Hi, welcome here. I like this question you raise. I believe before asking for logical expression in symbols, first try to deconstruct the sentence phenomenologically which is to say in terms of pure meanings and how each of those meanings meaningfully relates-connects to the other ones. This will allow an overall picture or ‘image’ to be constructed metaphysically, as a thought in your mind; Then you look at that thought in your mind’s eye, really try to see it in purely abstract-logical terms.
If you only want to know how to formalize this in the terms of a language of logical symbols, I can’t really help you there. But if you want to break this down philosophically, let’s try that.
“A long, narrow, generally shallow receptacle for holding water or feed for animals”
I identify 6 critical meaning-components in this sentence:
- physical object
- dimensions: long,
- …narrow
- …shallow
- designed to hold other physical things, specifically water or food
- designed for the purpose that such things being held within it are to be consumed by animals
Now we can break down each of those 6 points further into more refined eidetic analyses, such as:
- physical object. [This is close to a foundation of meaning here, but we should at least contextualize this in terms of what physics and metaphysics both have to say in terms of what a “physical object” is and means. Has dimensional extension in space and time; exists in this way, can interact with other similarly dimensionally extended objects; is composed of constituent materials which themselves are composed of or products of lesser materials, down into the level of chemistry and molecules, which level further reduces to the atomic level and then to the subatomic level, and so on; is subject to physical laws like entropy, gravity, etc.; is subject to the principle of sufficient reason, i.e. there is a set of causes that explains completely why and how this particular physical thing happens to be what it is and not rather something else; and we could probably keep going but I think this is getting close to a useful approximation of a sufficient accounting of the point here.]
- and also 3 and 4: dimensions are long, narrow and shallow. [We immediately understand what this means in geometric terms in our mind, as we can abstract each of these concepts from any specific reference to physical objects. long, as in extended in a direction more so than in the perpendicular direction; narrow, a further extension of the meaning of long toward a more extreme or polarized meaning of that concept; shallow, which means having a relatively limited-small extension perpendicular to the two-dimensional plane along which the first two concepts (long and narrow) exist. In otherwords this stuff here is just basic geometry of which is pretty simple to exhaust the meaning in abstract thought and direct understanding.]
- (this is really “5)” but the list formatting here changed it) designed to hold other physical things, specifically water and food. [Here we run into the concept of purpose, the reason why this physical object was designed as it was, which includes the further concept of intentionality and non-accidentalness as well as non-naturalness. Said another way, we know it was not the case that the thing described by this sentence appeared as an accident of nature but was specifically created with a function in mind. Although running tangent to this meaning is the further meaning pushed slightly out into the parallel space of possibility that it is certainly possible to find an object in the natural world that just accidentally happens to be shaped in such a way as could be used for this same purpose of holding water or food for other animals to eat. Certainly that is not impossible, although it would be rare compared to the number of instances in which such an object were intentionally created by humans with these functions in mind as reasons or rationale for the object’s construction in the first place. Of course we also have the additional meaning and basic logical concept of “inside-of” presupposing our understanding of the basic fact that some things hold within them other smaller things. Water and food deserve their own proper phenomenological eidetic reductions here too, although for the sake of time I’ll skip that if you don’t mind.]
- (likewise this is “6)”… for the purpose of such water or food to be consumed by animals. [Clearly adding on the meaning of what it means to consume, which includes the meaning of what is an animal and all this entains, consumption of water as drinking and of food as eating, and all of the reasons why these consumptions occur and are important to said animals. Also attached here is the further meaning/concept of why a human would value other animals being able to consume water or food, which gets into the whole meaning-space of animal husbandry and agriculture and the entire history of that, etc.]
Ok, now we have something more useful. We have an entire massive phenomenological structure existing in metaphysical space that we can observe, zoom in on here and there, rotate, compare/contrast with, etc. and this becomes something like what you were asking about in the OP, except obviously this is uncountably more complex and nuanced and rich and massive of a construct when compared with something like, " ∃x (Receptacle(x) ∧ Shape(x) = Long ∧ Shape(x) = Narrow ∧ Depth(x) = Shallow ∧ Purpose(x) = ToHold(Water ∨ Feed) ∧ Target(x) = Animals)".
Such merely symbolic reformulations of the words in a sentence achieves almost nothing. I suppose it may serve as a curiosity for certain analytic types who enjoy fantasizing about their minds residing within a computer or maybe they idealize being able to think as a computer “thinks” (processes information)-- but when it comes to philosophy which is to say in terms of meaning, value, understanding and yes even logic, we need to dive much deeper.
Also as you can see, it’s really interesting how far a simple concept can expand into literal meaning-space. The simple concept of a trough, in this case, expressed in what may be its most necessary and sufficient conceptual definition in terms of English language, can be deconstructed into its various parts and understood to actually be a massive phenomenological structure in pure mind-space and existing factually in the mental universe as a coherent metaphysical object. Try to wrap your mind around all the pieces of this object at once, it’s not easy. The object is actually that large we need to basically look at it one part and angle at a time. Pretty cool if you ask me. It really shows the unfathomed depths in the mind and the real sense in which so much of the work of understanding and philosophy is done ‘behind the scenes’ as it were. What we are cognitively aware of and formulating in concrete concepts and known logics in our active thinking minds is a small drop in a much, much larger ocean of pure facts and meanings. Philosophy ought to care about this, although based on what I have seen it remains ignorant of this, often deliberately so. I suppose that is because small minds need small problems to work on.
