Speakpigeon
Contributor
- Joined
- Feb 4, 2009
- Messages
- 6,317
- Location
- Paris, France, EU
- Basic Beliefs
- Rationality (i.e. facts + logic), Scepticism (not just about God but also everything beyond my subjective experience)
I'm going to have a bit more time to invest on fundamental research on logic. I think some of you here have real expertise on the subject to share.
I'm only really interested in the kind of logic that normally intelligent human beings seem to be able to apply, or use, intuitively, what I would call our "logical sense", or "sense of logic", something I believe we have without having first to think about it in any formal way. If you disagree with that, please explain.
So, if you know of any theory of that kind of logic, beyond the one proposed initially by Gottlob Frege and Bertrand Russell, that you happen to like and value, I'd like to hear any reasons you may have for that.
And, additionally, I'm just curious to see how many people around here will be interested!
EB
So, eventually, I guess I have to admit this one didn't elicit much interest!
So, I'll try a different angle. Here it is:
What would you say is the usefulness of the system of formal logic proposed initially by Gottlob Frege and Bertrand Russell, and later developed in the 20th century to become the de facto standard system of classical logic?
EB
________________________
It may help to have a few of the relevant terms and characters pinned down here.
Logicians
Ludwig Wittgenstein
The early Wittgenstein was concerned with the logical relationship between propositions and the world and believed that by providing an account of the logic underlying this relationship, he had solved all philosophical problems.
The later Wittgenstein rejected many of the assumptions of the Tractatus, arguing that the meaning of words is best understood as their use within a given language-game.
Gottlob Frege
(Biography). 1848–1925, German logician and philosopher, who laid the foundations of modern formal logic and semantics in his Begriffsschrift (1879)
Bertrand Russell
1872-1970. British philosopher, mathematician, social critic and writer who had a profound influence on the development of symbolic logic <snip>
Terminology
logic)
n.
1. The study of principles of reasoning, especially of the structure of propositions as distinguished from their content, and of method and validity in deductive reasoning.
2. a. A system of reasoning: Aristotle's logic.
3. any particular formal system in which are defined axioms and rules of inference.
deduction
n.
4. Logic
a. The process of reasoning in which a conclusion follows necessarily from the stated premises; inference by reasoning from the general to the specific.
formal system
n
(Logic) an uninterpreted symbolic system whose syntax is precisely defined, and on which a relation of deducibility is defined in purely syntactic terms. Also called: formal theory or formal calculus
formal logic
n
1. (Logic) Also called: symbolic logic the study of systems of deductive argument in which symbols are used to represent precisely defined categories of expressions. Compare philosophical logic
2. (Logic) a specific formal system that can be interpreted as representing a fragment of natural argument
philosophical logic
n
(Logic) the branch of philosophy that studies the relationship between formal logic and ordinary language, esp the extent to which the former can be held accurately to represent the latter
The three laws of logic
The three laws of logic
The law of non-contradiction, along with its complement, the law of excluded middle (the third of the three classic laws of thought), are correlates of the law of identity (the first of the three laws). Because the law of identity partitions its logical Universe into exactly two parts, it creates a dichotomy wherein the two parts are "mutually exclusive" and "jointly exhaustive". The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle, an expression of its jointly exhaustive aspect.
1. The law of identity
In logic, the law of identity is the first of the three classical laws of thought. It states that "each thing is the same with itself and different from another". By this it is meant that each thing (be it a universal or a particular) is composed of its own unique set of characteristic qualities or features, which the ancient Greeks called its essence. Consequently, things that have the same essence are the same thing, while things that have different essences are different things.
In its symbolic representation, "A is A", the first element of the proposition represents the subject (thing) and the second element represents the predicate (its essence), with the copula "is" signifying the relation of "identity".
Further, since a definition is an expression of the essence of that thing with which the linguistic term is associated, it follows that it is through its definition that the identity of a thing is established. For example, in the definitive proposition: "A lawyer is a person qualified and authorized to practice law", the subject (lawyer) and the predicate (person qualified and authorized to practice law) are declared to be one and the same thing (identical). Consequently, the Law of Identity prohibits us from rightfully calling anything other than "a person qualified and authorized to practice law" a "lawyer".
2. The law of non-contradiction
In classical logic, the law of non-contradiction (LNC) (or the law of contradiction (PM) or the principle of non-contradiction (PNC), or the principle of contradiction) is the second of the three classic laws of thought. It states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive.
3. The law of excluded middle
For any proposition, either that proposition is true, or its negation is true.
The law of excluded middle (or the principle of excluded middle) is the third of the three classic laws of thought.
The earliest known formulation is in Aristotle's discussion of the principle of non-contradiction, first proposed in On Interpretation, where he says that of two contradictory propositions (i.e. where one proposition is the negation of the other) one must be true, and the other false. He also states it as a principle in the Metaphysics book 3, saying that it is necessary in every case to affirm or deny, and that it is impossible that there should be anything between the two parts of a contradiction.