Welcome back to The Philosopher’s Lexicon. My primary goal in this series is to explore common philosophical vocabulary, hopefully transforming these words from useless jargon into meaningful terms. My secondary goal is to highlight how contentious some of these terms can be – especially those which seem obvious. These definitions will not be comprehensive by any means, so please feel free to add your own understanding of each term as we go.
This week’s entry into the Philosopher’s Lexicon will once again explore a distinction rather than a solitary term: the difference between logical possibility and causal possibility, a distinction which comes to me from Kant, quite generally, and Nils Ch. Rauhut’s Ultimate Questions, more specifically. What I find most interesting about Rauhut’s take is his shift away from the more common, yet slightly intimidating conversation about logical and causal necessity to the more open realm of possibility.
Like the difference between statements made de dicto and statements made de re, and between ontology and epistemology, the difference between logical and causal possibility is key to understanding, analyzing, and evaluating a philosophical theory. Understanding this distinction is also important when crafting theories and – especially – thought experiments and predictive models not just in philosophy, but in mathematics, the hard sciences, and the social sciences as well.
When we decide whether or not something could happen, we are typically speaking in terms of causal possibility. Causal possibility – and not “casual” possibility (as it is often mis-written) – refers to things that could happen in the world, given its present state. That means we have to take into consideration not just the laws of logic, but the laws of physics, the current circumstances, the available resources, and more.
One of the conditions of causal possibility is logical possibility. In order for a proposed scenario to be logically possible, you have to be able to imagine the proposal – either in literal images, or in symbolic representation (i.e., math, words, or formal language) – without experiencing any internal contradiction. The proposal doesn’t have to be physically possible, or likely to happen, but merely logically imaginable. To wit: for a proposal to be causally possible, it must be logically possible, but logical possibility has no requirement of causal possibility.
For example, the statement “Without the aid of technology, a man can fly to the moon” may not be causally possible (due to the physical limits of human beings and the distance to the moon, among other things), but it is logically possible. It’s easy to imagine, even picture. In Ultimate Questions, Rauhut offers a helpful rule of thumb for determining logical possibility: if you could picture the proposal happening in your mind, it is logically possible. In truth, you may need to elaborately track premises or do complex equations to “draw” the picture, but the principle stands.
On the other hand, the statement “Without the aid of technology, a man can walk ten miles” is both logically possible – easy to picture without experiencing an internal contradiction – and causally possible – humans are fully capable of walking ten miles.
Finally, the statement “Bill is both physically taller and shorter than Sam” is both logically – and thus causally – impossible. It cannot be imagined or depicted even in the most logically isolated circumstances, and thus could never causally happen.
In short, when crafting or assessing whether a proposition is realistic, it’s important to take stock of what kind of possibility you are intending to establish. If we mix up our categories, we’ll likely reject useful logical propositions because they’re causally outlandish, and fear unlikely causal scenarios because they make logical sense.
22 thoughts on “The Philosopher’s Lexicon: Logical and Causal Possibility”
SelfAwarePatterns
Interesting. I was aware of this distinction, but don’t recall having seen the term “causal possibility” before. Thank you!
Logic, it seems to me, along with mathematics (quantitative logic) is our most fundamental theory (or theories) about how reality works. So, when someone says that something is logically possible but not physically possible, I tend to see it as possible using these fundamental theories without taking into account constraints or freedoms introduced by theories built on top of those theories (such as physics, etc). Of course, many see logic and mathematics as more transcendental in nature and disagree with this characterization.
M. Joelle
I think I agree with you, but I’m not sure what you’re presenting are incompatible options – if we’re bracketing for theories like physics, aren’t we already casting logic/math as transcendent? I might just be misunderstanding.
SelfAwarePatterns
I could have used better wording. I should have said that I see logic as our most fundamental theory of how the *universe* works. Some people see it as transcending the universe. I’m open to the possibility that it may, but taking it as self evident, as many do, strikes me as too big of an assumption.
M. Joelle
I think I understand. I would say that logic/math is self-evident given certain assumptions, but that those assumptions have to be built somehow. My gut tells me that the relational form of reason/math is dependent on our language, and is in that way independent of causal reality in a lot of ways – but not necessarily superior in the way that “transcendence” often implies. Maybe I’d want to say that reality transcends our knowledge of it – and I’d put our logical and mathematical language skills squarely in the realm of epistemology.
