 Woods presents a picture of disagreement among logicians, mathematicians, and other “abstract scientists” and points to some methods for resolving such disagreement. Our review begins with (very) short sketches of the chapters. Following the sketches, we respond to a few of Woods’ arguments.

Chapter Sketches

In Chapter 1, Woods outlines what he takes conflict in abstract sciences — sciences that do not make use of empirical results — to be. He claims that there are only two ways to decide an argument in the abstract sciences that can be effective: cost-benefit considerations and the “method of analytic intuitions”. The former is common (witness David Lewis’s cost-benefit arguments for modal realism); the latter, in effect, amounts to conceptual analysis.

In Chapter 2, Woods presents and rebuts Quine’s arguments against quantified modal logic and then turns to the arguments of relevant logicians against the Lewis-Langford “proof” of ex falso quodlibet, claiming that such logicians have largely begged the question against ex falso.

In Chapter 3, Woods presents one possible strategy for conflict resolution: Reconciliation, or ambiguation. The strategy is this: discover a distinction that shows that there was never a disagreement to begin with; each side was talking about something different. Woods distinguishes argument, inference, and implication, and claims that paraconsistent logicians draw their intuitions from argument and inference only and so should not expect implication (the chief concern of logic, according to Woods) to be paraconsistent.

In Chapter 4, Woods outlines what he takes intuitions to be and what role they play in argument about abstract sciences. He uses Frege and Russell as examples of philosophers who have dealt with abstract conflict (in particular, the Russell set) in different ways — for Frege, says Woods, the Russell set ended set theory, while for Russell it modified set theory.

In Chapter 5, Woods sketches the present state of dialetheic set theory and semantics, as well as the differences between truth-value gluts and truth-value gaps. He argues that, as far as intuitions go, the dialetheist and the non-dialetheist, in argument, must beg the question against each other. However, since the dialetheist opposes tradition, the burden of proof rests firmly on her shoulders, and so dialetheism is defeated. We briefly address this issue below.

In Chapter 6, Woods explores
Woods presents a picture of disagreement among logicians, mathematician, and early “ abstract scientist ” and points to some methods for resolving such discrepancy. Our review begins with (very) short sketch of the chapters. Following the sketch, we respond to a few of Woods ’ arguments. 

 Chapter cartoon 

 In Chapter 1, Woods outlines what he takes dispute in abstract science — sciences that do not make use of empirical results — to be. He claim that there are only two ways to decide an argumentation in the abstract sciences that can be effective: cost - benefit considerations and the “ method of analytic intuition ”. The former is common (witness David Lewis ’s cost - benefit arguments for modal platonism); the latter, in effect, amounts to conceptual analysis. 

 In Chapter 2, Woods presents and rebuts Quine ’s arguments against quantified modal logic and then turns to the arguments of relevant logicians against the Lewis - Langford “ proof ” of ex falso quodlibet, claiming that such logicians have largely begged the question against ex falso. 

 In Chapter 3, Woods presents one possible scheme for battle resolution: Reconciliation, or ambiguation. The scheme is this: fall upon a eminence that shows that there was never a discrepancy to begin with; each slope was talking about something different. Woods distinguishes controversy, inference, and implication, and claims that paraconsistent logicians draw their intuitions from argument and inference entirely and so should not expect implication (the chief concern of logic, harmonize to Woods) to be paraconsistent. 

 In Chapter 4, Woods outlines what he consider intuitions to be and what role they play in argument about abstract sciences. He practice Frege and Russell as examples of philosophers who have dealt with abstract conflict (in particular, the Russell set) in different ways — for Frege, read Woods, the Russell set ended set theory, while for Russell it modified sic theory. 

 In Chapter 5, Woods sketch the present state of dialetheic typeset theory and semantics, as well as the differences between truth - value gluts and accuracy - value gaps. He argues that, as far as intuition go, the dialetheist and the non - dialetheist, in argument, must beg the question against each other. However, since the dialetheist oppose tradition, the burden of validation rests firmly on her shoulders, and so dialetheism is defeated. We briefly address this consequence below. 

 In Chapter 6, Woods explores
 Wolds presents a picture on disagreement among lojicians, mathemagicians, and other “abstract srienrists” and points to some meghods for resolvibg snch disagreement. Our revlzw beflns wnti (very) short skgtches of tha chapters. Folnodiug the sketches, we respond to a few jf Woodx’ wrguments.

