Does Aristotelian logic describe human reasoning? Valid syllogisms and canonical models

Transcription

1 Khazar Journal of Huanitie and Social Science Volue 19, Nuber 2, 2016 Doe Aritotelian logic decribe huan reaoning? Valid llogi and canonical odel Miguel Lóez-Atorga Univerit of Talca, Chile Introduction The ental odel theor (e.g., Johnon-Laird, 2004, 2006, 2010, 2012; Khelani, Orene, & Johnon-Laird, 2012, 2014; Khelani, Lottein, Trafton, & Johnon- Laird, 2015; Oakhill &Garnha, 1996; Orene& Johnon-Laird, 2012) i a current cognitive theor that rooe that huan reaoning i not baed on ntactic inference fro logical for. According to it, eole ake iconic odel or ental rereentation that are eentiall eantic and refer to all of the oibilitie that can be true given a rooition. In thi wa, the theor acknowledge that it fundaental coe fro Peirce ( ). However, an iortant oint of the theor to thi aer i that individual do not alwa identif all of the odel related to rooition. Soe of the odel are ea to be found and eole uuall note the quickl. Neverthele, other odel are harder to be identified without certain reflection or effort. Thi fact elain, for eale, wh individual ake certain itake and wh certain inference are ore difficult than other. A far a I know, the theor i ver develoed with reect to what i called rooitional inference in tandard logic, i.e., inference with not quantified entence. Regarding quantified ereion, the develoent i le, but undoubtedl there are work in that wa. One of the i that of Khelani et al. (2015), in which the odel ea to be noted are naed canonical odel and the harder odel requiring ore reflection are called noncanonical odel. Thu, the ain goal of thi aer i to how that all of the valid categorical llogi in Aritotelian logic can be conidered to be correct onl taking the canonical odel rooed b Khelani et al. (2015) into account. Thi fact i relevant becaue, if the ental odel theor i right, it ean that the theor ha clear rediction related to Aritotelian logic, and that it can be aid that thi logic hould be 5

2 6 Miguel Lóez-Atorga acceted b huan being in a natural and quick wa. In other word, if we aue the general thee of the ental odel theor, we ut alo aue, on the one hand, that the huan ind can conider the llogi of Aritotelian logic to be valid without utting a lot of effort, and, on the other hand, that thi logic can decribe how huan reaoning ontaneoul work when faced with inference with tructure akin to thoe of uch llogi. To rove all of thi, firtl, I will account for the ain idea of the ental odel theor about quantified aertion. Then I will elain the fundaental rincile of Aritotelian logic. Finall, I will analze each of the ood of each of the figure in that logic in order to how that the can be acceted a valid b conidering onl the canonical odel. The ental odel theor and quantified entence A aid, Khelani et al. (2015) ditinguih the canonical odel (i.e., the odel eail noted) fro the noncanonical odel (i.e., the odel requiring certain cognitive effort). Their thei i that, given a quantified ereion, individual think about oe eantic oibilitie correonding to that ereion. Obvioul, uch oibilitie are odel and rereent articular ituation. A roble i that it can be thought that the nuber of the odel that can be conidered b an individual at the ae tie i liited, ince hi (or her) working eor and ental abilitie are not infinite. Khelani et al. (2015) eoe the rocedure that can hel identif the aroriate nuber of odel in each cae. Neverthele, to the ai of thi aer, it i enough to aue, a convention, the nuber that aear on Khelani et al. (2015) table 1, that i, three odel in the cae of the canonical odel, and three, four, or five odel in the cae of the noncanonical odel. That table include i te of aertion, but onl four of the, thoe ued in Aritotelian logic, are relevant to thi aer: affirative univeral aertion, affirative articular aertion, negative univeral aertion, and negative articular aertion. I tart with the affirative univeral one. An affirative univeral ereion i uuall aid to have thi tructure: Ever i

