![There are many different dimensions that define "a logic". Some key ones:
Propositional vs predicate. Propositions are bare logical terms: in "if P then Q", P and Q
are propositions. Predicates are more general, e.g. in "if father(X,Y) then parent(X,Y)",
"father" and "parent" are predicates, and X and Y are variables.
Order. In first-order logic, the variables can't denote predicates. In second-order logic,
the variables can denote predicates, so the logic can talk about itself more easily. There
are higher orders beyond that.
Modes. Ordinary predicate and propositional logic cover "existence" and "universality"
(really, flip sides of the same coin), but other modes can cover things like "Jo believes
that..." or "It is possible [or necessary] that..." or other variants.
Time: temporal logics are another kind of modal logic
Probability
Ternary and other multi-valued logics
Negation. There are many different interpretations of the proposition "not x": first order,
negation-as-failure, paraconsistency, well-founded semantics, etc.](https://image.slidesharecdn.com/logicistheprocessofusingargumentstoarriveatthetruthorfalsityofaparticularconclusion-150127045416-conversion-gate02/85/Logic-is-the-process-of-using-arguments-to-arrive-at-the-truth-or-falsity-of-a-particular-conclusion-3-320.jpg)
Logic is the process of using arguments to arrive at the truth or falsity of a particular conclusion
- 1. 1 Logic isthe processof usingargumentstoarrive at the truth or falsityof a particularconclusion, throughreasoning.The reasoningprocessusediseithergoodorfaulty,resultinginsuccessful(validand sound) or unsuccessful(unsound) arguments.Logicisoftenusedwithinthe discipline of philosophy,but isalso seenwithinthe fieldsof science,politics,andlaw.Continuereadingbelow tofindoutmore about the definitionof logic,particulartypesof logic,andimportantusesof logic. 2 Deductive Versus Inductive Reasoning Deductive reasoning is most often seen within formal logic. It occurs when an argument uses a general rule to argue for a specific instance. For example, "Every human being will die at some point. Fred is a human being. Therefore, he will die at some point." Deductive arguments are able to be evaluated for validity and soundness. If there is no instance able to be imagined in which the conclusion is false while the premises are true, the argument is valid. For example, if there is no way to imagine Fred not dying at some point, if he is a human being, and all humans do, in fact, die at some point. A deductive argument is sound if it is valid and the content of its premises are true. Inductive arguments, which are often used in informal logic, use specific instances to argue for the adoption of general rules. For example, "I have only seen white birds since I moved to Toronto six months ago. Therefore, it is likely that all birds in Toronto are white." These arguments are not as definite as deductive arguments, and are unable to be defined as completely valid or sound; only the likelihood of validity or soundness is able to be suggested. For example, there is a good chance the conclusion of the above argument is true, but there might be a black, blue, or red bird somewhere in Toronto that the arguer has not viewed. People use both accurate and faulty forms of reasoning every day without thinking about them. However, once you understand the definition of logic, you will be able to consciously make your arguments more logical. Unless you are working as a professional logician, mathematician, or scientist (as science often employs formal mathematics), you will likely be making use of informal, inductive logic more than formal, deductive logic. In order to make the conclusions you come to using inductive reasoning more likely to be valid, make sure you base your general conclusions on many specific examples observed over a long period of time, not just a few examples observed over a short period of time. 3 Formal VersusInformal Logic Formal logic is the type of logic most frequently employed by philosophers and logicians. It is more concerned with the form of an argument than the argument's content. Arguments within formal logic use rules such as those espoused by Aristotle (described above), and they are divided into one or more premises and a conclusion. They often appear in symbolic form, such as, "If A, then B. If B, then C. Therefore, if A, then C." The logical progression of this argument is more important than what A, B, and C actually represent. Informal logic, while concerned somewhat with form, is more concerned with content. This type of logic is often found within politics, law, and journalism, and arguments using informal logic are written using common language, not symbols. Logicians who study informal logic evaluate the verbal arguments used, and attempt to come up with ways to improve them.
- 2. What are the Fundamental Principles ofLogic? The task of logic is to study the principles underlying the validity deductive arguments and the strength of inductive arguments. Since not all deductive argument are valid, we need to know the principles that ensures a valid argument to be valid and in valid argument to be invalid. It has been suggested that the arguments that satisfy or conform to the laws or principles of logic are valid and arguments that do not do so are invalid. In other won validity amounts to not violating any law of logic. Logic deals with these principles and also we their interrelation. Out of the various laws of logic there exists three fundamental principle namely, (I) the law of identity, (ii) the law of contradiction (or the law of non-contradiction) are the law of excluded middle. These are known as the laws of thought or fundamental principles logic. In calling these as laws of thought, there is a danger of interpreting them as psychological laws concerning mental processes of thinking. This would be a misunderstanding of their true nature. These are not descriptive laws. They do not tell us how people think. Rather these are prescriptive in nature. They tell us how one should think or, more precisely, how one should reason. So instead of calling them laws of thought, it is better to call them principles of logic. These three laws are considered as fundamental or basic in the sense that any correct or good argument must conform to these laws. This means that these laws are presuppositions of a good argument. What are the fundamental laws of logic? Answer1. Law of Identity 2. Law of contradicting 3. Law of the excludedmiddle 4. Law of SufficientGround A. Law of conservationof mass- mass isneithercreatednordestroyedduringanordinarychemical reactionor physical reaction. B. Law of definite porportions- achemical compoundcontainsthe same elemtentsinexactly the same proportionsbymassregardlessof the sample of the source of the compound. C. Law ofmultiple proportions- if twoor more differentcompoundsare composedof the same twoelements,thenthe ratiosof the massesof the secondelement,combinedwithacertain mass of the firstelementisalwaysaratioof small whole numbers
- 3. There are many different dimensions that define "a logic". Some key ones: Propositional vs predicate. Propositions are bare logical terms: in "if P then Q", P and Q are propositions. Predicates are more general, e.g. in "if father(X,Y) then parent(X,Y)", "father" and "parent" are predicates, and X and Y are variables. Order. In first-order logic, the variables can't denote predicates. In second-order logic, the variables can denote predicates, so the logic can talk about itself more easily. There are higher orders beyond that. Modes. Ordinary predicate and propositional logic cover "existence" and "universality" (really, flip sides of the same coin), but other modes can cover things like "Jo believes that..." or "It is possible [or necessary] that..." or other variants. Time: temporal logics are another kind of modal logic Probability Ternary and other multi-valued logics Negation. There are many different interpretations of the proposition "not x": first order, negation-as-failure, paraconsistency, well-founded semantics, etc.