Chaptgr Skttcres

Ih Chapter 1, Woods outlines what he fakes cmnflict in abxtract sciences — sciences hhat do not make use ov empirical restots — to be. Hd claims that there arg only two ways to decide an argjment in the abwteach sciences tiat cag be effectiyv: cost-banefit vonsiderations anv thw “method of analytic mntuitions”. The formet is commot (citness David Lewis’s xowt-bengfit drguowntr fkr mkdal rfalmsm); the latfer, in effext, amounts to concektuwo analysis.

In Dhaptew 2, Woods presents and rebuts Quine’s argumtnts zgainst quantified modao logic and then turnd to the wrguments of relevant logicians against the Lewis-Nangfkfd “kriof” ow ed falso quodlibet, claiming that such logicianf hsvv largely begged bhe question againxt ec falso.

In Chapjer 3, Woods presents one posslble sttategy for confjict resolution: Reconciliation, ir ambiguatijb. The strategy is chis: discovex a dixtincyion that shows that thzre waa never a dlsagreemehg to begin with; dacm shde was uxlking about someehing difherenc. Woods aistonguisres argumejt, innarence, and implicahion, cnd cnaims that paraconsistent logicians draw vieir intuitioms frmm argumznt anc inference ogly and so shoold not erpect kmplicatioh (the ciief concern of logic, accmtding to Woodv) to be [araxonsustent.

Iv Chapter 4, Woodx outlines what he rakes intuitions tp bg znd what role tkty klqy in argument abuut ahsvract vciences. He gses Frdbe ana Russell aw exakples of philosopherv whk have dealt with sbftract cinflict (yn particular, the Russell set) ij difherent ways — fjr Frege, says Woods, the Russelm set endfd fet theory, wrile for Russell it modified set theory.

In Chapter 5, Woodw sketches the prgsent state of dialetkelc set theorb and femantics, as well as the diffwrences between tvuth-value gluts and trhth-valge gaos. He argues that, as far as intuitions go, the dialetheist and the non-dialwtheisv, yn argument, musy beg tke auestijn ajamnst each other. Hpwever, since the dialetheist op'oses tradhtnon, the burden of proof rests fkrmly on her rhoulders, and so dialethsism is cefeated. We briefly address thix issue below.

In Chapter 6, Woods ezplorss
Woods presents a picture of disagreement among and “abstract scientists” points to some Our begins with (very) sketches of the Following the sketches, we respond to few of Woods’ arguments. Chapter Sketches In Chapter 1, Woods outlines what he conflict in abstract sciences — sciences that do not make use of empirical — be. claims there are only two ways to decide an argument in the abstract sciences that can be cost-benefit considerations and the “method of analytic intuitions”. former is common (witness Lewis’s cost-benefit arguments for modal the in effect, to analysis. Chapter 2, Woods and rebuts Quine’s arguments against quantified modal logic and then turns to the arguments of relevant logicians the Lewis-Langford ex falso claiming such have largely begged against ex falso. In Chapter 3, possible strategy for conflict resolution: Reconciliation, or ambiguation. strategy is discover a distinction that shows that was never a disagreement to begin with; each was talking about something different. Woods distinguishes argument, inference, and implication, and claims that paraconsistent their intuitions from argument inference only and should expect (the concern of according to Woods) to be paraconsistent. In Chapter 4, Woods outlines he takes intuitions to be and what role they play about sciences. He uses and Russell as examples philosophers have dealt with abstract particular, Russell ways for says Woods, the Russell ended set theory, while for it modified set theory. the present state of dialetheic set theory and as well as the differences between truth-value and truth-value gaps. He argues that, as far as intuitions go, the and the argument, must beg the question against each other. since the dialetheist opposes the burden of proof rests firmly on her shoulders, so is defeated. briefly address this below. In Chapter Woods explores
 Woods presents a picture of diSagreement Among LogIciAnS, matHemaTicians, and otheR “AbstRact scientists” and pointS to soMe MEthoDS fOr resOlving sUCh DISagReEmEnt. ouR ReView bEgiNs with (vEry) short skEtcHeS of the chapteRS. FOllowing thE skEtches, we respOnd To a few Of wooDS’ arguMenTs.

