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Continuing on Tarski's “The Semantic Conception of Truth and the Foundations of Semantics,” (1944), Hartry Field's “Tarski's Theory of Truth” (1972), and Donald Davidson's “The Folly of Trying to Define Truth” (1977).
What was Tarski really doing? What are the implications of his project? Does it even make sense to define "truth," and what should a definition look like?
Listen to part one first, or get the ad-free Citizen Edition. Look out for the Citizen-only bonus discussion of Shakespeare's Tempest, posting soon! Please support PEL!
End song: "In Vino Vertias" by Sunspot; Mark interviewed Mike Huberty on Nakedly Examined Music #64.
as you folks say Davidson seems on the right track (and is a pragmatist in any sense that is worth keeping) but reminds me that I need to get back to Read and Sharrock’s take on Kuhn vs Kripke/Putnam and their arguments against the idea of a social science.
Dreyfus read Heidegger on science via Kripke
for the dreyfus point, I dont understand how something is suddenly outside the world, weight atomic or otherwise is not independent from our concept of weight which is thouroughly within the world (of our experience), the universality that experiment and science gets to is still bound to who we are as even though we may use instruments to measure properties hidden to our immediate sense and symmetry is found through many experiments, that whole process is still dependent on our capacities and those capacieties remain in the world, which is of course the world of our experience. I do believe we expand our capacities but i highly disagree when some aging little man claims we can arrive at the universal essence; or god as it used to be called. The most comical contradiction there is: i m not man, i am more (precisely what man would say).
August Denys says
I find it oddly coincidental that two days before this series on Tarski I started reading and taking heavy notes on Martin Heidegger’s Logic. This Heidegger text comes from Indiana University Press translated by Thomas Sheehan is based on Heidegger’s lectures on Logic in November 1925. The reason I mention this, beside possibly remembering an aside in the first part to Heidegger’s Logic, is because it seems that much of what I’ve read so far is a critique relevant to the project of Tarski and, one who I’m a little more familiar with, Quine.
The reason I bring this up is because I think that Heidegger’s Prolegomena (which is as far as my pace has brought me so far) covers the problematic aspects of these analytic logicians. A word that I’ve seen thrown around a lot, but one in which I had not understood in any context till now was Psychologism. Adding some precursor, Heidegger starts off his lecture series going into the history of Logic, which for him means going into the word Logos (spelled in greek through the entire work because Heidegger). But he considers Logos as one aspect of a tripartite system of knowledge consisting of Physis, Ethos, and Logos in which he quotes Sextus Empiricus (in the greek) who is himself explaining Xenocrates as who is supposed to be the first philosopher to make this decision. This comes to the decision that Physics as the study of nature, everything, the totality of what is out there; Ethics being the study of human beings towards others and towards the self (not contemporary physiology or biology; rather, more in line with Aristotle’s virtues); and for logos, I’ll quote a passage in length,
“Logos, then, is what reveals an ontological connection between the other two universal regions we mentioned: human being (ethos) and world (physis). So the regions that these three words designate provide us with an essential (if rough) classification of beings. (Pg. 3)
Heidegger has shown his understanding of the being of Logic because it, from what I can tell as an amateur, shows Logic as the connection between the world and self.
