Discussion of Bradley's The Principles of Logic

Discussion of Bradley's The Principles of Logic

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Discussion of Bradley's The Principles of Logic

If I make the claim, “A wolf is a mammal,” I do not assert anything about my idea of a wolf, but rather something general about this real class of beasts. For Bradley, to admit this is to admit that ideas are general terms that refer to an independent reality. But notice that if, faced with one of these actual canines, I then say “Here is a wolf”, each term of this singular judgment is itself general and cannot possibly hope to capture in its particularity and wealth of detail the animal in question. If ideas are always general, then how can they relate to the real that presents itself as a unique event with determinate sensible content? They could just as easily be describing any wolf and any “here” without an adequate fit or representation of sensory experience. These are Bradley’s concerns in The Principles of Logic (PL)1, and since his proposed solutions to these problems were intended as a refutation of Hume’s empiricist psychology and Mill’s doctrine of inference, and since they shaped if not antedated many of Russell’s achievements in logical theory, they call for careful attention.2

I must note, however, that Bradley is particularly frustrating insofar as he eschews any sustained metaphysical investigations, claiming that metaphysics is a matter separate from his logical concerns. Just at the point that one would demand a more determinate account, he remarks that to really consider such questions would involve him in metaphysics, which is not his present objective. However, as I hope to show, his entire theory of judgment rests on a clearly metaphysical consideration of the nature of time and space and, in fact, commits him to rather bizarre claims about the nature and function of singular judgments and indexicals. The notion that objects of experience are themselves symbolic will allow Bradley to unite his metaphysic with his theory of intentionality and eventually fund those features of his account that are particularly relevant to our purposes: viz., his anti-psychologism, from which naturally follows his attack on the impoverished apophantic paradigm in logic, his insistence on a distinction between logical and grammatical form, and his claim that all judgments, properly understood, are hypothetical judgments.

I. Reference

We must first gain an appreciation for how pervasive the notion of reference is in Bradley’s account. In this section I will first characterize the

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relation between an idea construed as a mental event and an idea considered as a meaning, as well as the relation between the given in experience and reality in order to make it clearer that for Bradley both ideas and the given refer to an underlying reality.

I.i. Logic as an account of the symbolic

Bradley marks out the symbolic function of ideas as the proper domain of logic, and he does this with a distinction between the existence of the idea as a mental event, and its meaning. We judge only when we use ideas as “signs of an existence other than themselves.” (PL, 2). That is to say, when we are not concerned with asserting merely that we have ideas as private mental data, but rather with letting these ideas point to an independent reality, we are judging. In the above example, the judgment “A wolf is a mammal” is no claim about the truth or falsity of my idea of a wolf, occurring at this particular time, but rather an assertion about wolves that is to hold universally, even when this mental event is not occurring. And certainly it is not the claim that my idea of a wolf is itself a mammal! Quite the opposite: I use my mental image of a wolf as an idea precisely when I disregard its own reality or existence, and let it stand for the existence of something else. To use Bradley’s example, if I inquire of another whether he believes that a sea-serpent exists, it seems obvious enough that I am not asking whether he believes his idea of the creature exists. Rather, I am asking him whether reality is qualified by the existence of such a creature.

Thus, to judge that the sea-serpent does not exist is to “move” from one’s idea of the serpent to the reality in question and to hold that reality is not such that sea-serpents exist. Notice that we did not say that this idea fails to pick out an object x such that x is a sea-serpent, nor did we say that this idea fails to refer. It does indeed refer to and pick out an x, namely reality, and holds that sea-serpents are not compatible with this reality. We shall make this clearer below. It is this capacity for reference, for moving beyond the facts and particularities of its own existence, that distinguishes the special class of objects with which logic is preoccupied. As Bradley would put it, in the case of an idea, we perceive not only that it is and what it is, but also what it means. (PL, 3) And it is meaning, as opposed to the psychical fact of ideation, that logic must treat.