3 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 7 According to the ental odel theor, given uch an ereion, individual can quickl think that thee three canonical odel rereent all of the oible ituation to which it refer: Note that the three odel tand for the ae circutance: a cenario in which both and are true. Thu, in rincile, the affirative univeral rooition onl caue individual to conider cenario in which the two ter of the ereion are true. Onl after further reflection, the can realize that other ituation are oible. In thi wa, an eale of noncanonical odel correonding to the affirative univeral aertion can be, following Khelani et al. (2015), thi one: not- not- not- The firt odel i jut a the reviou one. However, the other two odel how that the individual i now aware that the aertion i alo conitent with a ituation in which oething i not but it i, and with a ituation in which oething i neither nor. Mabe an eale with theatic content can be illutrative in thi regard. Let u think about thi aertion: Ever frog i green The canonical odel refer to three different frog and indicate that the are all green: frog frog frog green green green Nonethele, if the individual ut ore effort, he (or he) can note that the aertion allow other oibilitie too:

4 8 Miguel Lóez-Atorga frog not-frog not-frog green green not-green Indeed, the econd odel how that oething, for eale, another anial, can be green and not a frog, and the third one refer to the oibilit that oething i not a frog and i not green at the ae tie. A far a the affirative articular aertion are concerned, it can be tated that the are thoe that uuall have thi tructure: Soe i According to Khelani et al. (2015), the canonical odel are in thi cae: not- Becaue all of the are not now, the third odel eree the oibilit that oething being and not. But the eale of noncanonical odel rooed b Khelani et al. (2015) include one ore oibilit: not- not- A it can be checked, in thi eale, the individual ha noted that at leat there i another additional oibilit: the cae in which oething i not but it i (the third odel). Baed on thi, it i not hard to deduce the eale of odel (both canonical and noncanonical) attributed b the negative aertion b Khelani et al. (2015). Let u conider an ereion uch a thi one: No i That i the tructure correonding to the negative univeral aertion and, following Khelani et al. (2015), it canonical odel are a follow:

5 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 9 not- not- not- But, of coure, noncanonical odel are alo oible for thi kind of aertion. According to the, an eale can be thi one: not- not- not- not- not- Finall, the negative articular aertion are aid to have thi tructure: Soe i not And Khelani et al. (2015) indicate that the canonical odel of an ereion of thi te can be: not- not- not- And the alo reent, a an eale of it noncanonical odel, the following: not- not- not- not- Thee are the kind of quantified aertion that are ued in Aritotelian logic. A aid, ain ai i to how that all of the valid categorical llogi in that logic can be conidered to be correct b taking into account jut the canonical odel. However, before arguing in favor of thi idea, it ee to be oortune to eoe the general fraework of Aritotelian logic.

6 10 Miguel Lóez-Atorga Aritotelian logic and it valid categorical llogi A it i well known, edieval author ued letter for referring to the te of entence analzed in the reviou ection. Baed on the Latin word afiro (I tate) and nego (I den), the aued thee equivalence: -A (the firt vowel in afiro): affirative univeral aertion. -I (the econd vowel in afiro): affirative articular aertion. -E (the firt vowel in nego): negative univeral aertion. -O (the econd vowel in nego): negative articular aertion. There i no doubt that detailed inforation on and decrition of Aritotelian logic are to be found in everal good work. Onl oe of the are clearl, for eale, Boger (1998, 2001, 2004), Burnett (2004), Gaer (1991), Johnon (2004), Miller (1938), Paron (2008), Sith (1991), or Wood and Irvine (2004), but arguent in thi ection will be baed ainl (although not ecluivel) on that of Paron (2008). Having aid that, a firt iortant oint about Aritotelian logic i that, a it i alo well known, the llogi conit of three entence: two reie and a concluion. In addition, three eleent can be ditinguihed in the llogi: the ajor ter, the iddle ter, and the inor ter. The ajor ter aear in one of the reie and i the ubject of the concluion (fro now on, I will refer to thi ter with the letter ). The iddle ter aear in the two reie, but it doe not in the concluion (fro now on, I will refer to thi ter with the letter ). And the inor ter aear in one of the reie and i the redicate of the concluion (fro now on, I will refer to thi ter with the letter ). In thi wa, deending on the lace in which,, and are, everal figure are oible. According to the claification eoed b Paron (2008), the for of uch figure are thee one: -Figure 1 (elained b Aritotle in AnalticaPriora I, 4): i i Ergo i -Figure 1 (indirect) (elained b Aritotle in AnalticaPriora I, 7):

