| 19360 | General principles, even if unconscious, are indispensable for thinking [Leibniz] |
| Full Idea: General principles enter into our thoughts, serving as their inner core and their mortar. Even if we give no thought to them, they are necessary for thought, as muscles and tendons are for walking. | |
| From: Gottfried Leibniz (New Essays on Human Understanding [1704], 1.01.20) | |
| A reaction: Famously, Leibniz identified sufficient reason and non-contradiction as the two foundational principles. Modern logicians seem less keen on this idea, but then they have less interest in how we actually think. |
| 19404 | Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz] |
| Full Idea: The principle of contradiction is the principle of necessity, and the principle that a sufficient reason must be given is the principle of contingency. | |
| From: Gottfried Leibniz (On Sufficient Reason [1686], p.95) | |
| A reaction: [this paragraph is actually undated] Contradictions occur in concrete actuality, as well as in theories and formal systems. If so, then there are necessities in nature. Are they discoverable a posteriori? Leibniz says not. |
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| Full Idea: Bolzano said the 'laws of thought' (identity, contradiction, excluded middle) are true, but nothing of interest follows from them. Logic obeys them, but they are not logic's first principles or axioms. | |
| From: report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837], §3) by George / Van Evra - The Rise of Modern Logic | |
| A reaction: An interesting and crucial distinction. For samples of proposed axioms of logic, see Ideas 6408, 7798 and 7797. |
| 6933 | The laws of reality are also the laws of thought [Feuerbach] |
| Full Idea: The laws of reality are also the laws of thought. | |
| From: Ludwig Feuerbach (Principles of Philosophy of the Future [1843], §45) | |
| A reaction: I like this a lot, though it runs contrary to a lot of conventionalist thinking in the twentieth century. Russell, though, agrees with Feuerbach (Idea 5405). There is not much point to thought if it doesn't plug into reality at the roots. |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| Full Idea: Frege disagree that logic should merely describe the laws of thought - how people actually did reason. Logic is essentially normative, not descriptive. We want the one logic which successfully tracks the truth. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Jennifer Fisher - On the Philosophy of Logic 1.III | |
| A reaction: This explains Frege's sustained attack on psychologism, and it also explains we he ended up as a platonist about logic - because he wanted its laws to be valid independently of human thinking. A step too far, perhaps. Brains are truth machines. |
| 5396 | Three Laws of Thought: identity, contradiction, and excluded middle [Russell] |
| Full Idea: For no very good reason, three principles have been singled out by tradition under the name of 'Laws of Thought': the laws of identity ('what is, is'), contradiction ('never be and not be'), and excluded middle ('always be or not be'). | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 7) | |
| A reaction: 'For no very good reason' seems a bit unfair, probably to medieval logicians, who deserve more respect. Russell suggests that the concept of implication deserves to be on the list. Presumably optimism about thinking is a presupposition of thought. |
| 5405 | The law of contradiction is not a 'law of thought', but a belief about things [Russell] |
| Full Idea: The law of contradiction is not a 'law of thought' ..because it is a belief about things, not only about thoughts. | |
| From: Bertrand Russell (Problems of Philosophy [1912], Ch. 9) | |
| A reaction: The principle is a commitment about things, but it is inconceivable that any experience, no matter how weird, could ever contradict it. It would be better to assume that we had gone insane, than that a contradiction had occurred in the world. |
| 9131 | Two long understandable sentences can have an unintelligible conjunction [Sorensen] |
| Full Idea: If there is an upper bound on the length of understandable sentences, then two understandable sentences can have an unintelligible conjunction. | |
| From: Roy Sorensen (Vagueness and Contradiction [2001], 6.4) | |
| A reaction: Not a huge paradox about the use of the word 'and', perhaps, but a nice little warning to be clear about what is being claimed before you cheerfully assert a screamingly obvious law of thought, such as conjunction. |
| 6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
| Full Idea: Traditionally many philosophers (Aristotle among them) have considered the law of noncontradiction to be the deepest, most fundamental principle of rationality. | |
| From: Robert Fogelin (Walking the Tightrope of Reason [2003], Ch.1) | |
| A reaction: For Aristotle, see Idea 1601 (and 'Metaphysics' 1005b28). The only denier of the basic character of the law that I know of is Nietzsche (Idea 4531). Fogelin, despite many qualifications, endorses the law, and so do I. |