It just means for any objects in the world “Add seven of them to three of them makes ten.” We all agree because the result is from the analytic reasoning, which is universally true.
The sign “2” denotes “two”, and can represent any abstract or concrete situation depending on the usage. Calculation comes from our analytic reasoning.
As a category becomes more abstract, detail is removed, and it becomes applicable to more things. The category expands. I think that math is an example of maximal abstraction, where all content is removed, allowing for it to be applied indiscriminately to everything. The only prerequisite is distinction, or individuation. As long as things are rendered discrete, they can be enumerated. The power in doing this is that being able to deal in very large sums of things, and formalize specific discrete units of quantification, allows for the conceptualization of phenomenon in complex ways. The advantages of systems of quantification for dealing with phenomenon cannot be understated. The advantage of being able to deal with massive amounts of information cannot be understated.
So ultimately I think that the power comes from being strictly formal, and truly universally applicable for having no content at all. They can be applied to anything and everything, requiring only discrete units.
I agree, and I speculate that this is why Plato identified the “one” and the “good.” The abstract thing is a “one” or “unity.” Scrub away all detail and just this is left.
So I sort of agree and yet want to push back a little. “Analytic” appeals to the “meaning” of a sign. You mention “universal.” But in fact people don’t seem to “mean” the same thing by the same signs. Philosophy is a collision, and misunderstanding is the rule rather than the exception.
My complaint with logical positivism, which I otherwise love, is the haziness of the “analytic.” I need dialogue if I care about the “meaning” of signs. Because I don’t own the language. I don’t control or detect how signs signify to others. I can’t hear or read words with the ears and eyes of others. I have to settle for talking to the fuckers.
I can of course say that this or that expression is “obviously universally true.” But then I come to the forum and others don’t see this “truth” that I find so exciting and obvious. Then I discover painfully that things aren’t so simple. That my “analytic” statement is “nonsense” to the positivist next door.
So you end up with little teams that all accept the same assumptions, more or less. And they are deaf to other teams as other teams are deaf to them.
I don’t think language or linguistic expressions are universally true. But we share the signs and meanings of words and sentences in the expressions. Some meanings of words and signs people use are different to each other, but largely we agree to them, and where different we try to discuss, understand or agree.
Could it be the reason why Derrida said words derive their meanings from difference from other worlds, and meanings are always deferred from other meanings because they are never fully fixed or captured?
We can see why Logical Positivists clashed with Derrida and his deconstruction.
Anyhow my point was the analytic reasoning we apply to number calculation must be universal and same to everyone on the planet, hence we accept the results of the calculations true.
Would they be numbers in Platonic forms? Can numbers be also concepts or ideas? If so, could they have qualities or properties like the geometrical figures?
So would you commit to behaviorism?
Yes, they hated Derrida. But Derrida had legitimate insight here. If he expressed himself in a different style, they might have been able to hear him.
And the gist of Derrida is already in the more “respectable and serious” Saussure. The “acoustic image” is the signifier. This is a “transcendent” repeatable and ideal thing. Actual signs are empirical events in the world, marks and noises. Basically the sounding of “truth” in a very particular situation is like a “numeral” of the “ideal acoustic image.”
The sound is heard as a saying of the repeatable ideal word “truth.” But its significance in that particular context is not only a function of that context but will vary from hearer to hearer. Each listener meets that sound with their entire projected past. And people will go home from the party and reflect on what has been said. The “meaning” of that saying of “truth” is fluid and evolving and unfinished. It’s like the fluid evolving meaning of a piece of music, that you play at different moments in your life.
Formal systems give us some escape from all of this fluidity and unfinishedness. Escape from ambiguity, deferral, perspective. So philosophers who want “eternal truth” love formal systems. And “fixed universal meaning stuff” that is safe from history and the accidents of the empirical world.
Note that I too — like any aspirant to foolosophy — want to forge enduringly valuable memes. Not “truth” but a fuzzier analogue, a less-perishable-than-usual “validity.”
No. It’s more like a tree with its roots in the soil of our embodiment. There is no gap between the natural and cultural, but only a fuzzy pragmatic distinction. Human vocalizations are on a continuum with the tweets of birds, but our tweets are insanely and wonderfully charged with compacted history. We are the supreme time-binders on this planet. We live in space too like other creatures, but our expertise is time. The North remembers.
You and I are mostly enacted inheritance. We are mostly the poets who came before. Like the conglomerate bard yclept “Homer.” I mean that’s how I currently see it. Newish flesh running mostly ancient software. But I believe in genuine novelty, however mitigated or constrained.
I agree on the point, that truth of logical positivism and truth of Derrida are totally different in its meaning and nature.
I can see Derrida’s point, when we look into the concept of truth with no content from the facts of the world, it is empty. Hence there is no “naked truth”.
But then there is definitely validity of truth in the formal sense, when we investigate or analyse propositions or statements from math or scientific claims.
I accept and agree with both ideas of mediated truth from Derrida and logical truth from the formalists.
Both methodologies and ideas on defining and pursuing truths seem useful and practical in understanding the world and also analysing propositions and claims by other subjects for their claims on the world.
However, one thing clear seems the fact that in some of the subjects or field such as aesthetics, literature, phenomenology, metaphysics, religion, epistemology etc, we look for the most reasonable truths (mediated truths in Derrida’s sense) which make sense to us in general.
