Implication Is Thus The Very Texture Of

The Three Main Medieval Points Of View Regarding Universals Are Designated By Historians As Realism, Conceptualism, And Nominalism. Essentially These Same Three Doctrines Reappear In Twentieth-century Surveys Of The Philosophy Of Mathematics Under The New Names Logicism, Intuitionism, And Formalism.

The Lore Of Our Fathers Is A Fabric Of Sentences. In Our Hands It Develops And Changes, Through More Or Less Arbitrary And Deliberate Revisions And Additions Of Our Own, More Or Less Directly Occasioned By The Continuing Stimulation Of Our Sense Organs. It Is A Pale Gray Lore, Black With Fact And White With Convention. But I Have Found No Substantial Reasons For Concluding That There Are Any Quite Black Threads In It, Or Any White Ones.

The Line That I Am Urging As Today's Conventional Wisdom Is Not A Denial Of Consciousness. It Is Often Called, With More Reason, Arepudiation Of Mind. It Is Indeed A Repudiation Of Mind As A Second Substance, Over And Above Body. It Can Be Described Less Harshly As An Identification Of Mind With Some Of The Faculties, States, And Activities Of The Body. Mental States And Events Are A Special Subclass Of The States And Events Of The Human Or Animal Body.

Irrefragability, Thy Name Is Mathematics.

If Pressed To Supplement Tweedledee's Ostensive Definition Of Logic With A Discursive Definition Of The Same Subject, I Would Say That Logic Is The Systematic Study Of The Logical Truths. Pressed Further, I Would Say That A Sentence Is Logically True If All Sentences With Its Grammatical Structure Are True. Pressed Further Still, I Would Say To Read This Book.