Certainly the content of my private idea of a wolf has some relation to the universal meaning wolf. But notice that what has happened while judging is that we have abstracted from the unique features of my wolf-image enough that its particular existence no longer concerns us. And part of this abstraction includes ignoring the temporal existence of this image, my psychological state at the time of its conception, and the fact that it is a part of my psychology. Strictly speaking, meanings do not exist since they are precisely what is left over when we abstract from the facts of spatiotemporality. This means they neither exist as private mental data nor as objects in the world. We will soon see that a radical distinction between meaning and existence will have serious consequences for Bradley’s theory: we can anticipate by saying that meanings never relate to existence, but always and only to reality. A distinction between reality and existence is therefore waiting for us downstairs.

To return to the matter at hand: we take something as a symbol when we use enough of its content to build a relation to another item, while ignoring those features that are not conducive or relevant to this construction. Thus in “Juliet is the sun”, the sun comes to symbolize Juliet insofar as we have built a relation between those features of the sun that bear a similarity to Juliet’s radiant beauty and to the fact that her love is a source of spiritual nourishment, while ignoring, for example, the fact that the sun is a ridiculously large ball of gas. (At least, I do not think this was Romeo’s point)3 Freed of its particular circumstances and now untimely, “merging its own quality in a wider meaning, [an idea] can pass beyond itself and stand for others.” (PL, 4) Reality can be reached only when we move outside of the very experience of having an idea: as we will see later when we confront judgment more directly, ideas are ultimately logically effective when they allow us to move beyond the very fact that we countenance reality through the use of ideas. Thus, the phenomenological experience of knowing reality through ideas and language is still part of the experience that must be extracted from if the referential power of ideas is to be realized.

We thus see that there is something both curious and familiar about this construal of the relationship between ideas and reality. But before we can get much further in our understanding of Bradley’s theory of judgment, we shall have to become more explicit concerning the particular subject matter of reality.

I. ii. Reference, reality, and the given

We will first have to arm ourselves with a distinction that Bradley draws between the given and reality, or between existence and reality. This was the distinction we alluded to above, and we remarked that it is structurally affinitive to the distinction between existence and meaning that constitutes the symbolic. The given, in all of its sensible particulars and spatiotemporal factuality, is our immediate contact with reality. It is, in fact, our only mode of access to reality: “It is impossible, perhaps, to get directly at reality, except in the content of one presentation: we never see it, so to speak, but through a hole.” (PL, 70) Elsewhere, Bradley likens the given to a light illuminating a particular spot on a moving river, a spot whose edges gradually fade into darkness, but which allows us to see that the current continues even outside of this illuminated region. It is clear from both images that the given is a perspective onto reality, and something quite distinct from this reality. And it can be this perspective only because it is so distinguished: reality itself, en toto, is not a possible object of experience, but can only make contact with human cognition through particular events. For Bradley, in contradistinction to Kant, this is not a point about the limits of human cognition and the laws of possible experience, but about the metaphysical structure of an infinite spacetime. Reality, properly construed, simply forbids the kind of completeness and discreteness that is necessary for anything to be an object of cognition. Correlatively, no cognition whatsoever could take reality as its object. The given, by contrast, is what is finite, discrete, occurring “now” and “here” and with particular and determinate sensible content and structure.

But notice that what defines the given as this particular and unique experience is the way in which it relates to and discloses its past and future and its relation to other events: nothing can be a particular except insofar as it embedded in relations with an entire class of objects, and ultimately, to everything else. In the temporal dimension we can follow it backwards and forwards along a causal chain, and in space, from side to side; thereby skipping along relations from one event and space to the next, without end. Its finitude and discreteness must therefore be understood in a qualified sense, for its “edges” are always dissolving into the next moment and the next space, and yet it is unified enough for us to say it is “here and now.” In being a particular, a sensory item helps disclose the total network of spatial and causal relations that define it. Bradley puts this beautifully: “Though given as fact every part is given as existing by reference to something elseÖIn space or in time its outside is made fact solely by relation to what is beyond. Living by relation to what it excludes, it transcends its limits to join another element and invites that element within its own boundaries.” (PL, 71) Bradley is therefore committed to a metaphysical holism that we will see has serious consequences for his epistemology and theory of judgment.