Whereas in math, science and logic, we look for the absolute truths which are the products of the analytic and synthetic reasoning which are accepted, can be verified and proved universally.
I prefer to say that there is strong shared belief. I prefer to understand the word “truth” as a way of indicating and discussing belief. In formal systems, we can come to a strong agreement. This is enough.
Why avoid a theory that needs truth ? Because I understand all human belief to be situated or owned. Belief is always someone’s belief. A perception is always someone’s perception. The word “truth” tends to be mystified.
The truth is what “God” believes. The “truth” is God’s take. I ought to believe what God believes. We ought to believe God rather than men.
“Objective reality” or “truth” in the context of consciousness as mediating internal stuff is just Berkeley’s theomaterialism in an updated secular context. We are sophisticated deists now, and all that’s left of the old God — all we need to ground our epistemological expertise— is truthmakers and the pseudo-physical dequalified but festishized things-in-themselves of the metaphysicians.
I’m having fun here, but basically I’m serious. Ontological perspectivism doesn’t need an “official” version of reality. My strong beliefs are also known as the current shape of the world from my perspective. Approximately. But we can also understand belief in terms of prejudicial comportment. Basically existence is the ongoing prejudicial disclosure of the world. I live in and as my evolving belief.
Yes and no. I mean you ( or most people ) have to trust experts about some long dense proof of a theorem in real analysis. And you have to be your own philosopher to say what the proof means. You have to believe in the axioms and logic employed to value what is derived from them. You probably want them to encode something about reality and your real-world reasoning.
There was a great civil war in math, and there are still marginal communities who don’t accept classical logic or layers and layers of completed infinities. It’s a battleground really, but this doesn’t matter much for applications.
No, I’m not a Platonist. I agree with some of the characterizations of concepts, as involving idealization, mostly, but due to specific human sensibilities.
As all form, and no content, I am suggesting that math is close to, if not purely conceptual.
Geometry is taken from the word root earth, or ground, and to measure. It is an allusion to surveying. It was devised to be able to infer hard to reach measurements from partial, or incomplete values. So, in the case of geometry it has a particular application. To infer the measurement of land plots, and structures that are difficult to reach, or measure directly.
What if God believes that God doesn’t exist? If God is omnipotent, then he can do anything. God can believe God doesn’t exist. Could it be a possibility? From your principle, we must believe what God believes. But if God believes he doesn’t exist, then we have no belief due to non-existence of God which we are supposed to believe what God believe? Or do we believe in God who believes God doesn’t exist?
This implies that atheists still believes in God. But atheist believes in God who believes God doesn’t exist. Hence atheists doesn’t deny the existence of God.
I tend to stick to simplest proof and analysis system which I could work out myself rather than relying on the experts. If whatever it is, getting too complicated for me to suss out, then I lose interest quickly, and move on. 
What are the limitations or possibilities of the specific human sensibilities, and how do they affect the idealization?
Logical limitations, or possibilities, rather than empirical, I think (though empirical realities play an important role, I do not think they set hard limits on conceivability). They affect it by conceiving of things in a more perfect form. As in when we establish a category, it isn’t like a statistical average of a large number of particulars, rather it is built of only good, or best examples, in our estimations. What are held to be quintessential, or exemplary examples of the category, both selected from real existent particulars, and conceived of in the imagination.
Keep in mind that I was parodying my opponents. I don’t believe in “truth” because I don’t believe in God.
Truth \implies deism.
Berkeley had the sense to call the bluff of a “stuff” hidden “behind” experienced objects, but then he had the non-sense of replacing “matter” with God’s perception. So he escapes atheistic/deistic materialism only to inject a reactionary theomaterialism. Still, his “immaterialism” was a breakthrough, and J. S. Mill purified Berkeley’s work, achieving a genuine phenomenalism, a genuine immaterialism that is simultaneously the rejection of consciousness as mediating stuff. Husserl and Heidegger further enrich this breakthrough.
For me, the “real” world is just the “boring” perceived world. Metaphysical adventures that contradict the primacy of the perception may be fun but they are divorced from the rest of life. I don’t mind if others enjoy that kind of philosophy, but it’s not part of my current project. I take you to be “realistic” also. I’m not a metaphysical realist for the same reason I don’t pack dehydrated water for a trip through Death Valley.
Right. I also insist on personal validation, whenever that is possible. Of course I find myself having to trust machines that I didn’t construct. I have to trust experts. Such is our highly differentiated economy.
I believe that there are various different types of truths.
Truth in Plato was something that was revealed from the hidden. So it could be anything, if one knew from the unknown, it could be truth.
But I go with the correspondent theory of truth. If a proposition or statement is found to correspond with the objects, state or situation in the world it is describing, then it is a truth.
In metaphysics, aesthetics, phenomenology or epistemology, claims supported with good rational arguments which sounds most reasonable and making sense is truth.
In science, findings or claims supported by evidence and experimental findings which can be tested when rehearsed with the same conditions specified producing the same claimed results anywhere in the world would be truth.
In logic and math, answers from the calculations and proofs from the analytic reasoning are truths.
So, I accept and believe in truths, but all truths needs to be checked out, reflected, investigated or analysed for the accuracy. This process is a part of my philosophy.