Second order Definition and 602 Threads

In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.
First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence




P


x
(
P
x

¬
P
x
)


{\displaystyle \forall P\,\forall x(Px\lor \neg Px)}
says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle). Second-order logic also includes quantification over sets, functions, and other variables as explained in the section Syntax and fragments. Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.

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  1. L

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  2. E

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  3. H

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  4. T

    I Second Order ODE with Exponential Coefficients

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  5. T

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  6. S

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  7. L

    I Solve second order linear differential equation

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  8. D

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  9. I

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  10. Safinaz

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  11. karush

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  12. Ron Burgundypants

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  13. Linder88

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  14. jisbon

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  15. agnimusayoti

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  16. chwala

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  17. M

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  18. V

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  19. redtree

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  20. anooja559

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  21. J

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  22. paulmdrdo

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  23. paulmdrdo

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  24. E

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  25. paulmdrdo

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  26. George Keeling

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  27. T

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  28. T

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  29. Buckethead

    B What is meant by "first order" and "second order"

    I see comments such as "explains ... to the first order" or "to the second order" quite a bit in physics discussions. Can someone explain in lay terms, what first order and second order refer to?
  30. B

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  31. B

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  32. karush

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  33. D

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  34. Peter Alexander

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  35. L

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  36. H

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  37. L

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  38. M

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  39. J

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  40. K

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  41. J

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  42. Telemachus

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  43. F

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  44. Saracen Rue

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  45. grquanti

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  46. Ron Burgundypants

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  47. C

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  48. S

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  49. G

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