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Logic is Metaphysics (2011) [pdf]
- jc763 8y ago>Does the number seven exist? Does the red color exist? What evidence do we have to answer these questions? What are the truth conditions for ∃x P(x) when P(x) stands for a number or a property? To respond to these questions is to set an ontology, and setting an ontology is to do metaphysics. This is exactly what Quine does when he states some reasons to include numbers and to exclude properties from the domain of our variables. Good paper.
- westoncb 8y agoSeems like from that it's just framework construction. It may have the same internal structure as an ontology, but to say the statements have any external correspondence (to the metaphysical; I'm using 'external' loosely) would require an extra step. I can set an ontology where `thingamajiggers` are the only entity (so I guess the only truth condition for '∃x P(x)' is that P(x) is a thingamajigger), and I guess if you want to you can say I'm doing metaphysics at that point, though it does seem a little pointless to do so.
- trhway 8y ago>Does the number seven exist? Does the red color exist? those ones seem to be easy. There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. It is only our mental construct (note: the construct itself, ie. neuron circuits and firing sequences do exist. It is like a map of non-existent land - the map exists while the land doesn't). The same is red color. There are EM waves of different frequencies. Color is mental construct triggered by perception of EM frequencies in specific range. Slightly different for different people. Completely missing for cats if i remember correctly. Like the number seven which is probably missing for cats too, and is known to be missing by various indigenous tribes separated from our civilization - people in this tribes know seven arrows, seven boats, ... yet completely don't understand just seven.
- bodi 8y ago> There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. It is our mental construct. Crows, horses, and dolphins all have well documented[1] abilities to count numbers therefore as inconvenient and suggestive as it may be, the "number seven" most definitely exists somewhere outside human mental constructs and likely originates inside the abstract fuzzy designs that produce elementary consciousness. 1 - https://www.scientificamerican.com/article/how-animals-have-the-ability-to-count/ https://www.scientificamerican.com/article/how-animals-have-...
- trhway 8y ago>likely originates inside the abstract fuzzy designs that produce elementary consciousness. that sounds pretty close to what i'm saying - similar brains (and i do think that many animals' brains are much closer to us than we casually think they are) given similar experience (seeing seven stones, seven birds) produce similar constructs (incl. an aggregation/averaging of some aspects of that experience). That doesn't necessarily mean though the real existence of that aggregation/averaging (ie. what we call "number seven"), only the neuron config/sequence what actually encodes it is real.
- dragonwriter 8y ago> There is no number seven. I mean there seven trees, seven stones, yet there is no number seven. There aren't trees or stones any more than there is the number seven: objects (other than elementary particles, maybe) are as much mental constructs as numbers.
- placebo 8y agoWhy stop at elementary particles? All objects are mental constructs of consistencies our brains detect in data that our senses pick up. Humans have a great advantage in picking up on what I'd call meta-consistencies (which is basically what abstraction is) - creating a new mental construct by detecting consistencies not only in what the senses pick up, but detecting consistencies in those consistencies, or "thoughts about thoughts" if you will. This gives you numbers and other abstract concepts that enable far more powerful manipulation.
- woodandsteel 8y agoWhether or not you should say they exist depends on the particular meaning of the term "exist" you are using. And that in turn depends on what are your motives and purposes for asking the question. Of course, if you are a Platonist then you will believe that there is a single, perfect meaning for the term that everyone should use.
- dmfdmf 8y agoLogic is based on the principle of non-contradiction (identified by Aristotle). The principle, in all its various forms, is used to guide valid thinking (i.e. truth) because contradictions cannot exist which is its tie to metaphysics.
