyze the meaning of a word.
- Synthetic: propositions that have factual content
Chapter 3: Assumptions
Scientist are constantly searching for an explanation to their questions referred to the natural laws that govern the universe. A general statement about the universe which is true. It is a description of what actually takes place.
In order to try to understand the law of nature we must:
Have 3 assumptions to start with:
Kinds of laws:
In order to try to understand the law of nature we must:
Have 3 assumptions to start with:
- We may assume that it is possible to learn exactly.
- We may assume that we can learn a good approximation to a law.
- We may assume that we can approximate a law as closely as we wish.
Kinds of laws:
- Causal laws: Determines the future given the present./ Teleological law: determines the present given the future.
- Time independent laws
- Conservation laws
- Minimum principles
- Continuous laws
- Laws involving a number of dimensions.
Chapter 4: Probability
In science, probability plays 3 roles:
1. statistical theories
2. measurements are subject to error
3. when asserting a statement, we have to assign some degrees of credibility (statement about science)
1. statistical theories
2. measurements are subject to error
3. when asserting a statement, we have to assign some degrees of credibility (statement about science)
Chapter 5: The Method
Start with facts and end with facts. Because: “A fact reports a single event, while theory reports an unlimited, perhaps infinite, number of events.”
Stages (after facts):
1. Induction: Formation of theories on the basis of factual knowledge. It's the process by which the scientist form a theory to explain the observed facts.
2. Deduction: Logical analysis of what the general law says about a particular event in the future.
3. Verification: Go back to the facts to check if the prediction was correct.
Stages (after facts):
1. Induction: Formation of theories on the basis of factual knowledge. It's the process by which the scientist form a theory to explain the observed facts.
2. Deduction: Logical analysis of what the general law says about a particular event in the future.
3. Verification: Go back to the facts to check if the prediction was correct.
Chapter 6 Credibility and Induction
The problem of explication
We are confronted with a concept about which all of us have an intuitive notion, but no one has succeeded in making the concept numerically precise.
New definition must be precise, second, it must agree with the intuitive concept.
The procedure is to put down clearly all those cases in which our intuition serves as a guide, and additional conditions for the concept to be useful and then select the simplest precise concept satisfying all these conditions.
The degree of credibility, is an absolute standard to which our personal beliefs can be compared. The closer our estimates correspond to the actual credibility of hypotheses, the more rational our decisions are.
Induction is the process of forming theories on the evidence of our observations. Deduction takes us from general, to the particular, while inductions carries us from the particular to the general.
It starts with observation, and leads to theories which are usually generalized propositions. Deduction the second step will give us certain observable particular facts which are consequences of our general theory.
We are confronted with a concept about which all of us have an intuitive notion, but no one has succeeded in making the concept numerically precise.
New definition must be precise, second, it must agree with the intuitive concept.
The procedure is to put down clearly all those cases in which our intuition serves as a guide, and additional conditions for the concept to be useful and then select the simplest precise concept satisfying all these conditions.
The degree of credibility, is an absolute standard to which our personal beliefs can be compared. The closer our estimates correspond to the actual credibility of hypotheses, the more rational our decisions are.
Induction is the process of forming theories on the evidence of our observations. Deduction takes us from general, to the particular, while inductions carries us from the particular to the general.
It starts with observation, and leads to theories which are usually generalized propositions. Deduction the second step will give us certain observable particular facts which are consequences of our general theory.
Chapter 7: Concepts of Science
Direct observations are those which cannot possibly be wrong, in the sense that we state only what we actually see at the moment.
Operationalism is often described as a modern version of Empiricism, which is a school which mantains that all knowledge must originate in experience, a belief that in its many variants is undoubtedly the msot popular tenet of modern philosophy.
Rules of interpretation: these rules will tell us which of the statements in our language describe observable phenomena, and just what observations will establish whether the predictions are right or wrong. Explanation is acceptable only if it could have been used to predict the outcome.
The difficulty arises in that it is often not easy to separate the theory from the rules of interpretation. The crucial requierement is that we be clear about these assertions and what facts they describe, so that when we make an observation in the field of the theory, there can be no doubt as to whether this agrees with the prediction of the theory or not.
Justification for each concept is its usefulness in building simple theories. Statements near the top connect with experience only through a long chain of conventions and mathematical arguments.
Operationalism is often described as a modern version of Empiricism, which is a school which mantains that all knowledge must originate in experience, a belief that in its many variants is undoubtedly the msot popular tenet of modern philosophy.
