miércoles, 31 de enero de 2007

Carnap

INDUCTIVE LOGIC AND SCIENCE
Rudolf Carnap

Carnap begins with an introduction about the importance of the logic and its main roll in the thinking. He state that the inductive logic does not imply new forms the thinking or reasoning, but news way by which to arrive at the knowledge (i.e., Aristotle); to change the customary implicit reasoning (thinking without rules, intuitive), to a explicit method to formalize the reasoning and to delimit it. He defines the inductive reasoning as “all forms of reasoning where the conclusion goes beyond the content of the premises, and therefore cannot be states with certainly”. Carnap was questioned if it is necessary to have rules in the inductive reasoning (inductive logic).

The main concept of inductive logic is probability, with two kinds: the Logic and the Statistical probability. Statistical probability is a physical characteristic that can to be empirically measured; something similar to frequency, but no frequency in itself. A statistical statement talks about a characteristic of given phenomenon in term of frequency. The previous affirmation leads to ask to us how to test those statements (how to confirm or disconfirm it). Results of the empiric content (experiment, test) are related with the magnitudes in question, whose values in themselves not directly observable, but like symptom of the state of the phenomenon. Thus, a question arises: as we delimited the number of experiment or series of test and its precision?? The experience of scientist and yours budget can be the answer. Other question is the explicit definition of statistical probability by means of limit (Reichenbach) or by an axioms system (statisticians); however neither concept can totally be rejected, because both are useful in its battle ground.

He concluded that the two kinds the logic cannot be rejected because to its useful in the science.

Logic probability: “Statement of inductive probability states relations between a hypothesis and a give body of evidence”. Where a high value of probability means the degree to which the hypothesis is confirmed or supported by the evidence. The degree of confirmation (C) is relative to the evidence; but only it is not based on observations. The premises are usually known, but not always. The statement can be false or true, those referred by the evidence. Carnap make reference to the empirical component as it leaves form the evidence. He postules that the “logic” probability statement is of a purely logical nature, and it isn´t related to factual statement (empiric, “tangible”). Thus the statements are not possible to test. Inductive logic statements are similar to deductive logic sentences, since they are based on the logic relation among the hypothesis and the evidence; without need of observations (test).

Carnap point out that the principle of indifference (“If no reasons are known which would favor one several possible events, then the events are to be taken as equally probable”) that is including within of the Classic theory of probability (Bayes, Laplace) cannot be discarded of the development of the inductive logic. Because it is applied only to logical sentences, not a factual sentences.

Therefore, the function of the inductive logic in science is to measure C (support) of the given hypothesis to the light of the evidence. A problem arises when the scientist chooses a hypothesis influenced by external factors to the evidence (intuition, political, religious, etc). Nevertheless, this fact also is important in the science. In addition, inductive logic does not eliminate external factors, only determines relation among hypothesis and evidence.

The inductive logic can to create rules of estimation, therefore it serves as instrument for the determination of rational decisions.

Finally; the goal is to establish rules for the thinking that are been worth for all kind task in science.

A definition of “Degree of Confirmation”

C. G. Hempel and P. Oppenheim
Philosophy of Science, Vol. 12, No. 2. 1945

A sentence which represents an empirical hypothesis has to be theoretically capable of confirmation or disconfirmation, allowing us to determine the acceptance or rejection of it. Because a general definition of the concept of Degree of confirmation has been not developed yet, the objective of the authors is to define, in purely logical terms, a metrical (quantitative) concept.

The confirmation is defined as follows: An objective relation between a hypothesis and the empirical evidence with which it is confronted. This relation depends exclusively on the content of the hypothesis and of the evidence and it is of a purely logical character; once a hypothesis and a description of certain observational findings are given, no further empirical investigations are needed to determine to what degree the evidence confirms the hypothesis.