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- pmoriarty 8y ago"Logic is based on the principle of non-contradiction" That's merely one type of logic. There are others which can deal with contradictions. See the Wikipedia entries on Paraconsistent logic[1] and Dialetheism[2]. Logicians enjoy coming up with new logics that have any desired or interesting properties. They are not limited to staying within the bounds of classical logic. [1] - https://en.wikipedia.org/wiki/Paraconsistent_logic https://en.wikipedia.org/wiki/Paraconsistent_logic [2] - https://en.wikipedia.org/wiki/Dialetheism https://en.wikipedia.org/wiki/Dialetheism
- hiker 8y agoThe key to understanding logic constructively goes through type theory, not philosophy. I'll just leave this here https://78.media.tumblr.com/bfc158b432199a3e4f5de2ddc1bd7381/tumblr_nuj7qbMUa71qc38e9o1_1280.png https://78.media.tumblr.com/bfc158b432199a3e4f5de2ddc1bd7381...
- arto 8y agoSource, pretty please?
- shawn 8y agohttps://books.google.com/books?id=LkDUKMv3yp0C&pg=PA11&lpg=PA11&dq=%22We+summarize+the+different+points+of+view+of+the+type-theoretic+operations+in+Table+1.%22&source=bl&ots=au08DGQydm&sig=v9DrnObM_x9ygzdCCNMsk0VZ63Y&hl=en&sa=X&ved=2ahUKEwjRkuPW6L_bAhVU_oMKHfSvC7EQ6AEwAHoECAEQKg#v=onepage&q=%22We%20summarize%20the%20different%20points%20of%20view%20of%20the%20type-theoretic%20operations%20in%20Table%201.%22&f=false https://books.google.com/books?id=LkDUKMv3yp0C&pg=PA11&lpg=P... Homotopy Type Theory: Univalent Foundations of Mathematics
- arto 8y agoThanks!
- hiker 8y agoIt's from https://hott.github.io/book/nightly/hott-online-1174-g29279f5.pdf#page=23 https://hott.github.io/book/nightly/hott-online-1174-g29279f...
- arto 8y agoThanks!
- curuinor 8y agoThe progenitor of types was Russell, who considered himself a philosopher.
- qntty 8y agoAncient Greek philosophy was divided into logic, physics and ethics. Metaphysics was categorized as logic.
- danbruc 8y agoI am not sure whether I really understand what the author argues for, probably because I read the paper in a rush. Does he argue that [the choice of] a logic is in some sense equivalent to [a choice of] what kind of entities exist? If that is indeed the case, I would tend to disagree. While we often think of logic as a provider of undisputable truth, I am not sure that this is justified. There is more than one type of logic and they lead to different conclusions or contradict each other in the general case. Therefore it seems to me that the obvious thing to say is that logic is a human construct we use to reason about the world, it does not reflect universal truths but was invented and constructed in a way to be useful to deal with our world. In consequence it is obviously very likely that logic and metaphysics are strongly correlated, but that would hardly be any deep insight but just a consequence of the way we constructed or choose the logic we use. If the logic I use to deal with the world makes a prediction about the world, for example the existence of a certain entity, then that entity might actually exist if may logic is a good match for the world, but I see no reason why the entity would have to exists, my logic could just be a bad choice.
- jjaredsimpson 8y agoWhat I took away: If you want to say 'Santa Claus doesn't exist', you can't write a formula ~E x. x=Santa Claus. Because then you are conceding in your logic that some object Santa Claus exists. So there is some connection between the structure of sentences we can construct in our logic and metaphysical claims. We should then try to understand differences in metaphysical claims by finding differences in logics. The author then tries to show this for the metaphysical claim, 'Statements are true or false independent of whether they can be verified.' Instead of arguing about what is truth, what does it mean for a proposition to be verified. We can instead as about the differences in the logic. Because to even talk about truth and existence we need a logic first. So don't think there is a claim that choice of logic forces claims about real world existence. I think is the more subtle connection, that choice of logic forces a choice about rules of inference. Real world claims would need to be based on introducing propositions (which are independent of the logic?) and then using rules of inference (which are dependent on the logic).