Furthermore, before I get into the prolegomena, Heidegger demonstrates a move that one might consider antithetical to Tarski and the others mentioned; this move is to differentiate between two kinds of Logic: 1) Scholastic Logic, and 2) a Philosophizing Logic. He claims that much of what was done between Aristotle and Hegel was not progress, and he attributes this to the first kind, Scholastic Logic. Scholastic Logic is the kind of logic that is taught in universities—e.g., P then Q, P, therefore Q—and Heidegger directly states,
“People say and think and believe, in an agreement that goes without saying, that studying scholastic logic teaches you how to think and helps you reach a higher level of learning and a greater exactitude in thinking. So it’s something we should strive for right from the beginning of our scientific studies. /P/ This is a basic misunderstanding. Thinking, and especially scientific thinking, can be learned only by getting involved with the subject matter.” (pg. 12)
Now, I taught myself logic from a textbook a former professor gave to me, Logic An Introduction by Robert Paul Churchill, and eventually went on to take a formal logic class in university, and these tasks did include examples such as, “Either the president is mistaken or the senator is telling the truth. If the senator is telling the truth, then either the president’s secretary is lying or the White House chief of staff is suppressing evidence. The president is not mistaken and the press secretary is not lying. Thus, the chief of staff is suppressing evidence.” (Churchill pg. 285) This is all well and good, but Heidegger would from what I can tell us that since this is not based on scientific or actual knowledge that is is 1) not teaching the person to think, and 2), which might be more accurate and to the point, that this promise to teach a person to think does not connect physis or ethos in which to think of or about. And I think it is in this second part that the big problem comes, contemporarily, about. Heidegger was of course writing before Computers were being programmed with Boolean logic examples, and even though he inspired Hubert Dreyfus in this matter, his logical project is to understand the Philosophizing Logic that comes from Husserl’s Critique of Psychologism and what he considers the co-unification of Logic of Aristotle and Hegel. Or in another way, his Logically endeavor, from again the point I am at, is the connection of truth between these three aspects of Being: World (physis), Human being (ethos), and Logos which seems to understand as, “Logic investigates speaking–the thinking that defines things–inasmuch as speaking uncovers things. The topic of logic is speech, specifically with regard to truth.” (Heidegger pg. 6)
Now, why did I go that far in covering the introduction before I get to the Prolegomena I wanted to mention? Because I needed to show what was meant as why Heidegger’s project is different to many contemporary logicians, why while there may have been practical applications of logical systems to computing Heidegger’s project is not invalidated, and to show that the semantics the contemporary philosophers work towards is possibly a false continuation of this Scholastic Logic which Heidegger and Husserl’s critique in regard to psychologism. This brings me to the term Psychologism. What is it?! As best I can understand, it was the 19th centuries attempt to connect Logic to Ethos or Physis by means of making Logic subservient to Psychology. When I first read this, I was dumbfounded because the thought had never crossed my mind that Logic, which was touted to be the science of correct thinking to be connected at all to Psychology, but that may be because what I know, what we know as Psychology today is wholly different from what Psychology was in the 19th century. Heidegger states,
“Today, for example, we speak of two psychologies. One of them specifically studies the causal interconnections of mind. Here we are thinking of a natural science… explanatory psychology. But at the same time, we realize that mental life–so called “lived experience”–cannot be subsumed under the laws of nature as if we treated these experiences like mere things of nature. Instead they can be understood… understanding psychology…. /P/ Nowadays, the project of psychology–if we can even delimit here a unified and self-clarified discipline–has an entirely chaotic form. Psychology is invaded by ethnology… anthropology…. parapsychology… psychopathology…. It’s everything and nothing.” (Heidegger pg. 30-31 sorry if this is a little muddled, There was a lot of clarification in between which I didn’t feel was necessary to include and I’m not a professional editor so I didn’t know how to chop it up).
I would say that today, in our time, we live with a priority of explanatory psychology which has taken the form of these latter disciplines that Heidegger states (the way he states this in full is a little telling of his anti-humanist tendency which makes a case for why he was won over by Nazis). However, Psychology still has the essence of understanding the causal connections of the mind which means that if psychology was of correct thinking, then logic would be subsumed under psychology. But as Husserl and Heidegger point out, this is problematic because it takes the connection of Logic (logos) from the world (physis). It makes it a completely mental activity just like math. Of course we have applied mathematics and the use of those mathematics have gotten humans to the moon, but that doesn’t explain the connection between Logos and Physis, or Space flight and Math.
Heidegger takes this idea even further: one of the primary principles that we take absolute is the Principle of Contradiction–The same proposition cannot at the same time be both true and false. If we take this at face value as computational logic or the state of truth values, then we miss the actual ontological implications of the principle. I have personally thought of this principle in terms of a light switch, it cannot at the same time be on and off, true and false. But this expression of the principle misses the implications of Being and Non-Being. The Principle of Contradiction is not merely a logical law, but a Law of Nature (physis), “He [H. Sigwart] calls the principle of contradiction a law of nature that says, ‘it is impossible at any given moment to say, with conscious awareness, that A is B and that A is not B.’ Because it is a law of nature, it can also be understood as a standard law aimed at the practical regulation of thinking. In other words, it ‘applies to the whole range of constant concepts.” (pg. 35) However, as this is the point I’m catching up to and need to spend time with. The principle of contradiction needs to be a physical law and not a law of thought. Personally, the part I understand the least is his quotation from Benno Erdmann in which the impossible judgement of the Principle of Contradiction rests on own representations in thinking. Thus, if 1) the problematic aspect of finding the Principle of contradiction being universalized from nature, induction, or 2) the principle of contradiction resting on Human nature, then Heidegger finds that these logical propositions are not absolute necessities; rather, they are merely hypothetical necessities.