What I would like to suggest now and make clearer later is that the given plays a role identical to that of an idea: its function in human cognition is to point to, to refer to, and thus to symbolize reality. For Bradley, human knowledge of the real would not be possible if the given sensible presentation did not provide a perspective onto a more general and underlying structure. Things never just appear for us as isolated events, but they bring with them a surrounding context of possibility, of past duration and extension into a possible future as well as relation to adjacent spaces: “The reference of the content [of the given] to something other than itself lies deep within its internal nature.” (PL, 98) It is not the exact representation of the given that we are concerned with in order to have knowledge, but with the way in which its content can be used by us to access the real of which it is a part. It is because the given is both a unit and fundamentally contiguous to the rest of reality that it can be used to refer to an existence other than itself. But this is precisely the procedure through which ideas relate themselves to the real, by ignoring their existence for the purpose of exercising their meaning. As creatures fundamentally attuned to the possibility of knowledge, objects and the given are for us fundamentally symbolic. Strictly speaking, reality does not exist because it is a whole and as such never appears in space and time: only the given or objects appear in any kind of spatiotemporal context. Thus Bradley: “It is one thing to seek the reality in that series; it is quite another thing to try to find it as the series.” (PL, 71) Epistemically and metaphysically speaking, time and space are for Bradley structures of reference, and thus the conditions of possibility of judgment about the real. Even the infinite is still but a sign of reality, and not itself the real. Reality remains forever beyond the reach of time and space, and has already moved on whenever we stop to look for it. It thus always compels us to look elsewhere for it. For Bradley, it is the movement of reality, so to speak, that compels us to make judgments.

II. Judgment

Now that we understand that both ideas and the given are vehicles of reference, we can turn to a more direct consideration of Bradley’s theory of judgment. I hope to show that it is Bradley’s commitment to the notion that ideas always and only relate to reality, as distinguished from existence, that funds his entire attack on traditional theories of the nature and function of judgments and of proper logical form. I will first sketch the various problems Bradley has with traditional notions of logical structure.

II. i. Anti-psychologism and Bradley’s attack on the subject-predicate form

We have seen the rudiments of Bradley’s attack on psychologism in our consideration of the particular symbolic use of ideas in judging. Bradley uses this idea to challenge Hume directly. He argues that sensations, be they lively or not, simply never enter into judgments and are in fact, precisely what is filtered out: judgments are true regardless of whether these ideas exist as mental events. The vividness of our belief at the time of its inception is irrelevant to the meaning, which has no distinct sensory or spatiotemporal qualities. If we simply had ideas with no reference, then we would be faced merely with the empirical existence of our ideas, without being “brought” by our ideas to an independent reality. Moreover, Bradley attacks Hume’s associationism on the grounds that sensations are particulars that can be clustered together in certain aggregrates, but it is precisely this particularity that forbids the kind of unity that is required for judgment. If I simply associate ideas of objects, I make no claim about how the properties of these objects can logically fit together in a unity that ignores the particulars of their empirical presentation or their occurrence in my mind. There is no one quality of reality being asserted that would explain the relations among these objects, but merely a bundle of sense data.

Once again, we see that judgments always involve one idea referring to one subject. Bradley therefore rejects the aphophantic model of a synthesis of ideas or concepts in a subject-predicate form. If judgments asserted that a relation existed between two ideas, then we would be asserting a relation between two mental items. But we saw that judgment never asserts about ideas, but about reality. Thus Bradley: “The relations between the ideas are themselves idealÖThey do not exist between the symbols, but hold in the symbolized. They are part of the meaning and not the existence.” (PL, 11) Even though phenomenologically we are faced with what appear to be two ideas related to one another, the force of the assertion is based upon its attempt to represent a reality that comes to us as a unified whole, without artificially interjected relations between isolated items. That is, the judgment is effective precisely to the degree that it moves us beyond the phenomenological presentation of reality through language to the reality itself. The composition of this idea into various components is part of the mental experience that must be extracted from if we are to have knowledge of the real. That is, we must allow these ideas to become symbolic, and thereby refer us away from the very fact that they are ideas.

