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.