Rules of interpretation: these rules will tell us which of the statements in our language describe observable phenomena, and just what observations will establish whether the predictions are right or wrong. Explanation is acceptable only if it could have been used to predict the outcome.
The difficulty arises in that it is often not easy to separate the theory from the rules of interpretation. The crucial requierement is that we be clear about these assertions and what facts they describe, so that when we make an observation in the field of the theory, there can be no doubt as to whether this agrees with the prediction of the theory or not.
Justification for each concept is its usefulness in building simple theories. Statements near the top connect with experience only through a long chain of conventions and mathematical arguments.
Chapter 8: Measurement
Without measurement there is no progress possible in modern science, and that progress is connected with refinement of our measuring instruments.
Start with the simple concept of classification and work our way up to a full measuring scale.
Classification must be such that it is possible to classify every single day into one of these several classes,
No one day could conceivably be classified under two different headings, otherwise the resulting confusion would make the concept useless.
A relationship that is asymmetric and transitive is known as a partial order. It will allow us to arrange our various classes in an ordering where, we cannot give complete information as to what class is ahead of which other class, some answers are supplied
Simple orders: the requirement that we would like to add to the previous ones is that, given any two objects from different classes, it should be possible to tell which one is ahead of the other .
Numerical scales: the concept of measurement is closely related in our minds with numbers. It consists of real number assigned to the objects under consideration. In order to connect the length of something we have to observe that there is a certain relationship between them. We also need to find many other objects that could have been used as measuring scales.
Measurement plays an important role in science, because by assigning numerical values to various objects or phenomena in nature we are able to incorporate these phenomena in numerical laws.
Start with the simple concept of classification and work our way up to a full measuring scale.
Classification must be such that it is possible to classify every single day into one of these several classes,
No one day could conceivably be classified under two different headings, otherwise the resulting confusion would make the concept useless.
A relationship that is asymmetric and transitive is known as a partial order. It will allow us to arrange our various classes in an ordering where, we cannot give complete information as to what class is ahead of which other class, some answers are supplied
Simple orders: the requirement that we would like to add to the previous ones is that, given any two objects from different classes, it should be possible to tell which one is ahead of the other .
Numerical scales: the concept of measurement is closely related in our minds with numbers. It consists of real number assigned to the objects under consideration. In order to connect the length of something we have to observe that there is a certain relationship between them. We also need to find many other objects that could have been used as measuring scales.
Measurement plays an important role in science, because by assigning numerical values to various objects or phenomena in nature we are able to incorporate these phenomena in numerical laws.
Chapter 9: Scientific Explanations
The key to explanation is that "all objects heavier than air fall if not supported"
After having the theory:
For teleological law we might perhaps select the law of Entropy: We will eventually reach a state of complete disorder and that nature tends in this direction, but it does not tell us anything very useful about the next moment or the moment just passed.
LET US NOT LIMIT OURSELVES FURTHER BY ARBITRARILY BINDING OUR HANDS IN THE FORMATION OF THEORIES.
After having the theory:
- We must have general theories
- These theories must be well established
- We must be in possession of facts which are known independently of the facts to be explained
For teleological law we might perhaps select the law of Entropy: We will eventually reach a state of complete disorder and that nature tends in this direction, but it does not tell us anything very useful about the next moment or the moment just passed.
LET US NOT LIMIT OURSELVES FURTHER BY ARBITRARILY BINDING OUR HANDS IN THE FORMATION OF THEORIES.
Chapter 10: What is Science
Chapter 11: Determinism
Doctrine of determinism... that every fact in the universe is guided entirely by law. Laws guide facts, or that laws determine facts. The law is a description of the past present and future. We can distinguish four factors influencing the problem:
The laws are available
The cfact available
The reasoning powers available
The time available
Our more precise laws cannot be casual, but statistical.
The third factor, that of limitation on our powers of analysis.
First, we assumed that we somehow have the laws governing such physical problems. Secondly, we assumed that somehow we had all the initial data necessary available to us. Thirdly, we assumed that the machine can carry out the necessary calculations, while it may be the case that such problems prove unsolvable to it.
Difficulty in solving the mathematical problems involved in predictions
The laws are available
The cfact available
The reasoning powers available
The time available
Our more precise laws cannot be casual, but statistical.
The third factor, that of limitation on our powers of analysis.