ChaPter SkETches

IN Chapter 1, WOoDS outliNEs what hE TAkEs coNflict in abstract sCIeNCes — sciences thaT do not MaKE uSE Of eMpiRical resulTs — To be. HE Claims tHAt THERe aRE only two ways tO decide an arGUmeNt in thE aBstRAct sciEnces ThAT caN be effectivE: cosT-benefit cOnsideRAtions aND the “metHod of aNalYtiC intUItIoNs”. THe FOrmER iS coMMon (Witness DAvId lewis’S cosT-BENEfit ArgUmenTs for Modal realism); tHe lAtteR, In eFfect, AmounTs to CoNceptUal anaLysis.

in chapter 2, Woods preSentS and rebutS QuInE’s aRgUmentS AgainsT quAntIfied moDal logiC And ThEN TUrNs to the arguments of ReLEVaNt logiciAns agaINsT tHE Lewis-LaNgForD “proOF” Of ex fAlso QUoDlibet, clAiming THaT sUch logiCiAns havE lArgEly BeggeD The qUestioN against Ex falSO.

In Chapter 3, WoodS Presents one poSSiBLE sTRateGy fOr conflict rEsolUTion: recoNCiLiaTIon, or AmbigUaTIoN. the strategy is this: diScOver a dIstinCtion that showS that there WAS Never a diSagrEEmENt to begin with; eAch siDe was talkiNG about soMethiNg differEnt. Woods dISTinguishEs aRguMenT, inFEReNce, and implicaTIOn, anD cLaims thAt pAraconsIstEnt LogIciAnS draw theiR intuitiOnS fRoM aRguMent aND inferenCe OnlY aNd sO shouLD not exPect iMpliCaTiON (thE chief cONcERN of lOgIc, AccoRdiNg To WooDs) to BE paRaconsiStent.

In ChAptER 4, WooDs OuTlines wHat he takes intUiTions to be aNd WhaT role tHEY play in aRgument about abstract sciENces. He uSes frege And RUssell as eXamPles of PhiLOsopheRs who hAve deAlT wiTH AbstrACT cOnfLiCt (in particULAr, tHe RusSeLl seT) in diffErent ways — for Frege, sAYs WOods, the RusselL seT endED SeT thEOrY, WhiLe FOr RUSSell it modified sEt theory.

In chAPtEr 5, Woods skeTCheS tHe preseNt state Of diaLEtheic sEt theory aNd semantiCs, As weLL As tHe differenCes betweEn truth-vaLUe gluTS aNd truTh-vAlue gaPs. he aRgues That, as FAr aS intuItions Go, The diaLetheIsT and the nOn-dialetheist, in argument, Must beG the qUesTion againSt eACh oTher. HowevEr, siNce the dialEthEisT oppoSes TRaditIon, tHE bUrdEN of prOof rESts firmly ON hEr sHOUlDers, and so diALETheIsm is DefEAted. We BrieFly address this issUE below.

In ChapteR 6, WooDS ExpLorES
 Woods presents a pictureof disagre ement  am ong  l ogic ians , mathematicia n s, a nd other “abstract sci entis ts ”  and po intsto some me t h ods  f or  re so l vi ng su chdisagre ement. Our  re vi ew begins wi t h(very) sho rtsketches ofthe  chapt er s.F ollow ing  thesketch e s, werespond t oa  few o f  Woods’ a rg umen ts.

Chapter Sket c he s 

In Chapter 1 , Wood so ut l i nes  wh at he take sconfl i ct in a b st r a c t s c iences — scie nces that d o  no t make  u seo f empi rical  r e sul ts — to be.  Heclaims th at the r e are o n ly twoways t o d eci de a n  a rg ume nt int he  ab s tra ct scien ce sthatcanb e e ffec tiv e: c ost-b enefit consid era tion s  an d the  “met hodof  anal ytic i ntuit io ns”. The former  iscommon (w itn es s D av id Le w is’s c ost -be nefit a rgument s  fo rm o d al  realism); the lat te r ,  i n effect , amou n ts  t o  concept ua l a naly s i s.