SelfAwarePatterns
Just as an additional clarification, I’ve become increasingly more attracted to the idea recently that the foundations of logic/math are empirical (although it doesn’t all “feel” empirical because we have innate evolved intuitions about them), and less attracted to logical/mathematical platonism.
I like the phrase “reality transcends our knowledge of it.” I’ll have to remember it. Totally agree about epistemology.
M. Joelle
I think that taking up this position – that logic/math/language is empirically built – requires a rethinking of the status of epistemological frameworks., seeing more value in the creative intellect and more creative malleability in the axiomatic. I’m currently reading some Bronowski (where’s s7hummel these days?) that’s giving me some new ways to phrase my thoughts on this, but I’m still sort of figuring things out.
SelfAwarePatterns
I think there’s an important distinction between saying that the foundations of logic/math are empirical, and that logic/math is empirically built. I think the former is plausible, but would be skeptical of the latter (as would, I think, most mathematicians). The existence of pi was probably initially an empirically observed ratio, but the 4000th digit of pi is an a priori deduction that no conceivable measurement would ever be accurate enough to confirm.
Hmmm. I hadn’t heard of Bronowski before. Maybe you’ll have a post on his views at some point? Stan (s7hummel) does still regularly Like posts, but rarely seems to comment anymore. He does occasionally still comment on my Google page though.
M. Joelle
I like that distinction too, but I’m less willing to take a clear stance on it just yet. I think you would really enjoy Bronowski!
bloggingisaresponsibility
Have you read “Where Mathematics Comes From?”. It makes the argument that math is an abstraction of some fundamental conceptual metaphors. Here’s the wiki: http://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
SelfAwarePatterns
I hadn’t heard of it. Thanks! I’ll keep it in mind.
I am currently reading (slowly) ‘The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy’ by Roberto Unger and Lee Smolin. They have some things to say about mathematics, calling it a simulacrum of our universe sans time and “particulars.” They assert that there is only one universe (no multiverse), an absolute now (I’m curious to see how they deal with relativity), and a “selective realism” to mathematics.
Steve Morris
I just read that wiki. Sounds like a compelling argument to me.
SelfAwarePatterns
A wiki on The Singular Universe? Is it public? Would you mind providing a link? (I didn’t find anything on Wikipedia.)
Steve Morris
I meant the wiki that bloggingisaresponsibility posted – http://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
whitefrozen
My philosophy prof put it this way: there’s nothing illogical about saying ‘copper boils at 563 degrees when you have eight arms’. It’s just a dumb thing to say, because its physically impossible.
The relation between logical and physical/nomological possibility has long fascinated me. As Donald Davidson has observed, the relation between sensation and belief is not and cannot be logical since sensations are not beliefs or propositional attitudes to which logic would apply. If we take this general principle, than it might be possible to draw an analogy between physical events and their nomological possibility – and here I think we end up with roughly Hume’s position on causality, which tells us (correctly) that causality is metaphysical and not empirical. But if this is in fact the case, then we might be guilty of logicism – of trying to apply logic to matters of metaphysics (causality/causal laws). I haven’t quite worked out exactly where to go from here, though.
M. Joelle
The temptations is to take this distinction and then say “Aha! Logical possibility is metaphysical, and epistemological and casual possibility is empirical and ontological!”, but unfortunately it’s not quite as simple as that. I have a few other distinctions coming up (Analytic vs Synthetic reasoning and a priori vs a posteriori knowledge) that are also tempting to neatly divide up this way – I think I’m going to have to spend a week mapping out how these phrases do and do not relate. I think looking at it like that might help me parse out the details of your comment!
whitefrozen
On those topics, I can only say: read Kripke ( if you haven’t already)
Steve Morris
I think we must always be on our guard in saying whether particular scenarios are logically possible. In the framework of quantum physics, “Bill is both physically taller and shorter than Sam” may be causally possible, even though this may appear to be a logical impossibility.
The famous “double-slit experiment” is a good example of how this works in practice.
“Logical” statements are often built on a particular mental model of how the universe is. For example, causality is a principle that philosophers have traditionally discussed in various contexts, yet quantum physics demonstrates that at the most fundamental level of reality, the universe is not strictly causal. Arguments built on this principle may not have such secure foundations as people think.