Why did I bring this up? Well, one, it was a nice trying to formulate and restate everything that I had read so far, but mainly because the projects of Tarski are so far different that I wonder if the analytic philosophers brought forth from Frege fall victim to this problem of Psychologism. To make Logic mathematical, I wonder if it needs to go beyond the a priori side which would be the classical type of Psychology of trying to make things consistent. I have listened to your podcast episode on Godel, and I wonder if he was inspired by Heidegger. I know that Deleuze and Guattari (but most only mention Deleuze) in their book What Is Philosophy?, which you have also covered in part, deals with Godel’s incompleteness theorems in a way that is very nuance and might have connection to this topic. Basically, Heidegger’s project which I have jumped into makes me ask the question of whether the mathematical logic of Davidson, Quine, and Tarski escapes this problem of Psychologism or not. It would also be the case that at this time I have no sufficiently understood the problem myself to make that judgement call, but the project being so vastly different makes me wonder. In another way, to borrow from Hegel’s logic, Heidegger’s project seems to delve into the Being (in-itself) of logic and truth, and in the introduction Heidegger’s gives the Notion (for-itself) of logic and truth while the Semanticians of logic only go into the Notion (for-itself) of logic and truth and claim that this Notion is the Being. I got this last part of Hegel from Marxists.org reference article on Hegel’s Logic.
Nathan Harvey says
Ouch. I was really looking forward to this discussion because of my intense love of Tarski’s work. I was really eager to hear you guys get into his theory.
But then you really didn’t get into his theory. You got confused. And some of the “big picture” discussion just never happened because of tangents that really were more about understanding his point than discussing it.
I think a much better way to start with Tarski is to look at 3 things:
– A Syntax. This is the language, the symbols, their structure and representation, and it’s premises or axioms. This is also known as a Theory. For your discussion, this is the object language.
– A semantics. This is also known as a model. In realist semantics, this would be the world. In phenomenological accounts it would be the landscape of perception. In simulations and the semantics of formal languages, it is an executing model.
– A function that interprets the syntax in the semantics. This is the meaning association. It is whatever ties that language meaningfully to what it represents.
This most certainly can be done with informal languages when we talk about their meaning, and this is common in the field – he is only staying away from it in his formalization to not get sidetracked with the ambiguities and self reference issues. The interpretation mapping is very general and left without a lot of constraints in Tarski’s theory. Also, the point of calling it “free of metaphysical assumptions” is precisely because of the flexibility in the kind or nature of semantics. As I know you guys are aware from your readings, this same distinction of symbol and referent is throughout many different philosophical traditions.
This structure can interpret correspondence theories of truth. Tarski was not avoiding those theories or providing an alternate. In fact, it can interpret both direct mapping correspondence as well as correlationist and other exotic relationships, with different kinds of interpretation functions.
The point of using this structure to describe what truth is that – which was the one thing I think you guys really got right – truth is a semantic concept. The truth of a sentence is a property of the interpretation of a sentence in a particular model..
This is in contrast to many coherence theories of truth where truth is a structural concept in the syntax.
And I think there are a lot of important things that are captured by the semantic concept of truth that are common in the way we informally talk about truth. The same theory may have different interpretations – we see this in quantum mechanics, for instance. Statements’ truths may vary from model to model, even when they have the same theory.
I think a lot of time was spent on this “list”. It seemed humorous and weird to you guys. I think, not being mathematicians, you may have missed what that was all about. That was just the interpretation function. That was the mapping. There are lots of ways you can specify this function – a list from sentences to their semantic representatives, or – as he also describes – more structurally.. It sounded like some of the confusion on the podcast was around how or if this interacted with the presence or absence of free variables in the sentence, and it’s not clear to me what the actual difficulty was. The interpretation function deals with an input sentence with free variables the same way any function composition would. Free variables vary over some collection (or list). You create a truth function instead of a truth value. Tarski doesn’t really go over this in his papers much because that’s diversionary from the description of truth.