7 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 11 i i Ergo i -Figure 2 (elained b Aritotle in AnalticaPriora I, 5): i i Ergo i -Figure 3 (elained b Aritotle in AnalticaPriora I, 6): i i Ergo i Fro thee figure, Aritotle rooed 19 ood b cobining the aertion of the te A, I, E, and O indicated above. Thu, for eale, a ood of the firt figure can be ereed a follow: A( ) A( ) Ergo A( ) Where the initial caital letter tand for the kind of quantified aertion (in thi cae, A infor that the aertion i affirative univeral) and ean i. Actuall, a Paron (2008) ention referring to Arnauldand Nicole (1662) arguent, there are five ore ood. However, I will onl focu on thoe indicated b Aritotle. Such 19 ood were given nae in the Middle Age. In articular, Peter of Sain, in hi Tractatu (or Suulaelogicale) reented a nuber of nae that could be learned in a relativel ea wa and that rovided data about the ood. Thoe nae are the following: Figure 1: Barbara, Celarent, Darii, and Ferio. Figure 1 (indirect): Baraliton, Celante, Dabiti, Faeo, and Frieooru.

8 12 Miguel Lóez-Atorga Figure 2: Ceare, Caetre, Fetino, and Barocho. Figure 3: Darati, Felato, Diai, Datii, Bocardo, and Ferion. Neverthele, what i intereting for the goal of thi aer i that the nae how the for of the ood. The firt three vowel of each ood correond to the te of quantified aertion included in it. Thu, the firt vowel indicate the te of quantified aertion correonding to the firt reie, the econd one indicate the te of quantified aertion correonding to the econd reie, and the third one indicate the te of quantified aertion correonding to the concluion. In thi wa, for eale, the tructure of Celarent i thi one: E( ) A( ) Ergo E( ) Thee are the baic notion of Aritotelian logic that are relevant and that need to be taken into account to achieve the ai of thi aer. A aid, I have baed decrition on the verion of it rooed b Paron (2008) and I will continue to do that in the following age. A alo entioned, ain goal i to how that jut the canonical odel reented b Khelani et al (2015) enable to conider the valid categorical llogi (i.e., Aritotle 19 ood) to be correct without the need to ake a further effort. I will tr to do that in the net ection, each of which i devoted to a figure. The figure 1 and the canonical odel The firt ood of thi figure i Barbara. Reall, it for ha alread been reented above. It i thi one: A( ) A( ) Ergo A( ) According to the fraework baed on the ental odel theor rooed b Khelani et al. (2015), the canonical odel of the firt reie are:

9 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 13 But, given that the econd reie tate that i not oible without, the reviou cenario can be coleted in thi wa: Thu, thee three odel include the inforation rovided b the two reie (that whenever i true, i true too, and whenever i true, i true a well), and, according to the canonical odel, no ore inforation can be conidered. Therefore, what need to be checked now i whether or not the inforation given in the concluion i conitent with the reviou three cenario. It i ea to do that becaue what the concluion ean i that it i not oible a cenario with and without, and, a it can be oberved in the reviou odel, there i no uch a cenario. In all of the, if haen, i alo reent. The tructure of Celarent ha been indicated too. It i a follow: E( ) A( ) Ergo E( ) Now, the odel of the firt reie are: not- not- not- And the inforation of the econd one i that it i not oible without. So, in thi cae, it i allowed adding to the odel in which not- i not: not- not- not-