As a precursor to Russell, Bradley also argues that the subject-predicate paradigm is simply impoverished insofar as it can’t treat of things as basic as relations between items. Insofar as it always seeks a subject that is to be related to a predicate, it cannot handle statements in which there are not such clearly defined roles, such as “A and B are synchronous” or “A and B are equal” (PL, 22) The subject-predicate form simply does not see past its own grammatical structure to recognize its logical and intentional function of pointing to an independent quality of reality. Moreover, to point at a deer running and to say “running”, or “beautiful” is, for Bradley, still an assertion about reality even without the use of subject, predicate, or copula.

In all of this, the lessons to be learned are that judgments only assert of one unified content, namely the logical subject which is always reality broadly construed, and that this logical subject must always be distinguished from the grammatical subject. If we understand this, then we can deal with the familiar problem of non-referrring terms. Take the following worn-out example:

1.1. Unicorns do not exist.

If we fall victim to the subject-predicate form, we take the actual subject of the sentence to be that strange class of entities known as unicorns, and we are then faced with considering the nature of the entity to which this term refers. However, on Bradley’s view, that is, the view according to which the actual subject of the sentence is reality, the logical assertion of this statement is:

1.2. The world is no place that creatures such as unicorns inhabit.

Or consider Bradley’s example:

2.1. A four-cornered circle is impossible.

Here we seem to be predicating a certain quality, “impossibility”, of a class of objects, namely “four-cornered circles.” We are then left with the problem of considering whether this statement can have any assertoric force if we cannot even assume that the subject term picks out anything. On Bradley’s reading, the meaning of the sentence, considered as to how it qualifies reality, is:

2.2 The nature of space forbids the conjunction of the square and the circle.

And this certainly does pick out something, namely the geometry of Euclidean spacetime.

But Bradley rejects the notion that the logical function of judgment is the synthesis of ideas for a much more troubling reason. If judgments are concerned only with relating ideas, then they are doomed as vehicles of truth, for ideas can never adequately represent particular experiences—ideas are always universal terms. We turn now the actual judgment forms in order to address this properly.

II. ii. A hierarchy of hypotheticals

I would like to organize our consideration of the various forms and functions of judgment around a particular problem that should have announced itself a while back. In section I.i., I remarked that the claim, “a sea-serpent does not exist” referred to an object x, and that object was reality. We have just seen this again in Bradley’s distinction between logical and grammatical form. However, later, in section I.ii., I remarked that reality, properly construed, could never be the object of cognition or judgment because reality is fundamentally incomplete. To what do judgments refer then? We seem now to be on the verge of incoherence, and it’s up to Bradley to get us out of this troubling situation. Luckily, he has provided us with the resources to do this. Moreover, if we can do this then we will be able to understand how judgments fit together with reality—and if we do that, we will understand what judgments are and what reality is that they go together this way. No small obstacle to be surmounted, but an exciting task nonetheless.

Bradley divides all judgments into two broad classes: 1) hypothetical judgments and 2) singular judgments. The later can be subdivided into two subsets: 2a) analytic judgments of sense and 2b) synthetic judgments of sense. As we shall see, and as Bradley warns, these latter subsets should not be construed as adopting the Kantian distinction between the analytic and the synthetic.

Taking hypothetical judgments first, we must remember the general nature of ideas and understand that these judgements never assert about presently existing objects. This would violate the condition we noted in 1.i. according to which ideas must abstract from the temporal series in which they are found. If this were not the case, then the statement “ice melts in the presence of fire” would be true only if ice and fire are around, and we would have to wait for their spatiotemporal conjunction in order to make our assertion. Once the event passed, it would no longer be true. Thus in judging, we are asserting that these qualities of the real hold outside of the act of judging. But notice also that hypothetical judgments aren’t any kind of empirical generalization of a class of objects, for they treat of past and future objects. Moreover, consider the following sentence:

3.1 If you had applied the brakes sooner, you would not have crashed.

This counterfactual clearly does not assert about any existing object or event whatsoever: quite the opposite, it asserts regarding what could never happen—unless we can somehow reverse time!