And I think by getting sucked into the weeds here, you never got to actually touch some of the really cool things that have come about from Tarski’s model theory and the semantic conception of truth. For example, the idea that formal languages – like mathematics and computer languages – have an interpretation in their physical execution in our universe, and that is their meaning and where we get truth is an idea that has fueled many schools of radical constructivism throughout the 20th and 21st centuries. It was implicit in the BHK semantics, it’s natural to see the Curry-Howard Isomorphism as an interpretation function, etc.
Tarski’s model theory is everywhere in formal languages – from the foundations of science to mathematics, computer science, and formal automation in the world, But it is also quite a natural fit to theories of personal languages and the pattern recognition capabilities we have for inference and private concepts, and the theory of how we build language through semantic interaction is a really interesting area where the structure of model theory plays an important role. In all of these, we naturally apply Tarski’s description of truth.
Mark Linsenmayer says
So what’s a good follow-up topic that we should do and have YOU on as a guest to help us get the bigger picture??
Nathan Harvey says
Hey Mark! I really hope I wasn’t too brusque in my response. My hope was to revive Tarski in your eyes, not attack the effort.
You know, I feel my interest in this area is not widely shared. I fell in love with the Tarskian approach from its place in discussions on the foundations of mathematics. I was deeply influenced by LEJ Brouwer’s intuitionism and later formalisations, so if I had my druthers I’d be pushing you guys to discussions of Heyting algebras and their ubiquity in operationalist accounts of math and science.. I’d be asking you guys to review nonclassical logics, the Russian constructivist school of Kolmogorov and Markov, the development of computational constructivists, Per Martin-Löf, and eventually stuff like univalent foundations and homotopy type theory. Along the way, I’d have you visit predicativist theories of meaning and extreme positions (that I have deep affinities towards) like ultrafinitism.
But I fear those directions don’t make for good podcasts, despite them being what drew me into Tarski and model theory. You won’t have a large audience eager for mathematics.
So… if you really are interested in pursuing some of these ideas deeper and want to consider topics that you already have an audience for, I might suggest a different approach: constructivist epistemology and some neighboring fields. This was something I touched on tangentially in my own education, mostly through Piaget, but is something I have become far more studied in now that I have kids and have them going to a constructivist school. This touches directly with your past few episodes on pedagogy.
I think you guys should do an episode on the ideas around how epistemological constructivism interact with computationalism and connectionism. Stuff like:
Connectionism and Computationalism
Much of this has Tarski in the background (you’ll notice the asides in the papers), but it’s really about how models get formed in the brain and how this is where we get meaning from. Honestly, as someone who has deep phenomenological roots, I feel most “philosophers of the 21st century” should be familiar with these ideas on the origins of meaning in perception as it is understood in neuroscience. These aren’t necessarily the best descriptions of the full connection, but I feel these kinds of directions do follow some of your natural interests in pedagogy and phenomenology in ways that you would feel more capable of interacting positively with, and might pull you closer to the dark side of understanding and maybe even sympathising with Tarski’s outline.
Mark Linsenmayer says
Excellent. I will be in touch when we get a break in the schedule to approach one of these things!
have you read:
Arrio Hoffman says
Would you articulate the distinction between a theory and a model?
Additionally, would you explain how Tarski’s model theory has pertinence in computer science?
You mentioned that formal languages have “an interpretation in the physical universe and that is their meaning”; would you elaborate?
Nathan Harvey says
For the theory/model distinction, my tendency is to go with mathematics because it is made clear there. For instance, we have a theory of arithmetic, where we describe a kind of number (integers) that have properties like a “next” number (the successor) and can do counting. The way we normally conceive numbers (1, 2, 3, …) is one possible interpretation of these numbers and their defining properties. But there are “nonstandard” models of these defining properties, models which have numbers “past infinity”. Like infinity + 1, +2, … These models interpret the same rules, but differently.
Theories are syntactic – they deal with statements in the language. Models are semantic. They deal with the different interpretations of this language.
Now, concerning how this applies to computer science: I’d start with something like: “The Semantics of Programming Languages” by Carl Gunter. We often know how to specify programming languages, but their semantics is often left unclear. This is the point of the “abstract machine”, and the interpretation is often left rather informal. But there is a long mathematical history from Stone to Lawvere working on this, and everything has moved to Cartesian categories these days. You might look to people like Per Martin-Löf who defined constructive terms to build such a semantics of computation. There is a long history here, building off of Tarski and model theory to provide a rigorous theory of meaning in computer science.