10 14 Miguel Lóez-Atorga In thi wa, the concluion i alo correct in thi cae becaue it tate that no i and, in the reviou odel, an cenario in which both and are true cannot be found. On the other hand, the tructure of Darii i: A( ) I( ) -- Ergo I( ) The canonical odel of the firt reie are now: Neverthele, if the inforation contained in the econd one i taken into account, becaue it indicate that there can be a cae in which haen and doe not, it i necear to add a new odel: not- But thi doe not ake the concluion incorrect becaue it onl tate that there are cae of and and, a it can be checked, there are uch cae. Finall, the for of Ferio i: E( ) I( ) Ergo O( ) The firt aertion lead to thee oibilitie: not- not-

11 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 15 not- But, becaue the canonical odel of I indicate two ituation in which both ter occur and one ituation in which the firt ter aear and the econd one doe not, it i onl necear now to add a to each odel: not- not- not- And the concluion i correct again, ince it onl tate that there are cae of and not-, and we have two of thoe cae. The figure 1 (indirect) and the canonical odel The tructure of Baralitoni obvioul a follow: A( ) A( ) Ergo I( ) Thu, the canonical odel of the firt reie are: Becaue the econd one i alo a entence of te A, it i onl necear to add to each cenario: Therefore, the concluion i conitent with thee odel. It clai that there are cae of and, and the odel how that that i o in all the oibilitie. A econd ood of thi figure i Celante:

12 16 Miguel Lóez-Atorga E( ) A( ) Ergo E( ) In thi wa, the odel of the firt aertion are a follow: not- not- not- On the other hand, the econd reie rovide the inforation that i not oible without. So, onl can be added in the cenario in which i true: not- not- not- And, becaue the concluion a that i ioible with, and, in the onl cenario in which i, i not, the concluion i valid here a well. Another ood i Dabiti, and it for i, evidentl, the following: A( ) I( ) Ergo I( ) The canonical odel of the firt aertion are: And, given that the econd one i affirative articular, it i necear to include a cae of without : not-

13 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 17 And, ince aear in all of the cae in which alo aear, there i no doubt that the concluion i correct here too. The following i Faeo, which ha thi tructure: A( ) E( ) Ergo O( ) The canonical odel of the firt reie continue to be the ae: But the econd one tate that no i. Therefore, becaue in thee three odel aear, it i necear to add not- to the. However, in addition, it i alo necear to include cae of and not-. Thu, the reult i: not- not- not- not- not- Neverthele, the concluion onl require and not to be together, which occur in all of the oibilitie. The lat ood i here Frieooru, and it nae, a in all of the other cae, reveal it for: I( ) E( ) Ergo O( ) The canonical odel correonding to the firt entence are, of coure:

14 18 Miguel Lóez-Atorga not- Nonethele, the econd one i of te E, which ean that in all of the odel with onl not- i oible, and that the cae of not- ut be added: not- not- not- not- not- not- The concluion onl clai that there are cae of and not-, and a it can be checked, that i what haen in the two firt odel. Therefore, thi ood i coherent with the canonical odel rooed b Khelani et al. (2015) a well. The figure 2 and the canonical odel A indicated, the firt ood of thi figure i Ceare. So it for i the following: E( ) A( ) Ergo E( ) Thu, the canonical odel of the firt reie are thee one: not- not- not- However, the econd reie infor that i onl oible when haen too. hence can be added onl in the third odel: not- not- not- And thee cenario allow checking that, indeed, a the concluion a, there are not cae of and.

