{ localUrl: '../page/modus_tollens.html', arbitalUrl: 'https://arbital.com/p/modus_tollens', rawJsonUrl: '../raw/2vr.json', likeableId: '1784', likeableType: 'page', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], pageId: 'modus_tollens', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'wiki', title: 'Modus tollens', clickbait: 'Deriving a negation from another negation', textLength: '471', alias: 'modus_tollens', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'JeremyPerret', editCreatedAt: '2016-03-26 21:36:37', pageCreatorId: 'JeremyPerret', pageCreatedAt: '2016-03-26 21:36:37', seeDomainId: '0', editDomainId: 'AlexeiGigster', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '29', text: 'We also can work with negations to create a valid argument:\n\n> $ \\begin{array}{l}\n\\text{If Socrates is a fish, then Socrates can live underwater.} \\\\\n\\text{Socrates cannot live underwater.} \\\\\\hline\n\\text{Therefore, Socrates is not a fish.} \n\\end{array} $\n\nAlso known as *law of contrapositive* or *denying the consequent*, modus tollens works by reversing modus ponens. Formally,\n\n> $ \\begin{array}{l}\nA \\rightarrow B \\\\\n\\neg B \\\\\\hline\n\\therefore \\neg A\n\\end{array} $', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '1', maintainerCount: '1', userSubscriberCount: '0', lastVisit: '', hasDraft: 'false', votes: [], voteSummary: [ '0', '0', '0', '0', '0', '0', '0', '0', '0', '0' ], muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'false', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, proposeEdit: { has: 'true', reason: '' }, delete: { has: 'false', reason: 'You don't have domain permission to delete this page' }, comment: { has: 'false', reason: 'You can't comment in this domain because you are not a member' }, proposeComment: { has: 'true', reason: '' } }, summaries: { Summary: 'We also can work with negations to create a valid argument:' }, creatorIds: [ 'JeremyPerret' ], childIds: [], parentIds: [ 'logic' ], commentIds: [], questionIds: [], tagIds: [ 'work_in_progress_meta_tag' ], relatedIds: [], markIds: [], explanations: [], learnMore: [ { id: '2717', parentId: 'modus_tollens', childId: 'modus_tollens', type: 'subject', creatorId: 'AlexeiAndreev', createdAt: '2016-06-17 21:58:56', level: '1', isStrong: 'false', everPublished: 'true' } ], requirements: [ { id: '2715', parentId: 'logical_negation', childId: 'modus_tollens', type: 'requirement', creatorId: 'AlexeiAndreev', createdAt: '2016-06-17 21:58:56', level: '1', isStrong: 'false', everPublished: 'true' }, { id: '2716', parentId: 'arguments', childId: 'modus_tollens', type: 'requirement', creatorId: 'AlexeiAndreev', createdAt: '2016-06-17 21:58:56', level: '1', isStrong: 'false', everPublished: 'true' } ], subjects: [ { id: '2717', parentId: 'modus_tollens', childId: 'modus_tollens', type: 'subject', creatorId: 'AlexeiAndreev', createdAt: '2016-06-17 21:58:56', level: '1', isStrong: 'false', everPublished: 'true' } ], lenses: [], lensParentId: '', pathPages: [], learnMoreTaughtMap: {}, learnMoreCoveredMap: {}, learnMoreRequiredMap: {}, editHistory: {}, domainSubmissions: {}, answers: [], answerCount: '0', commentCount: '0', newCommentCount: '0', linkedMarkCount: '0', changeLogs: [ { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '9090', pageId: 'modus_tollens', userId: 'JeremyPerret', edit: '1', type: 'newEdit', createdAt: '2016-03-26 21:36:37', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }