1. PERCEPTUAL ACCOUNT OF SYMBOLIC REASON LANDY, ALLEN, ZEDNIK 2014 Rishav Raj Agarwal Arpit Agarwal

2. WHAT IS SYMBOLIC REASONING?  The science of reasoning by the aid of representative symbols 2+2

3. CONTEMPORARY VIEWS WHAT HAD BEEN PROPOSED PREVIOUSLY

4. COMPUTATIONAL VIEW 2+2 Expression C1C2C 3 Abstract concepts Central Reasoning System Computations C4 Concepts 4 Output

5. SEMANTIC PROCESSING VIEW += 2 + 1 = 3 Source: www.clipartbest.com

6. CYBORG VIEW  Faster computation by “Scaffolding”  Extraneural storing  Inspection  Deletion  Manipulation of information 89x9 8 CARRY 9x9=8 1 1 ADD 8 8X9=7 2 801

7. SUMMING IT UP  Symbolic Reasoning as grounded in the ability to internally represent numbers, logical relationships, and mathemat ical rules in an abstract, amodal fashion.

8. THE HYPOTHESIS WHAT THE PAPER SUGGESTS

9. PERCEPTUAL MANIPULATION THEORY  Symbolic Reasoning is done by:  Complex visual and auditory processes  Affordance learning  Pattern-matching  Grouping of notational structures  Role of magnitude and quantity detection systems.

10. MAGNITUDE AND QUANTITY DETECTION A 5 X A 3 = A 8 (AAAAA)X(AAA)=(AAAAAAAA)

11. BLURRING

12. GROUPING Source: Landy and Goldstone 2007A

13. DISTANCES MATTER 100 2 > 38 22 > Landau and Moyer, 1967

14. fMRI DATA & MEG  fMRI and MEG evidence that mathematical expressions are parsed quickly by visual cortex, using mechanisms that are shared with non-mathematical spatial perception tasks. Source: Masaki Maruyama et al 2012

15. CONCLUSIONS PMT i

16.  Symbolic reasoning is likely to be idiosyncratic and content specific.  PMT suggests that notations and the sensorimotor processes that engage them are often at the very heart of high-level mathematical and logical cognition  Perception, visualization, and interaction may play a crucial constitutive role in mathematical and logical reasoning.

17. REFERENCES

18.  Clark, A. (2003).Natural Born Cyborgs. Oxford: Oxford University Press  Maruyama, M., Pallier, C., Jobert, A. Sigman, M., and Dehaene, S. (2012). The cortical representation of simple mathematical expressions. Neuroimage61,1444–1460. doi: 10.1016/j.neuroimage.2012.04.020  Dörfler, W. (2002). Formation of mathematical objects as decision making. Math. Think. Learn.4, 337–350. doi: 10.1207/S15327833MTL0404_03  Landy, D., and Goldstone, R. L. (2007a). How abstract is symbolic thought? J. Exp. Psychol. Learn. Mem. Cogn.33, 720–733. doi: 10.1037/0278-7393.33.4.720  Fodor, J. A. (1983).Modularity of Mind. Cambridge, MA: MITPress

19. Thank You Questions?