15 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 19 The econd ood i Caetre. So it tructure i thi one: A( ) E( ) Ergo E( ) Therefore, the firt entence ha the canonical odel correonding to the affirative univeral aertion, i.e., But, given that the econd one i a negative univeral aertion, it i necear to add certain data. Firtl, odel in which i true and i fale ut be included. Secondl, it i alo required to indicate that, when haen, it i onl oible not-. In thi wa, the reult i a follow: not- not- not- not- not- Neverthele, the two lat odel can be coleted. The firt reie infor that, if occur, ha to occur too. So, thi udate of the odel i correct: not- not- not- not- not- not- not- The final reult hence i that, a tated b the concluion, in the ituation in which haen, it cannot be acceted that haen at the ae tie. Another ood of thi figure i Fetino, and thi nae lead u to thi for:

16 20 Miguel Lóez-Atorga E( ) I( ) Ergo O( ) If we think about the canonical odel of the firt reie, we can a that the are thee one: not- not- not- The econd one tate that oe i. Therefore, it allow two oibilitie: i) both and are true, and ii) i true and i fale. Thu, a wa of udating the reviou odel i to add to all of the, whether i in the or not: not- not- not- And, a it can be noted, thi ake the concluion true, ince it how that, indeed, there i at leat a cae of and not- (the lat odel). The final ood of the econd figure i Barocho, and it tructure i: A( ) O( ) Ergo O( ) Obvioul, a in the cae of Caetre, the firt entence lead u to thee canonical odel: But the econd one i a negative articular aertion, which ean, on the one hand, that it i necear to add cae of not- (in which i true), and, on the other hand, to include not- in the cae in which haen:

17 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 21 not- not- not- not- not- Neverthele, for reaon akin to thoe indicated for Caetre ( i onl oible if i true), the lat two odel can be udated here a well: not- not- not- not- not- not- not- And the reult i that the concluion of thi ood i clearl valid becaue there are cae in which haen and doe not (the lat two odel). The figure 3 and the canonical odel A indicated, thi i the lat figure that I will analze in thi aer, and it firt ood i Darati. A in the reviou cae, the nae reveal it tructure: A( ) A( ) Ergo I( ) And thi tructure ilie that the canonical odel of the firt aertion are the following: The econd entence, on the other hand, indicate that ha to be included in all of thee odel, ince aear in all of the:

18 22 Miguel Lóez-Atorga So, the concluion i true becaue oe are (in fact, all of the are). The net ood i Felato, i.e., a ood with thi for: E( ) A( ) Ergo O( ) The firt odel are therefore a follow: not- not- not- Nonethele, the econd reie clai that cae of without are not oible and that thee odel hence decribe better the oible cenario: not- not- not- Evidentl, the fact that doe not haen in the third odel can lead u to add not- in it. However, it i obviou that the two firt odel how that the concluion i true: there are cae in which occur and doe not. Another ood correonding to thi figure i Diai, whoe tructure i clearl: I( ) A( ) Ergo I( ) So, the canonical odel of the firt reie are now: not-

19 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 23 And the econd reie caue to be included in all of the odel, ince i true in all of the: not- Thu, thee oibilitie how that the concluion i correct, ince there are cae of and (the firt one and the econd one). The fourth ood of the third figure i Datii, and it for hence i: A( ) I( ) Ergo I( ) Thi ean that the firt entence refer to thee canonical odel: And, becaue aear in the three cae, the odel of the econd reie can be conidered b including in the two firt oibilitie and not- in the lat one: not- In thi wa, it concluion i alo abolutel correct. The reaon i the two firt odel, which how that oe are. Bocardo i alo a odel of thi figure. A it nae reveal, it tructure i: O( ) A( ) Ergo O( )

20 24 Miguel Lóez-Atorga The negative articular aertion that aear in the firt reie lead u to thee odel: not- not- not- And the affirative univeral aertion that aear in the econd one lead u to add in all the cae in which i true: not- not- not- So, it can be noted that there are cae of and not- (the two firt oibilitie), and that that fact ean that the concluion i correct. Finall, the lat odel i Ferion, which ha thi for: E( ) I( ) Ergo O( ) The canonical odel of it firt reie are: not- not- not- Thu, the odel of it econd reie can be taken into account b including in the cenario in which haen, and b adding another cenario in which i true and i not: not- not- not- not- Again, the two firt reie how that the concluion i true, ince the reveal that, indeed, oe are not. In thi wa, it can be aid that all of the ood analzed