Thus in hypotheticals, we don’t assert the existence of the subject or the predicate, or the cause and the effect, and therefore cannot assert the existence of any relation between them. What we have are “ideal experiments” meant to bring out the latent character of reality. In order to appreciate this, we must again look past the grammatical form of the sentence: in the above example, we are, through this thought experiment, asserting something about the connection between momentum, forces, and pressure rather than about brakes and cars directly. Thus, in extricating the universal meaning from the grammatical trappings we realize that meaning discloses the logical constraints on the way in which properties of the physical world can be related. Universal judgments are, for Bradley, hypothetical and not categorical: they never point to objects as existents but to reality as the ground of possible connection between certain qualities. Thus even in the statement “If God is just, the wicked will face retribution” we are making an assertion about what is logically possible if we apply the conjuction of justice and omnipotence to the problem of punishment—but we do this without asserting the existence of a god. This first has to be recognized as the ideal experiment, “If there is a just God, then the wicked will be punished”, a thought experiment that affirms “not the actual existing behavior of the real, but a latent quality of its disposition, a quality which has appeared in the experiment, but the existence of which does not depend on the experiment.” (PL, 87) And the ground of this connection can be explicated and refined according to further investigation. But this requires that we first look past the particular phenomena in question, to the more basic qualities of reality of which they are products.

We turn now to singular judgments in order to bring out finally the relationship between reality and judgment. But first we must note that what distinguishes the analytic judgments of sense from the synthetic is that the former assert of a present sensory experience whereas the latter assert of some fact of time or space that is not directly perceived. Thus the difference is between “That is a tree over there” and “The fastest route to Los Angeles is the 5”, or “It snowed about a week ago”.

For our present purposes, however, we can effectively ignore the differences between them because they both suffer from the same problem that is occluding our understanding of the function and limits of judgment. We saw that the terms of which a singular judgment is composed are always universal terms and thus could never be an adequate representation of the richness of any sensory experience or any series of events. Again, saying “this tree” or “this past Tuesday” does not help for “this” and “past Tuesday” are themselves universals and could apply to any “this” and any “this past”. If the unique presentation of reality with which we are faced can never be adequately represented, then by what link can we unite our universals with reality? Before we can address this, we must realize that the given experience cannot be represented for yet another reason: it is always passing into the next moment and next space and is never itself a fixed fact but an infinite series. In order to assert of it with any claim to certainty, one would have to assert with certainty of this infinite series as well, which is simply impossible because it will never be completed in the past or in the future. Whereas our first problem was epistemic, this second is metaphysical. Our singular judgments cannot, by this account, purport to be true if by this is meant the direct representation of the given in experience. In order for ideas to do any work, they must do something else.

Since it is metaphysically and epistemically impossible for singular judgments to be grounded in established facts to which they then point, they must be relegated to the position of a lower form of hypothetical judgment. A singular judgment must therefore “cease to predicate its elements of the real and must confine itself to asserting their connection as adjectives generally, and apart from the particular existence.” (PL, 104) When I say “That is a wolf”, what I’m really affirming isn’t the present wolf itself, but the wolf as a product or sign or symbol of the more basic ground of the connection between wolves and the general features of the environment. Thus for Bradley, an observation language as the basis of knowledge is a non-starter: no truth can be context-dependent or particular. The truth-value of the claim derives from its pointing to a quality or latent disposition of reality that is the mysterious fund of the relations among sensory items, and this involves bringing an elaborate theoretical apparatus to bear on any particular statement. Since statements and sensory items never exist in isolation but are mere instantiations of much more fundamental epistemic and metaphysical processes, respectively, the meaning of every singular judgment and every use of language is theoretic and cannot be understood in isolation. Like Quine, Bradley holds that the unit of meaning isn’t even the whole sentence, but the inferential and logical structure in which this sentence is embedded. Unlike Quine, Bradley’s holism isn’ t based on the notion of universal revisability, but on his construal of time, space, and experience. Moreover, it isn’t clear that he goes as far as Quine in taking the unit of meaning to be “the whole of science”. However, since every statement is for him, proto-scientific, it does seem that every judgment is a commitment to a theory that is open to revision.4

