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Unfortunately, all set diagrams, as well as the Venn diagram, are static, i.e. they always assume an actual state. In reality, however, everything is in motion, everything is history. ** **
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Mathematics is not free of irrationality. But it seems to be the last discipline which is still able to integrate, to include, to control parts of the irrational. Physics has already given up.
Nevertheless, mathematics has problems. And these problems started at the same time as the problems of physics - with the difference I mentioned above.
With mathematics one can do almost everything - thus also nonsense. ** **
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8446 |
The two-valued logic is also not suitable for the treatment of propositions about future events, because it implies a false determinism and leaves no space for the freedom of man.
If A is a proposition about future events, then the statement »A is true« can be more accurately described by the statement »There are (that is: present) causes that force the occurrence of A in the future«, and the statement »A is false« can be more accurately described by the statement »There are causes that force the occurrence of non-A in the future«.
A sentence like »Bill will be home tomorrow« will not usually be true or false in this sense, because there are usually no compelling causes that determine Bill's behavior. Thus, to deal with such cases, one must introduce a third truth value, which can be assigned the property »unknown« or the property »not yet« (cf. the arrows in my diagram [**|**]), which a proposition A about future things takes on precisely when there are no compelling causes for A or not-A to occur.
A roughly similar argument is already found in Aristotle (the famous example of tomorrow's sea battle). ** **
Classical logic includes only propositional logic and predicate logic, in which the principles of forbidden contradiction (principium contradictionis) and excluded third party (principium exclusi tertii) and, related to them, the bivalence principle (see my earlier posts) are valid.
Non-classical logics are those in which at least one of the principles of classical logic is not valid. Particularly important are those systems in which the principle of the excluded third or the bivalence principle is invalid. Such logics were developed because they were motivated by developments in mathematics (cf. for example my earlier posts about antinomy).
Non-classical logics include e.g.:
- Multivalued logic (generic term for all other logics in which the bivalence principle is not valid).
- Modal logic (also: Alethian logic).
- Intuitionistic logic.
- Dialogic logic.
- Temporal logic.
- Deontic logic.
- Conditional propositional logic.
- Doxastic logic.
- Epistemic logic.
- Relevance logic.
- Non-monotonic logic.
- Fuzzy logic. ** **
Fuzzy logicians say that most concepts are factually fuzzy in the sense that they can apply to different objects to different degrees. The fuzzy logicians are right. Whether or not a particular term applies to an object is often not a matter of a simple yes or no, but often a matter of degree. In fuzzy logic, one specifies the degree to which a term applies to a particular object by a number from the continuum between 0 and 1: If an object does not fall under a certain term at all, the term in degree 0 applies to it; if it falls completely under it, the term in degree1 applies to it; and if it falls only more or less under it, the term in degree g with 0<g<1 applies to it. For a term one has to specify a function which determines under which circumstances it applies to an object and in which degree. (This function determines a fuzzy set.) For example, one can specify that the predicate »x is a tall man« applies to men up to 1.60m in degree 0, to men from 1.90m in degree 1, and to men between 1.60m and 1.90m in certain (with height increasing) degrees between 0 and 1; a 1.75m tall man may be tall in degree 0.5, for example.
Since the 1980s, fuzzy logic has increasingly found its way into technical applications under the keyword »fuzzy control«, especially where exact mathematical calculations of the processes to be controlled are complicated, lengthy or hardly possible due to the many and unmanageable influencing variables. In this case, precise measured variables are first translated into fuzzy terms such as »quite fast«, »quite close to the target», etc. (»fuzzification« is the word for this), which then form the basis for simple rules that are easily accessible to human intuition: »If the car is quite fast and quite close to the target, then brake quite hard«. The »outputs« of these rules are then transformed back into precise control instructions according to specific procedures. This procedure allows control on an »intuitive« basis without the availability of an exact mathematical model of the process to be controlled. Fuzzy control has found its way, for example, into the control of video cameras, washing machines, elevators and even subways. ** **
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I have already read through the book. ** **
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Or a question! A good philosopher should be a good questioner.
One could proceed in such a way that opening posts that do not contain arguments or questions are moved to the non-philosophical chat subforum. In case of repetition, a warning or ban will be issued. ** **
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The best-selling philosophy book of the 20th century. ** **
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