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tgt
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How is this definition ( I made up):
Logic is the deductive (as opposed to empirical) science of all possible worlds.
Logic is the deductive (as opposed to empirical) science of all possible worlds.
tgt said:How is this definition ( I made up):
Logic is the deductive (as opposed to empirical) science of all possible worlds.
Dragonfall said:That definition is pretty murky.
SW VandeCarr said:How about checking out some real definitions instead making things up?:
"The analysis, without regard to meaning or context, of the patterns of reasoning by which conclusions are validly derived from sets of premises."
Borowski and Borwein, Harper Collins Dictionary of Mathematics (1991).
There are other more specific definitions citing axioms and rules of inference, all of them considerably better than yours
tgt said:Well, just say logic wasn't invented then I'd probably be interested to investigate (create) a field that has the definition that I gave. It's a first definition which usually is intuitive.
SW VandeCarr said:Well, your definition describes aspects of the current state of theoretical physics. I suggest you investigate the Many Worlds interpretation of quantum mechanics.
HallsofIvy said:What is your definition of "science". In the usual definition, "a study that follows the scientific method", logic is not a science at all because it does not involve experimentation on the real world.
tgt said:From a modern view point, the terminologies have all been mixed up. But pretend it's 400BC before anything that resemble logic has been thought up of. Back in those days science and maths were closely linked and there wasn't the scientific method.
SW VandeCarr said:So is the pre-Aristotle world your ideal?
SW VandeCarr said:EDIT: By the way, don't you think that mathematics and science are closely linked now?
tgt said:Well, if I was to put myself in that period which is without a lot of any theoretical maths then it would be interesting to work something in the area of the definition in the OP. Just to get some undisputable truth.
SW VandeCarr said:Indisputable truth?? You're winging off into deep metaphysical philosophy now. What makes you think these guys were any closer (to whatever your idea is) than we are now?
EDIT: Would you agree that 2+3=5 at least, is a bit of indisputable truth?
tgt said:Probably indisputable truth in not just mathematics but other areas. That is why my definition has an empirical feel to it even though it shouldn't have anything to do with the world. I was trying to define something that includes more then just maths. It is a bit philosophical which isn't surprising as most philosophers enjoy logic more than maths.
SW VandeCarr said:Are you simply rebelling against rationality as we know it?
tgt said:I've just made a very naive definition with the view point of someone in 400BC would have. Would it be wrong to say that at that time science = maths? But obviously the word science and maths would have had different meanings as well at that time. Certainly the definition of science would be very different to the definition we would have now.
The objection that non-empirical sciences do not exist seemed to be precluded by the OP's qualification "deductive (as opposed to empirical) science". I think a more general definition of a science along the lines of a systematic investigation and description, perhaps with certain requirements concerning, e.g., consistency, precision, or repetition, would be acceptable. Of course, empirical sciences still use deductive reasoning, so the distinction between deductive and empirical sciences could use clarification.HallsofIvy said:What is your definition of "science". In the usual definition, "a study that follows the scientific method", logic is not a science at all because it does not involve experimentation on the real world.
SW VandeCarr said:You just contradicted yourself again. The great thinkers of ancient Greece were not naive. They were brilliant. They just didn't have the level of knowledge (or the technology) we have. Earlier you indicated they would be closer to "indisputable truths" than we are.
SW VandeCarr said:I'm still interested in your answer to my direct question to you: Do you consider your reference to "all possible worlds" to be equivalent to "..without regard to meaning or context,..." ?
honestrosewater said:Math seems to include logic more than logic includes math, especially if you only consider the deductive parts of logic.
what count as logical objects or logical ways are not static or precisely predefined.
Would you consider mathematical logic as logic or maths or an independent field? It's considered to be meta maths so it's not maths.
honestrosewater said:What is the purpose of this definition anyway?
For interest sake.
Depends on how I defined them and what criteria I was using to categorize them. I don't know all of the options, so I'm not sure which, if any, I would prefer. Are you attempting a partition? Do you know whether it is possible?tgt said:Would you consider mathematical logic as logic or maths or an independent field? It's considered to be meta maths so it's not maths.
Yeah, it really depends on what you're focusing on. If by "mathematical logic" you mean the study of the kinds of structures found in logic by mathematical means for their own sake (like model theory), then that's a branch of mathematics. Otoh, if we study the structures because they model valid inferences, then we're doing logic.honestrosewater said:Mathematical logic is not considered metamathematics by everyone. This thread has already shown that these things are not agreed upon.
honestrosewater said:Logic does investigate and describe classes of all possible worlds using deductive methods, though I'm not sure this covers everything it does. A possible world is an abstract object. It doesn't have to be interpreted as or modeled by any physical object. I don't see what the problem is.
Same word, different meaning. I have been speaking of logic as a field of study, with subject matter, methodologies, and practitioners. You are talking about mathematical structures. This is much easier to answer because the objects are already well-defined. The only thing to argue about is what to call them. I think a useful way to distinguish logics is by their inference relations: what they allow to follow from what, by derivation or consequence. Different axiomatic systems might be considered different logics. In a narrower context, I have seen a logic defined as the set of all logically true sentences in a (formal) language.SW VandeCarr said:There are a number of logics for a number of 'worlds'.