21 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 25 in thi aer can be acceted following the ental odel theor, and, in articular, following jut the canonical odel rooed b Khelani et al. (2015). Concluion The recedent age rovide iortant conequence for the tud of the huan ind if the ental odel theor i aued. Given that the concluion of all of the reviewed ood can be drawn b uing jut the canonical odel indicated b Khelani et al. (2015), it can be tated that Aritotelian logic reent a et of inference cheata that are natural for huan reaoning. B thi, I ean that, becaue the valid categorical llogi of that logic can be conidered to be correct b taking onl the canonical odel into account, according to the ental odel theor, huan being hould accet uch llogi in a quick wa and without aking further cognitive effort. Thu, it can alo be tated that thoe llogi can be ver ueful for elaining, decribing, and even redicting the reult of the reaoning tak in which the are involved. Thi oint i relevant becaue, a it i well known, the ae cannot be aid about tandard logic and the natural deduction calculi (ee, e.g., Gentzen, 1935). Indeed, the literature on cognitive cience how that there are everal ituation in which ile rincile, rule, or requireent of tandard logic are not followed or fulfilled b eole (ee, e.g., Orene& Johnon-Laird, 2012). Aart fro that, another roble of that logic i that, when it addree quantified aertion (for eale, when firt-order redicate calculu i ued), it reort to ver cole forulae, and it i unclear which the ental roce wh individual ake or contruct thoe forulae could be (ee, e.g., Lóez-Atorga, 2014). But the ental odel theor ee not to have thee roble. In alot all of the book, chater, and aer related to it, one ight check that thi theor can account for and redict an of the reult offered b articiant in reaoning tak that tandard logic or theorie ore or le baed on that logic cannot elain. Furtherore, given that logical for i not relevant for the ental odel theor, which i eentiall a eantic aroach (ee, e.g., Johnon-Laird, 2010), the roble of the tranlation of individual ental rereentation into well fored forulae doe not eit in that fraework.

22 26 Miguel Lóez-Atorga But the ot iortant finding of thi aer can be that the ental odel theor can rove that it i worth continuing to conider Aritotelian logic. If the recedent arguent are right, it i obviou that Aritotelian logic i not obolete, that it ha cognitive value, and that it can be ver ueful to decribe and ake rediction about huan inferential activit. In thi wa, it could be ver intereting that the roonent of the theor checked eiricall and eerientall arguent uch a thoe rooed here, and that the deigned eerient uing Aritotelian valid llogi in order to review whether or not anali in thi aer and, of coure, their thee on quantified aertion are correct. And I a aing thi becaue, at leat a far a I know, uch a work i not ade at reent. In an cae, a oint ee to be abolutel clear: the ue of the ain thee and the ethodolog of the ental odel theor can be ver helful in checking whether or not the logical theorie of the at continue to be oehow alicable tool toda. Reference and note: Arnauld, A. & Nicole, P. (1662). La logiqueoul art de ener. Pari, France: Charle Savreu. Boger, G. (1998). Coletion, reduction, and anali: Three roof-theoretic rocee in Aritotle Prior Analtic. Hitor and Philooh of Logic, 19, Boger, G. (2001). The odernit of Aritotle logic. In D. Sfendoni-Mentzou (Ed.), Aritotle and Conteorar Science. Volue 2 ( ). New York, NY: Peter Land Publihing, Inc. Boger, G. (2004). Aritotle underling logic. In D. M. Gabba& J. Wood (Ed.), Handbook of the Hitor of Logic. Volue 1. Greek, Indian and Arabic Logic ( ). Aterda, The Netherland: Elevier. Burnett, C. (2004). The tranlation of Arabic work on logic into Latin in the Middle Age and Renaiance. In D. M. Gabba& J. Wood (Ed.), Handbook of the Hitor of Logic. Volue 1. Greek, Indian and Arabic Logic ( ). Aterda, The Netherland: Elevier. Gaer, J. (1991). Aritotle logic for the odern reader.hitor and Philooh of Logic, 12, Gentzen, G. (1935). Unteruchungenüber da logicheschließen I. MatheaticheZeitchrift, 39, Johnon, F. (2004). Aritotle odal llogi. In D. M. Gabba& J. Wood (Ed.), Handbook of the Hitor of Logic. Volue 1. Greek, Indian and Arabic Logic ( ). Aterda, The Netherland: Elevier. Johnon-Laird, P. N. (2004).The hitor of the ental odel. In K. Manktelow& M. C. Chung (Ed.), Pcholog and Reaoning: Theoretical and Hitorical Perective ( ). New York, NY: Pcholog Pre. Johnon-Laird, P. N. (2006).How We Reaon. Oford, UK: Oford Univerit Pre. Johnon-Laird, P. N. (2010).Againt logical for.pchologicabelgica, 5(3/4), Johnon-Laird, P. N. (2012).Inference with ental odel. In K. J. Holoak& R. G. Morrion (Ed.), The Oford Handbook of Thinking and Reaoning ( ). New York, NY: Oford Univerit Pre.

