Science Quotes

"Logical consistency is the minimum requirement for a viable theory."

"Mathematical truth is discovered, not invented, though it requires human creativity."

"Numbers are not properties of physical objects but are objective abstract entities."

"Mathematics is the science of quantity, but number is an abstract object."

"The true nature of number cannot be understood through empirical observation alone."

"Mathematics deals with objective entities that transcend time and space."

"Numbers are not invented by humans; they are discovered as objective truths."

"Numbers exist in a realm of abstract objects independent of the physical world."

"Scientific progress depends upon rigorous logical analysis of our concepts."

"Numbers are objects of thought that exist eternally and necessarily."

"Twin Earth cases show that content is not intrinsic to the organism."

"Scientific realism requires a robust notion of truth."

"The success of science does not require metaphysical realism."

"We need a new philosophy of science that avoids both realism and anti-realism."

"The unity of science is not a given; it must be justified."

"Quantum mechanics shows that reality is not classically structured."

"Scientific theories are underdetermined by evidence."

"Explanation does not always require reduction to fundamental particles."

"Emergence is real and cannot be eliminated."

"Science is one perspective among others, though a powerful one."

"Information cannot be reduced to physical properties."

"Logic and mathematics are not purely formal sciences."

"Scientific revolutions transform not just our theories but our concepts."

"Incommensurable theories may still have points of contact."

"A formal system is a set of symbols and rules for manipulating them."

"Church's thesis connects the intuitive notion of computability to formal mathematical definition."

"Formal systems are humanity's most precise instruments for thinking."

"Effective procedures represent the intersection of mathematics and the real world."

"Computation is the language in which the universe writes its laws."

"The development of recursion theory was an exploration of the very foundations of mathematics."