First, we assumed that we somehow have the laws governing such physical problems. Secondly, we assumed that somehow we had all the initial data necessary available to us. Thirdly, we assumed that the machine can carry out the necessary calculations, while it may be the case that such problems prove unsolvable to it.
Difficulty in solving the mathematical problems involved in predictions
Chapter 12: Life
The doctrine that phenomena of life possese a character sui generis by virtue of which they differ radically from phsyco- chemical phenomena. Evolution- every species must fight to find room to live in and for the means of existence
lamark states that the characteristics gained through life can be inherited, this is the way in which we tried to account for the way species adapt themselves to their environment.
We must anote that there seems to be a strange tendency in evolution for "straight-line" development.
There is a natural surplus of life, creating the celebrated struggle, and hence a natural selective process preserves the individuals showing minute advantages over their brothers. Physics was reduced to Biology and not the other way around.
lamark states that the characteristics gained through life can be inherited, this is the way in which we tried to account for the way species adapt themselves to their environment.
We must anote that there seems to be a strange tendency in evolution for "straight-line" development.
There is a natural surplus of life, creating the celebrated struggle, and hence a natural selective process preserves the individuals showing minute advantages over their brothers. Physics was reduced to Biology and not the other way around.
Chapter 13: The Mind
What distinguishes "mere" living things from those higher creatures that think.
The materialistic position must look at the brain as a very complex machine and hold that any sufficiently complex machine is able to think. We are concious and machines are not.
The crudest activity classified as learning is memorization, we admire man for their large store of knowledge. The simplest method is trial and error. We have a definite goal, which we recognize when we reach it, and we keep trying various approaches until one gets us there.
One argument says that our will cannot be free, because the universe is determined
We do have free will, the only problem is to find out the mechanism by which we make decisions.
Behaviorist approach of looking at him from the outside only and forming generalizations about the pattern of his behavior. The second approach is to try to find out the internal factors as well, partly by studying his body and partly by questioning him.
Complete predictability of events seems out of the question even in the inanimate world. Prediction of human actions is perhaps the most complex problem facing the scientist. We must remember that we are human beings, the
The materialistic position must look at the brain as a very complex machine and hold that any sufficiently complex machine is able to think. We are concious and machines are not.
The crudest activity classified as learning is memorization, we admire man for their large store of knowledge. The simplest method is trial and error. We have a definite goal, which we recognize when we reach it, and we keep trying various approaches until one gets us there.
One argument says that our will cannot be free, because the universe is determined
We do have free will, the only problem is to find out the mechanism by which we make decisions.
Behaviorist approach of looking at him from the outside only and forming generalizations about the pattern of his behavior. The second approach is to try to find out the internal factors as well, partly by studying his body and partly by questioning him.
Complete predictability of events seems out of the question even in the inanimate world. Prediction of human actions is perhaps the most complex problem facing the scientist. We must remember that we are human beings, the
Chapter 14: Science and Values
A complete scale of values is one that enables us to give a simple ordering of states of the world. We must call upon science to tell us what the possible states of the world are and to help us in measuring the various factors that seem relevant to us. On the other hand, we must call upon Logic and Mathematics to assure us that our scale of values is consistent and that it really leads to a simple ordering.
Chapter 15: The Social Sciences
Whether man can be studied by the same methods that apply to lower beings or inanimate nature
We find that laws are harder to form because of the tradition of vagueness, ambiguity, and emotive overtones in the subject matter, and because of the inherent complexity of human beings. Ideally the progress of all of Science should reach a stage where the nonscientist would be relieved of all considerations of technical questions, and the sole decisions left up to him would be questions of right and wrong.
We find that laws are harder to form because of the tradition of vagueness, ambiguity, and emotive overtones in the subject matter, and because of the inherent complexity of human beings. Ideally the progress of all of Science should reach a stage where the nonscientist would be relieved of all considerations of technical questions, and the sole decisions left up to him would be questions of right and wrong.
Chapter 16: Quo Vadis?
We know that our information is only approximation, so a prediction is reliable only if minor errors in our original information do not change the prediction much. The philosopher's faith that an increase in knowledge is instrinsically good, and hope that philosophers will continue in their role as critics and as question-raisers to stimulate the unending progress of Science.
No scientific theory is final, tomorrow we may find a new, better theory, which shows us that the present theories are only approximately right.
No scientific theory is final, tomorrow we may find a new, better theory, which shows us that the present theories are only approximately right.