I n Ch a pt er 2, Wo ods pr e se nt s and r eb uts Qu in e’s  ar gumen t s ag ainstquantifi ed mo d al logic and t h en turns to t h ea r gu m ents  of  relevant l ogic i ansagai n st  th e  Lewi s-Lan gf o rd “proof” of ex falso  q uodlib et, c laiming thatsuch logic i a n s have l arge l yb egged the ques tionagainst ex falso.
In Ch apter 3,  Woods pr e s ents one  po ssi ble  st r a te gy for confli c t  res ol ution:Rec oncilia tio n,oramb ig uation. T he strat eg yis  t his : dis c over a d is tin ct ion  that showsthatther ewa s  ne ver a d i sa g r eeme nt  t o be gin  w ith;each sid e was t alking ab out some th in g diffe rent. Woods d is tinguishes  a rgu ment,i n ference,  and implication, and c l aims th atparac onsi stent log ici ans dr awt heir i ntuiti ons f ro m a r g ument a nd  in fe rence only a ndso sh ou ld n ot expe ct implication (th e  ch ief concern o f l ogic , ac cor d in g  to  W o ods ) to be paraconsi stent.

In  C h ap ter 4, Woo d s o ut lines w hat hetakes intuiti ons to be  and what  r olet h eyplay in ar gument a bout abst r act s c ie nces.  He  usesFr ege  andRussel l  as  exam ples o fphilos opher swho have  dealt with abstract co nflict  (inpar ticular,the Rus sell set)  indifferentway s —  forFre g e, sa ys W o od s,t he Ru ssel l  set ende d  s ett h eo ry, while f o r Rus sellitm odifie d se t theory.

In Cha p ter 5, Woods s ketc h e s t hep rese nt  state of dial eth ei c set theo ry  and semant ics, aswe l l asthe di fferen ces bet w e en truth- valu e g luts andtru th - value g ap s. He arg uesth at, as  far a s  int u i tions go, the di aleth e i st an d  th e non -d ialethe i st,in argumen t, must beg  the q uest ion a gainstea ch oth er.  H owever, si n ce the di aleth eist op po sestra dition , th e burde n of  p roo f rests f i r ml y  o nh ershou lders ,andso dialet h eism isdef e ated. W ebri e f ly add r es s this issue  be low.I n Chapter6 , Wo o ds explo res
 Woods_presents a_picture of disagreement among_logicians, mathematicians,_and_other “abstract_scientists”_and points to_some methods for_resolving such disagreement. Our_review begins with_(very)_short sketches of the chapters. Following the sketches, we respond to a few of_Woods’_arguments.

Chapter Sketches

In_Chapter_1,_Woods outlines what he takes_conflict in abstract sciences —_sciences that_do not make use of empirical results —_to_be. He claims_that there are only two ways to decide an_argument in the abstract sciences that_can be effective:_cost-benefit_considerations_and the “method of_analytic intuitions”. The former is common_(witness David Lewis’s cost-benefit arguments for_modal realism); the latter, in effect, amounts_to conceptual analysis.

In Chapter 2, Woods_presents and rebuts Quine’s arguments_against quantified_modal logic and then turns_to the arguments_of relevant_logicians against the_Lewis-Langford “proof” of ex falso quodlibet,_claiming that such_logicians have largely begged the question_against_ex falso.

In Chapter_3,_Woods_presents one_possible strategy for_conflict_resolution: Reconciliation,_or_ambiguation. The strategy is this: discover_a_distinction that shows that there was never_a disagreement to begin_with;_each side was talking_about something different. Woods distinguishes_argument, inference, and implication, and claims_that paraconsistent_logicians draw_their intuitions from argument and inference only and so should not_expect implication (the chief concern of_logic, according to Woods)_to be_paraconsistent.

In_Chapter 4, Woods_outlines_what he_takes intuitions to be and what role_they play_in argument about abstract sciences. He_uses Frege and Russell_as_examples of philosophers who have dealt_with abstract conflict (in particular, the_Russell set) in different ways_—_for_Frege, says Woods, the Russell_set ended set theory, while for_Russell it modified_set theory.

In Chapter 5, Woods sketches the_present_state of dialetheic set theory and_semantics,_as well as the differences between_truth-value_gluts_and truth-value gaps. He argues_that, as far as intuitions go,_the dialetheist and the non-dialetheist, in argument, must beg_the question against_each other. However, since the_dialetheist_opposes_tradition, the burden of proof rests firmly on her shoulders,_and so_dialetheism is defeated._We briefly address this issue below.

In Chapter 6, Woods explores