What very general logic? It should be definable in what language? If it's not definable, it's not very intelligible.If you mean logic in a very general way, I agree (maybe). But just what is this very general logic? I believe the definition I quoted in post 3 of this thread is as good as any. It seems that this very general logic should be definable, otherwise it's not..well, very logical is it?
OK. Your saying that logic is a discipline, not unlike mathematics or perhaps even medicine or law. I see a problem in that its subject matter is logic (ie it's a category of itself). In math you have somewhat distinct but related kinds of subject matter: arithmetic, algebra, analysis, geometry, etc each with their special identifying features. In law you have constitutional law, tort law, criminal law, etc. In medicine there are the broad classes of diagnostics, surgery and therapeutics further broken down into numerous specialties and sub-specialties. Logic as a discipline, as far I know, has only itself as the subject matter and I argue again that the definition I quoted is quite adequate in defining that subject matter. (I have no vested interest in the definition. I didn't create it.)honestrosewater said:Same word, different meaning. I have been speaking of logic as a field of study, with subject matter, methodologies, and practitioners.
Logic _is_ a discipline. I don't have to say so. The real world says so.SW VandeCarr said:OK. Your saying that logic is a discipline, not unlike mathematics or perhaps even medicine or law.
Why? Calling a discipline and its subject matter by the same name is precisely the norm. Do you also have a problem with logic being studied by logicians?I see a problem in that its subject matter is logic (ie it's a category of itself).
First, you can split up logic in the same way that you split up the other disciplines. Second, what does it matter? You have just moved the problem that you have with disciplines to subdisciplines. The subject matter of geometry is geometry -- and it is studied by geometers. The subject matter of Euclidean geometry is Euclidean geometry.In math you have somewhat distinct but related kinds of subject matter: arithmetic, algebra, analysis, geometry, etc each with their special identifying features. In law you have constitutional law, tort law, criminal law, etc. In medicine there are the broad classes of diagnostics, surgery and therapeutics further broken down into numerous specialties and sub-specialties. Logic as a discipline, as far I know, has only itself as the subject matter
What you just did is stating more than arguing. You have given no justifications for why the definition is adequate.and I argue again that the definition I quoted is quite adequate in defining that subject matter. (I have no vested interest in the definition. I didn't create it.)
Says who? Give me one example of a discipline whose subject matter is always well-defined. The whole purpose of studying something is to develop new knowledge about it, to make progress, i.e., to _change_ it. The subject matter of disciplines changes.EDIT: This may seem pedantic, but disciplines are defined in terms of their subject matter. So if logic is the subject matter of logic the discipline, then logic the subject matter should be defined.
?it's difficult to define mathematics as a whole. Russell and Whitehead tried and failed.
Says who?Mathematics is mostly defined in terms of its major branches of subject matter:
How?(geometry can be incorporated into algebra).
No, the subject matter of logic is (valid) inference.SW VandeCarr said:OK. Your saying that logic is a discipline, not unlike mathematics or perhaps even medicine or law. I see a problem in that its subject matter is logic (ie it's a category of itself).
honestrosewater said:Logic _is_ a discipline. I don't have to say so. The real world says so.
Why? Calling a discipline and its subject matter by the same name is precisely the norm. Do you also have a problem with logic being studied by logicians?
First, you can split up logic in the same way that you split up the other disciplines.
Second, what does it matter? You have just moved the problem that you have with disciplines to subdisciplines. The subject matter of geometry is geometry -- and it is studied by geometers. The subject matter of Euclidean geometry is Euclidean geometry.
What you just did is stating more than arguing. You have given no justifications for why the definition is adequate.
Says who? Give me one example of a discipline whose subject matter is always well-defined. The whole purpose of studying something is to develop new knowledge about it, to make progress, i.e., to _change_ it. The subject matter of disciplines changes.
?
Says who?
How?
Preno said:No, the subject matter of logic is (valid) inference.
Logic is the science of reasoning and argumentation. It is a deductive system that studies the principles of valid reasoning and allows us to make logical conclusions based on given premises.
Logic is a fundamental part of science, as it helps us to construct arguments and draw conclusions based on evidence and observations. It is used in various fields of science, from mathematics to philosophy, to ensure that our reasoning is valid and sound.
Possible worlds refer to hypothetical scenarios or situations that may or may not exist in reality. In logic, possible worlds are used to explore all possible outcomes and scenarios to determine the validity of an argument or statement.
Deductive reasoning is a method of logical thinking that uses general principles or rules to draw specific conclusions. In logic, deductive reasoning is used to determine the validity of an argument or statement by examining the relationship between the premises and the conclusion.
Yes, logic can be applied to everyday life in various ways. It can help us to make better decisions, evaluate arguments and claims, and solve problems by using sound and valid reasoning. It can also improve our critical thinking skills and help us to avoid fallacies in our thinking.