23 Doe Aritotelian logic decribe huan reaoning? Valid llogi and 27 Khelani, S., Orene, I., & Johnon-Laird, P. N. (2012). Negation: A theor of it eaning, rereentation, and inference. Pchological Review, 109(4), Khelani, S., Orene, I., & Johnon-Laird, P. N. (2014).The negation of conjunction, conditional, and dijunction.actapchologica, 151, 1-7. Khelani, S., Lottein, M., Trafton, J. G., & Johnon-Laird, P. N. (2015). Iediate inference fro quantified aertion. The Quarterl Journal of Eeriental Pcholog. DOI: / Lóez-Atorga, M. (2014). The conditional introduction rule and huan reaoning: Finding fro the ental odel theor. Cogenc, 6(2), Miller, J. W. (1938). The Structure of Aritotelian Logic. London, UK: Kegan Paul, Trench, Tubner& Co., Ltd. Oakhill, J. &Garnha, A. (Ed.) (1996). Mental Model in Cognitive Science.Ea in Honour of Phil Johnon-Laird. Hove, UK: Pcholog Pre. Orene, I. & Johnon-Laird, P. N. (2012). Logic, odel, and aradoical inference.mind& Language, 27(4), Paron, T. (2008). The develoent of uoition theor in the later 12 th through 14 th centurie. In D. M. Gabba& J. Wood (Ed.), Handbook of the Hitor of Logic. Volue 2. Mediaeval and Renaiance Logic ( ). Aterda, The Netherland: Elevier. Peirce, C. S. ( ). Collected Paer of Charle Sander Peirce. C. Harthorne, P. Wei, & A. Burk (Ed.). Cabridge, MA: Harvard Univerit Pre. Sith, R. (1991). Predication and deduction in Aritotle: Airation to coletene. Tooi, 10, Wood, J. & Irvine, A. (2004). Aritotle earl logic. In D. M. Gabba& J. Wood (Ed.), Handbook of the Hitor of Logic. Volue 1. Greek, Indian and Arabic Logic ( ). Aterda, The Netherland: Elevier. Suar Doe Aritotelian logic decribe huan reaoning? Valid llogi and canonical odel Miguel Lóez-Atorga Univerit of Talca, Chile In the cae of quantified rooition, the ental odel theor ditinguihe between canonical and noncanonical odel. While eole identif the canonical odel in an iediate, raid, and ea wa, the noncanonical odel cannot be detected without reflection and cognitive effort. In thi aer, I tr to how that all of the valid llogi in Aritotelian logic can be conidered to be correct b reorting onl to the canonical odel of their entence. In thi wa, I argue that thi ean that Aritotelian logic can be a ueful criterion to elain, decribe, and even redict eole concluion fro quantified aertion. Keword: Aritotelian logic, ental odel, quantification, reaoning, llogi