The question of interest is: what degree of confirmation shall be assigned to H on the basis of E? And is represented such as ‘dc (H, E)‘ [‘Dc’: Degree of confirmation, ‘H’: Hypothesis, ‘E’: Empirical evidence; ‘E’ and ‘H’ are sentences in a model language ‘L]’. ‘E’ will usually consist in a report of a finite number of observations findings and have not to be contradictory [to satisfy the condition: dc (H, E) + dc (Not H, E) = 1]. The determination of ‘dc (H, E)’ requires reference only to the structure (Formal or syntactical) of ‘H’ and ‘E’, and its value can be found by an analysis of that structure and the application of certain purely deductive mathematical techniques.

To determine ‘dc (H, E)’ if required the maximum likelihood principle and a hypothetical distribution in such a way that on the basis of the given evidence ‘E’ we infer the optimum distribution ‘deltaE’ and the assign to ‘H’’, as its degree of confirmation’ the probability which ‘H’ possesses relatively to ‘E’ according to ‘deltaE’; then “dc (H, E) = pr (H, E, deltaE)”. A given ‘E’ does not uniquely determine a fixed frequency distribution ‘delta’, it may confer different degrees of likelihood upon the different possible distributions, therefore the optimum distribution ‘delta’ is such that the probability ‘pr (E, T, delta)’ which ‘delta’ confers upon ‘E’ is not exceeded by the probability that any other distribution would assign to ‘E’.

‘dc (H, E)’ can not be called the probability of the hypothesis ‘H’ relatively to evidence ‘E’ in a strict sense (is just an arbitrary terminological decision) because ‘dc (H, E)’ not satisfy some postulates of probability and therefore ‘dc’ is not a probability. Is better to use the concept of measure of a sentence which refers to the assignation, by means of some general rule, a measure (which depends on the given empirical evidence) ‘m(s)’ to every sentence in ‘L’ in such a manner that some logical conditions are satisfied and then ‘Dc (H, E) = m(H.E)/ m(E)’. In this case, the determination requires reference not only to the structure of the sentences, but also, to ‘E’.

Finally the concept of Degree of confirmation that has been presented here reflects the assumption which might be called the statistical version of the principle of induction and implies that the relative frequencies observed in the ‘past’ will remain fairly stable in the ‘future’.

martes, 23 de enero de 2007

Logical positivism: a new movement in European Philosophy
Albert Blumberg & Herbert Feigl. 1931

The paper is divided in four sections, where the first three are dedicated to frame the logical positivism and to show its dependence upon and application to in formal and factual sciences. The last section is about the nature and aim of Philosophy.

At the begining of the 20th century converged two significant traditions in philosophy: the positivistic-empirical and the logical. The essence of the movement (called logical positivism) was a new interpretation of the nature, search and purpose of philosophy. That idea involved the clarification of the meaning of propositions and the elimination of the meaningless pseudoporositions, and the way to achieve it was through inquires into the foundations of logic, mathematics and physics.

The union of empiricism with the logic theory is which differentiates logical positivism from the older positivism, empiricism and pragmatism. This marriage is what allows an unified theory of knowledge in which both factors are regard. And what makes possible this convergence was the use of the analytic character of logic.

I: Summary of the advances in pure logic till 1930’s, which have made this Philosophy possible.

The purely logical problem of knowing is that it is the analysis of language, because it is shown to be the system of conventions that determine the syntactical order required to have a consistent language. The theorems of logic are rules for tautological transformations, and the “laws of thought” (principle of identity, contradiction, excluded middle…) constitute as a group the stipulation that the concrete interpretation given to symbols should be definite and lack of ambiguity. In general any proposition is a tautology when it is true whatever may be the truth-value of the component propositions. For example, “p or not-p” is tautologically true because of the definitions of “or” and “not”. Thus the validity of deduction since deduction has nonsense, and represents nothing in reality, so it can’t be contradicted by empirical facts.

In empirical science the problem of application is solved through a system of “aplicational” definitions which lay down the empirical meaning of the symbols employed. The importance of logic as a tool lies in its ability to develop new and complicated forms or patterns for the representation of facts.

