“Since reasoning , or inference, the principal subject of logic, is an operation which usually takes place by means of words , and in complicated cases can take place in no other way: those who have not a thorough insight into both the signification and purpose of words, will be under chances, amounting almost to certainty, of reasoning or inferring incorrectly.” WayMeanPurposeChanceCasesSubjectsLogicInsightComplicatedCertaintyOperationsReasoningPrincipalThoroughInference Book:A System Of Logic, Ratiocinative And Inductive: Mill's Works Source: A System Of Logic, Ratiocinative And Inductive: Mill's Works
“Reading a book should be a conversation between you and the author. Presumably he knows more about the subject than you do; if not, you probably should not be bothering with his book. But understanding is a two-way operation; the learner has to question himself and question the teacher, once he understands what the teacher is saying. Marking a book is literally an expression of your differences or your agreements with the author. It is the highest respect you can pay him.” IfsKnowsWayShouldTwoBookReadingUnderstandingDifferencesPayTeacherSubjectsExpressionConversationHighestBotherOperationsAgreementTwo WaysLearners Author:Mortimer Adler
“In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.” CoursesSpaceResultsNumbersSubjectsParticularInvolvedRelationMathematicsOperationsAbstractConsiderationPeculiar Author:Ada Lovelace
“It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe.” KindMayMeanTwoUniverseProcessSubjectsRelationDefinitionsOperationsMutualDesirable Author:Ada Lovelace
“It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.” ShouldHumansWellsProcessBrainStudyClearSubjectsIndependentFundamentalsConnectedMediumsDefinedMathematicalOperationsAnalysisReasoningBranchesIngredientsEnginesMechanismHuman Brain Author:Ada Lovelace
“But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.” MayValuesProcessSubjectsLogicMathematicsOperationsAbstractReasoningPeculiar Author:Ada Lovelace
“The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.” NumbersSubjectsOperationsAbstractPeculiarEngines Author:Ada Lovelace