In mathematics, many theories are built on assumptions that are taken to be true, and they are most often called axioms, and then, with the help of logical laws and definitions and with various methods of proof statements are proven to be true or false.
Should philosophy also be axiomatized? And do you think that such an axiomatizations are possible? What would, in that case, be methods of proof?
If there are some assumptions on which all philosophers agree, or almost all, I think that those should be found and stated explicitly, of course that there are many differences among various philosophers, but is there any base, some set of assumptions, on which almost all of them agree?
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2Short answer: no. Mathematics (and hard sciences) roughly cover what most people agree on, so it makes sense to establish common truths and notions, and then reason from them. Philosophy, again roughly, covers the complementary ground, both the truths and the reasoning are highly individual and based on subjective preferences and judgment calls about plausibility. There will be too many "axioms" that vary from person to person, and "methods of proof" would be too vague to make it worth the while. See See e.g. [ethics/mathematics disanalogy](https://philosophy.stackexchange.com/a/41574/9148) – Conifold Jun 12 '19 at 01:44
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Two great philosophers – Wittgenstein (Tractatus) and Spinoza – came quite close to the axiomatic method. Maybe also some scholastics (of which I know less) – Rushi Jun 12 '19 at 03:08
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@Conifold Of those too many axioms, some are more important, is there anything on which all philosophers agree? – Grešnik Jun 12 '19 at 06:16
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2No. What is or is not more important varies as well, and some of those "axioms" are too cumbersome to even state explicitly. Many of them amount to accepting some inferences with multiple conditions as plausible enough based on citing (or even just alluding to) a laundry list of specific cases, or commonly reported intuitions. – Conifold Jun 12 '19 at 17:43
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As I see it, it is exactly one of defining characteristics of philosophy, as an overall activity (not specific theories), that there are no axioms. Nothing is agreed upon, except tentatively. – Ram Tobolski Jun 12 '19 at 20:01
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@Rusi Descarte used an axiomatic method also. – Jonathan Cender Jun 14 '19 at 01:13
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Godel Incompleteness was the death-knell for this project, as discussed by Hawking here http://www.hawking.org.uk/godel-and-the-end-of-physics.html A far more compelling conception of philosophy is Wittgenstein's idea of a kind of it as a kind of therapy, I would add to linguistic, also of social 'psychic plumbing' as discussed here https://aeon.co/ideas/whence-comes-nihilism-the-uncanniest-of-all-guests There's also the idea we are trying to knit our different types of understanding together into a coherent world view, like Deutsch outlines in The Fabric Of Reality – CriglCragl Apr 25 '20 at 14:39
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In my view the entire purpose of philosophy is axiomatization. If you want to know what happens when this is forgotten just note the endless battle between rootless opinions that characterises the academic literature. A useful philosophical theory must be a formal axiomatic system. This would be why Russell's paradox is so important in metaphysics. If a person is not trying to axiomatize philosophy then I would say they are not doing it. . – Apr 26 '20 at 13:03
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This depends on what you mean by "philosophy." I study philosophy as a discipline which asks questions there's not yet been a consensus on how to answer. This makes sense of why sciences like, say, linguistics, psychology, physics, etc. used to be considered branches of philosophy. Enough agreement was reached as to how to answer questions about each domain. It also makes sense of, say, why we still discuss questions that vexed ancient scholars. We've not yet agreed on how to answer, say, ethical questions.
With this understanding, I'd say axiomatizing should be a goal of philosophical inquiry, much the same way axioms constituting scientific models are a goal in scientific inquiry. I'm in fact part of a growing number of formally trained philosophers working in applied ontology (I work specifically with the Basic Formal Ontology: https://basic-formal-ontology.org/), where we construct axioms for 'everyday dry goods' but also for more fundamental entities. In these projects, philosophers are often claiming one or other ontology is more accurate than others but for my part, I think it's wise to curate various axiomatic systems reflecting philosophical investigation, on the model of the Stanford Computational Metaphysics project here: https://mally.stanford.edu/cm/.
It's of course one thing to work in applied ontology and another to axiomatize philosophy. I actually spend a lot of time axiomatizing philosophical papers too though, especially for teaching purposes. If you're interested, last quarter I axiomatized several papers in existentialist literature: http://johnbeverley.com/nu-existentialism-winter-2020
John Beverley
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Should philosophy also be axiomatized?
Yes. This is the task for metaphysics.
And do you think that such an axiomatizations are possible?
Yes.
What would, in that case, be methods of proof?
The proof would be a logical argument. A fundamental theory would be a formal axiomatic system.
If there are some assumptions on which all philosophers agree, or almost all, I think that those should be found and stated explicitly, of course that there are many differences among various philosophers, but is there any base, some set of assumptions, on which almost all of them agree?