Michelle, are you aware of how philosophy has adapted to such discoveries? I remember reading about a philosopher who built a model of quantum mechanics based on logic. Was that on your blog? I can’t remember.
M. Joelle
I’m not sure I understand how Bill could be both taller and shorter than Sam, unless we’re re-defining the words in the some way, i.e.: “Bill was shorter than Sam, but because of his pride he stood taller”, or something more metaphorical. I think what it comes down to is that our “logic” (be it prosaic reason or mathematical reason) is a structure we build with symbols, and at present my “language” is too limited to make sense of Bill being both taller and shorter than Sam in any other way. Maybe you can help me out there?
But the double slit experiment, Godel’s incompleteness theorem, and also the position/momentum paradox, among other examples, I can see being relevant to your point. I can see better how these examples exist outside the general paradigm of logic as we know it – this is one of the reasons I’m less willing to draw a line in the sand about whether or not logic is empirically built, or just empirically based (as per my conversation with SAP above).
To answer your question about how philosophy has adapted to such discoveries, I don’t really know. Most of my knowledge of philosophy is pre-Cartesian, but I’m starting to work my way into the field of metalogic (quite accidentally, too – I’m working on a problem in Augustine’s Soliloquies!). My interest is still fledgling, though, and I’m mostly focused on introductory models of logic itself as a language – I’m not quite ready to get into the particulars. I doubt that what you read was on my blog – I’ve got miles to go before I dare tackle anything to do with quantum mechanics! Please leave a link here, though, if you find it!
Steve Morris
I think my point is similar to what Mike said about mathematics being inspired by empirical experience of our world. The same may apply to logic. In logic there are self evident notions such as AND and OR, but what I am suggesting is that these notions are rooted in our empirical experience of everyday things.
For example, we are familiar with the idea that an object may be spinning clockwise or anti-clockwise. These seem to us, from our everyday experience, to be mutually exclusive states of being. The object is spinning one way OR the other way (or not at all.) However, subatomic particles such as electrons have the property that they may spin clockwise, anti-clockwise, or in a superposition of both states simultaneously. We cannot process this notion with any of the ways of thinking that we have derived from everyday experience. Something that we thought was logically impossible turns out to be causally possible.
Quantum physics is full of such apparent contradictions and absurdities. What it tells us is that ideas that we hold to be absolutely bulletproof and beyond science, are actually limited ways of thinking. I don’t think this is a problem with our language, but with our experience as humans in the physical universe. Quantum effects are too small for us to observe unless we build machines to test them.
You make a distinction between logic being empirically built, or just empirically based, and I don’t really grasp that difference. I’m out of my depth trying to take this forward, but a search reveals that there are people working in this area of research: http://en.wikipedia.org/wiki/Quantum_logic
M. Joelle
I think for me the distinction is that (and this is still very much a thought in progress) if mathematics were empirically inspired, it would mean that we take an empirical starting point and then from there move in a purely deductive fashion out to the logical conclusions contained within the premise, whereas an empirically built vision would require a continued relationship with observation. Obviously the former is the model we work generally work with, but your thoughts about how our logic matches our common experience of the world – and the limitations of this common experience – leads me to think there’s more of a connection between the formal relationships we build in logic (language and math) and this experience. We can go further with logic and math than we can noticeably observe, but I’m not sure that means we’re really leaving experience behind after that first level of inspiration. But again, I don’t really know what I’m talking about here, or if I’m really saying anything.
Steve Morris
I lack the formal education in philosophy and logic to express my views cogently, but essentially my feeling is that mathematics and logic are sets of rules we invented, based on our implicit assumptions about how we think the world works. They turn out to be powerful tools for thinking, much like how language helps us to organize and generalize our thoughts. But like all tools, we invented them. But as you say, this is a thought in progress for me. I’ve changed my mind more than once!
PeterJ
Great discussion.
Mike – You say – “I think my point is similar to what Mike said about mathematics being inspired by empirical experience of our world. The same may apply to logic. In logic there are self evident notions such as AND and OR, but what I am suggesting is that these notions are rooted in our empirical experience of everyday things.”
There is an opposite way of looking at it (as always). One could explain our empirical experience of the logical behaviour of Nature as a consequence of our innate inability to countenance contradictions.
Iow, we could blame the logical structure of the psycho-physical universe on the innate rationality of primordial consciousness.
It’s both a logically and nomically/causally possible scenario and quite a popular idea.
Just confusing the issues…