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- danharaj 8y agoA philosophical discussion of logic in this decade should at least be aware of the Curry-Howard isomorphism and Linear Logic. This paper makes a passing mention of this by treating the law of excluded middle. I would say that denying that law has led to the most fruitful developments of logic in the last century. Philosophy without technical input is sophistry, technical developments without philosophy end up answering questions of no interest. Girard is an entertaining source of both philosophical and technical insight: On the meaning of logical rules I : syntax vs. semantics http://girard.perso.math.cnrs.fr/meaning1.pdf http://girard.perso.math.cnrs.fr/meaning1.pdf Per-Martin Lof's ideas are also important: ON THE MEANINGS OF THE LOGICAL CONSTANTS AND THE JUSTIFICATIONS OF THE LOGICAL LAWS https://uberty.org/wp-content/uploads/2017/06/Martin-Lof83.pdf https://uberty.org/wp-content/uploads/2017/06/Martin-Lof83.p... This only scratches the surface.
- empath75 8y ago> Philosophy without technical input is sophistry, technical developments without philosophy end up answering questions of no interest. This is such a great formulation.
- danharaj 8y agoI should say, definitely not mine. I don't know where I got it, or where they got it.
- omon 8y agoWholly irrelevant, the paper is specifically concerned with recovering a dialectic between W. O. Quine and M. Dummett. Even if the question was the more general, "Is Logic Metaphysics?", knowledge of formal logics isn't even of concern. It's trivial that we can construct a plethora of axioms with their own definitions, the problem remains: to even adhere to those definitions one is exercising another intuitive logic—even in the case of computation which is an engineered construction to proxy this very intuition, otherwise we would have never been concerned with the linear properties necessary for computation to begin with.
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- carapace 8y agoThe first step in any logic is to make a distinction. This act is within the mind. The world itself is unknown except as sensory experience. Leaving aside the so-called "Hard Problem of Consciousness" for the sake of discussion, the fact that distinction happens in our heads means that all of our logic is contingent (as opposed to inherent) if our thinking is wholly internal to our brains. However... none other than Kurt Gödel believed that thinking about e.g. infinities involved a kind of perception of a "higher" world. "Science does not remove the Terror of the Gods."
- woodandsteel 8y agoLogic, to be of any use in the real world, must in some important ways match the reality of the world. So any system of logic assumes a metaphysics. And going the other way, reality must be such as to be able to have creatures who can think logically. This is one instance of a larger principle, namely the inherent mutual interconnectedness of the various areas of philosophy. So for instance, epistemology depends on reality being such that it can be known, and we can know about that reality only the sorts of things that a valid epistemology can determine. Similar mutual relations exist between every two main areas of philosophy. This mutual interconnectedness is a key reason for Neurath's insight that in philosophy you can't tear it all down and change it radically, but only modify it.
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- raincom 8y agoLogic is metaphysics, only when one smuggles in one's intuitions as definitionally true; otherwise, it is not so: "If we look more closely how it comes about that these existential statements are logical truths in these logical systems we see that it is only so because, by definition, a model for (standard) first order logic has to have a non-empty domain. It is possible to allow for models with an empty domain as well (where nothing exists), but models with an empty domain are excluded, again, by definition from the (standard) semantics in first order logic. Thus (standard) first order logic is sometimes called the logic of first order models with a non-empty domain. If we allow an empty domain as well we will need different axioms or rules of inference to have a sound proof system, but this can be done." (From Hofweber, Thomas, "Logic and Ontology" https://plato.stanford.edu/archives/sum2018/entries/logic-ontology/ https://plato.stanford.edu/archives/sum2018/entries/logic-on...)
- yedawg 8y agoIsn't logic simply the understanding of cause and effect and choosing to deny or approve of a cause depending on the level of accuracy of the effect on the context. eg. Santa doesn't exist inside conventional norms. Santa could have existed, however we don't know. We have no cause to say he does exist.