Assumptions would be no good. The facts are what count. Philosophers almost all agree that positive metaphysical theories are logically indefensible, rendering metaphysical problems undecidable. If we assume that their failure in logic is due to their falsity, then we must conclude that the Universe is a Unity. This is an excellent axiom for philosophy and it works. This is the axiom rejected by those who find metaphysics useless such as the logical positivists, mysterians and those who endorse scientism.
It is a failure to axiomatise philosophy (or Reality) that distinguishes the 'western' tradition. The problem is intimately related to mathematics, which is why in his book Laws of Form George Spencer Brown is able to axiomatise philosophy and resolve Russell's paradox at the same time.
The difficulty is that the only known way to axiomatise philosophy by assuming the Unity of All, and this is a step too far for many philosophers for it means opening the door to mysticism and the philosophy of Plotinus, Brown, Nagarjuna and Lao Tsu. Consequently, the common view in academic philosophy is that it is impossible to axiomatise philosophy.
How long this disagreement between traditions can continue now that we have the internet is a interesting question. I don't think it can be maintained for much longer.
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Are you implying that Nagarjuna, et al, would support an axiomatic method? Or that their ideas are amenable to such method? I ask because doubtful. – Jonathan Cender Jun 14 '19 at 01:16
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@JonathanCender - I would say yes on behalf of Nagarjuna and Brown. They reduce the world to Unity and the Unity of All would be their first axiom. From this Unity would follow the falsity and logical indefensibility of all other global theories, and the rest of the system. Just as in real life the appearance of our world follows inevitably from the nature of Reality. This is not a speculative philosophy so its axiom is a discovery rather than a formal construct, but it works as an axiom for a formal axiomatic system. Big topic for a small text box. . . . – Jun 14 '19 at 13:04
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It is a big topic for a small text bos, lol. Please let me know why you or Brown think Nagarjuna "reduced" the world. Reduced to unity would be a bonus:) My personal reading, following Kalupahana, is to interpret Nagarjuna in light of the pragmatism of James and Dewey. Hence a nonreductionist point of view. – Jonathan Cender Jun 16 '19 at 00:30
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@JonathanCender - Nagarjuna is famous for explaining the philosophical foundation for the Buddha's teachings. Brown is praised for explaining the arising of form from formlessness. Both axiomatise the manifest world on a distinctionless, undifferentiated ultimate encompassing all, which would be the only phenomenon that is truly real. Thus Bradley's 'Appearance and Reality' where Reality is Unity and Appearance is multiplicity. All three explain the logical failure of positive metaphysical theories and favour a neutral one for which the world reduces to the unmanifest. . . . . – Jun 16 '19 at 10:44
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This does not exactly fit the common use of "axiomatic" IMHO because while it may have similar, logical reasons to be stated, there are no other axioms which would allow for derivation of a set of philosophical propositions based on an axiomatic system. Rather, the only judgements made possible are negative, since they can allegedly be shown to contradict the axiom (something that is, IMHO, itself based on too restrictive an assumption). – Philip Klöcking Jul 12 '19 at 21:54
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@PhilipKlöcking - I can't quite follow you. Do you mean Unity is nor capable of being a founding axiom? I would disagree since it's heavily pregnant with ramifications. But I may not be grokking your point. – Jul 13 '19 at 10:53
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@PeterJ A single axiom cannot be fruitful in axiomatic systems since they depend on multiple axioms which, when combined, allow for derivative new propositions. Single propositions only allow for the rejection of contradictory statements. This is the formalistic/logical part. The last sentence refers to the problematic reduction of metaphysics to Reality and the assumption that it *is* just the way our thinking and logical laws allow us to *conceive* it. – Philip Klöcking Jul 13 '19 at 12:52
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@PhilipKlöcking - I see your two main objections but do not believe they hold in this case. For a discussion we'd have to open a chat-room - which I'll do if you wish. – Jul 14 '19 at 11:25
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@PhilipKlöcking PS. Just saw this again and felt I hadn't said the right thing. I agree that more axioms are required, but they're easy to formulate. My first would be 'The Universe is reasonable'.(Aristotelian). The second would be 'All positive metaphysical theories are logically absurd'. Etc etc. But the crucial one would be an axiom of Unity. . .; . – Apr 25 '20 at 13:12
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Philosophy is a lot more about questions than answers as such. An axiom would be a kind of answer, so... But there are plenty of systematic philosophers out there, so people have attempted to do what you are asking about. Is there much consensus when it comes to the systems developed? Not obviously, but then one might say much the same thing about the foundations of mathematics.
Kristian Berry
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