II: The terms: Knowledge, language and meaning

For logical positivism the definition of “knowledge” is crucial, since is the formal structure or relations of the given, but not the content of experienced. The “real” knowledge (Erkenntnis) comes when the relations of similarity or dissimilarity between experiences are recognized; when an object is recognized by comparison with others.

-The purpose of language is to mirror or express facts. This is done by means of some syntax so selected that the relations of words in the proposition represent the relations of elements in the fact. The proposition represents the relations of elements in the fact. The proposition expresses the fact, therefore, in virtue of a structural similarity between it and the fact. To express this similarity is required a different language in which a proposition would expresses this similarity in virtue of a similarity between it and the similarity. The isomorphy of the system of language and the system of facts, however, would be hold until all molecular propositions had been analyzed into their constituent atomic propositions.-

-To know the meaning of a proposition is to know what must be the case if the proposition is true. The meaning of a complex proposition is revealed when it is analyzed into its component atomic propositions. The meaning or sense (sinn) of an atomic proposition is the “being-the case” or “not-being-the-case” of the fact which it expresses. The meaning (Bedeutung) of a complex word or concept is given by explicit definition: that of a simple word or name by pointing what it stands to experience. -

By the procedure of verification, a general axiomatization of knowledge can decomposed (carried out in the original). The most fruitful way to get at the atomic propositions is to inquire under what conditions a given proposition is true. If we can not give these conditions, we do not know the meaning of the proposition; if the conditions can not possibly be given, the proposition has no meaning.

III: Foundations of sciences.

By formal sciences are meant logic and pure mathematics, are formal in that they say nothing about facts. As they are tautological, they are engaged, in elaborating symbol patterns (in my point of view it is the “knowledge”). The factual or empirical sciences (physical, natural, social) are concerned with applying these patterns to the description of the relational structure of experienced.

Only through the “applicational” definitions (correlation between formal concepts and empirical content (verification)) the transition between the formal sciences to factual sciences can be arise, and the question of truth or falsity can be arise. However, the question of falseness can not be answered simply, because, there are two elements which can be varied: the axioms and the “aplicational” definitions. So the choice between different theories could be a question of simplicity. On whether, we prefer simpler axioms or simpler “aplicational” definitions. But the term “simplicity” sensu Rsichencach could be descriptive or inductive. The first one has nothing to do with truth or falsity, but is simply a matter of convenience. Inductive simplicity contrary, presupposes descriptive simplicity, but involves more. For example, when someone selects the (descriptively) simplest set of axioms which covers the given facts with a minimum of complication in the concrete definitions, it is no longer a question of convenience, but a question of truth and falsity, or rather of probability.

Other problem to choose between systems (theories) in factual sciences is the ad hoc “metrical” forces that affect all material bodies and are clearly different from ordinary forces. If, however, it is stipulate that the “applicational” definitions are to be selected that all metrical forces are set equal to zero, then the choice between systems can be made by direct comparison with fact (the system’s ability to predict). So again it is a problem of probability.

For the Viennese, the concept of probability is definable either (a) purely logically, for the mathematical theory of probability, or (b) as statistical frequency. A concept that is not categorically important for logical positivism, but is a model for building laws of nature, is the principle of causality; that also is link lo the concept of probability. The classical principle of the occurrence, formulated, asserts that the probability of the occurrence of a particular event is greater the more exactly certain definite initial conditions are ascertained, so here the limits are practical and the complete certainty doesn’t exist.

-> All factual sciences then are essentially applications of pure symbol-patterns to the description of facts. But since the laws, are universal propositions and induction is not logically justifiable, the propositions of science though synthetic assert probabilities and are therefore not a priori. <- IV: The aim For the new positivism, metaphysical propositions are, strictly speaking meaningless, since a proposition has meaning only when we know under what conditions it is true or false (empirical verification, that could have practical or real problems). The concept of empirical reality in logical positivism means orderability in the space-time physical universe; this is always determinable through a specific means of empirical verification. To say that something is real is to say that certain data are observed, that certain facts are the case, nothing more. So the purpose of philosophy is the clarification of the meaning of propositions and the elimination of the meaningless pseudopropositions.