Logically speaking, the above statement has the same assertoric force as the hypothetical: “Given the nature of wolves, and the nature of this environment, wolves will be found here.” We must look past the wolf, both as a sensory item and as a grammatical subject, and take it as symbolic of certain qualities of reality. In so doing, we let the wolf refer us to this ground of connection, rather than to any particular object. The function of the wolf in judgment and knowledge is thus to actuate this reference beyond the particular sensory experience. Again, it is Bradley’s metaphysical holism that commits him to an attenuated version of semantic holism.

To return to the problem announced at the beginning of the section: we see now that judgments never affirm of the series of phenomena with which we are presented, but rather the qualities of the real that make these phenomena possible. Thus, the object of a judgment is always this quality or logical structure of reality and never reality itself as it appears in an infinite series of phenomena. As we saw in section I.ii., reality is never to be identified by this series, but is that which is forever extricating itself from spatiotemporality, the latter being a mere sign of reality. In our example of the sea-serpent, we assert something to the effect that the process of natural selection is not such that a sea-serpent has been one of its products. And this can form the basis for an even deeper investigation into the logical structure of natural selection. But we must begin with phenomena because they are our only contact with reality, and we must allow them to refer to much more basic structures of experience. Our language and universals go together with reality because the former’s abstraction allows us to move beyond the given experience to the conditions of possibility that make any empirical presentation possible.

In this sense, judgments don’t treat or assert of extensional classes but are concerned with the logical structure of the world and the possible ways in which properties can fit together coherently. We saw this above in the judgment concerning a just god, which considers the possible relations between justice, omnipotence and punishment and the results of their conjuction. Insofar as it does this, it makes an assertion about possibility. However, Bradley clearly thinks that the way properties and qualities of reality can fit together isn’t necessarily mimicked by the way linguistic terms fit together. In this sense, he isn’t interested in understanding the compositionality of language or concept formation. He does, however, hold that logical assertions must be a direct representation of the logical structure of reality. If that is true, the fact that language is comprised of universals isn’t for Bradley a drawback, but a requirement of articulating this logical structure. It is only a drawback when we think the purpose of language is to re-present or point directly to the given in experience.

It is uncertain why hypothetical judgments should, ultimately, be more warranted than singular judgments. However, Bradley’s point seems to be that the former at least make no pretense of representing reality directly. Rather, hypothetical judgments recognize that they are funded by a particular perspective and must attempt an articulation of the logical struture of reality based on that perspective. I leave you with a quote from Bradley that will give us a sense that our present frustrations are warranted: “Do we ever get to a ground of judgment which we can truly ascribe to the real as its quality?ÖMust we say, in the end, that the quality, which we know is the base of our synthesis, remains in other ways unknownÖ? We seem here to be askingÖfor the limits of explanation, and it would be the task of metaphysics to pursue an enquiry that must here be broken off.” (PL, 88)

Bibliographical References

Bradley, F.H. The Principles of Logic. (Oxford: Oxford University Press), vol 1, 1883.

Hylton, Peter. Russell, Idealism, and the Emergence of Analytic Philosophy. (Oxford: Oxford University Press), 1900.

Notes

1 I will be focusing in particular on chapters 1 & 2, “The General Nature of Judgment”
and “Forms of Judgment”

2 See The Encyclopedia of Philosophy for a very general historical account of the impact
of Bradley’s ideas, as well as Hylton’s Russell, Idealism, and the Emergence of
Analytic Philosophy for a more detailed account of Bradley’s influence on Moore and
Russell.

3 Bradley does not require or comment on the arbitrarity of the sign used as a symbol;
he therefore lacks a notion of uninterpreted syntactical arrangements manipulated
according to transformation rules.

4 Cf. Quine’s “Two Dogmas of Empiricism,” in From a Logical Point of View, (Cambridge:
Harvard University Press), 1953.
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